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<?xml version="1.0" encoding="utf-8"?>
<feed xmlns="http://www.w3.org/2005/Atom">
<title>sysuNie</title>
<subtitle>Morning, Noon, Night.</subtitle>
<link href="/atom.xml" rel="self"/>
<link href="http://yoursite.com/"/>
<updated>2018-01-28T14:35:45.908Z</updated>
<id>http://yoursite.com/</id>
<author>
<name>JiKang Nie</name>
</author>
<generator uri="http://hexo.io/">Hexo</generator>
<entry>
<title>numberof1inbinary</title>
<link href="http://yoursite.com/2018/01/28/numberof1inbinary/"/>
<id>http://yoursite.com/2018/01/28/numberof1inbinary/</id>
<published>2018-01-28T14:19:32.000Z</published>
<updated>2018-01-28T14:35:45.908Z</updated>
<content type="html"><![CDATA[<h3 id="面试题：二进制中1的个数"><a href="#面试题：二进制中1的个数" class="headerlink" title="面试题：二进制中1的个数"></a>面试题：二进制中1的个数</h3><p><strong>题目</strong>：请实现一个函数，输入一个整数，输出该数二进制表示中1的个数。例如把9表示成二进制是1001，有2位是1。因此如果输入9，该函数输出2。</p><p><strong>思路1</strong>：举个例子进行说明。对于任何一个数字，和1进行<strong>与运算</strong>，判断得到的结果。设置一个count进行技术，如果结果与运算得到的结果为1，那么count就加1，每计算此意，１就向向左移动一位，直到完成所有的计算，最后得到的count值就是输出。</p><div class="table-container"><table><thead><tr><th style="text-align:center">１</th><th style="text-align:center">０</th><th style="text-align:center">０</th><th style="text-align:center">１</th><th style="text-align:center">count</th></tr></thead><tbody><tr><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center">１</td><td style="text-align:center">1</td></tr><tr><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center">1</td><td style="text-align:center"></td><td style="text-align:center"></td></tr><tr><td style="text-align:center"></td><td style="text-align:center">1</td><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center">1</td></tr><tr><td style="text-align:center">1</td><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center">2</td></tr></tbody></table></div><a id="more"></a><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><iostream></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><cstdio></span></span></div><div class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">Numberof1_solution1</span><span class="params">(<span class="keyword">int</span> n)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> count = <span class="number">0</span>;</div><div class="line"> <span class="keyword">unsigned</span> <span class="keyword">int</span> flag = <span class="number">1</span>;</div><div class="line"> <span class="keyword">while</span>(flag)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(n & flag)</div><div class="line"> count++;</div><div class="line"> flag = flag << <span class="number">1</span>;</div><div class="line"></div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> count;</div><div class="line">}</div></pre></td></tr></table></figure><p><strong>思路2</strong>：举个例子进行说明。对于任何一个数字n，和n-1进行<strong>与运算</strong>。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">Numberof1_solution2</span><span class="params">(<span class="keyword">int</span> n)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> count = <span class="number">0</span>;</div><div class="line"></div><div class="line"> <span class="keyword">while</span>(n)</div><div class="line"> {</div><div class="line"> ++count;</div><div class="line"> n = (n<span class="number">-1</span>) & n;</div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> count;</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="built_in">cout</span><<Numberof1_solution1(<span class="number">11</span>)<<<span class="built_in">endl</span>;</div><div class="line"> <span class="built_in">cout</span><<Numberof1_solution2(<span class="number">11</span>)<<<span class="built_in">endl</span>;</div><div class="line"></div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">}</div></pre></td></tr></table></figure>]]></content>
<summary type="html">
<h3 id="面试题：二进制中1的个数"><a href="#面试题：二进制中1的个数" class="headerlink" title="面试题：二进制中1的个数"></a>面试题：二进制中1的个数</h3><p><strong>题目</strong>：请实现一个函数，输入一个整数，输出该数二进制表示中1的个数。例如把9表示成二进制是1001，有2位是1。因此如果输入9，该函数输出2。</p>
<p><strong>思路1</strong>：举个例子进行说明。对于任何一个数字，和1进行<strong>与运算</strong>，判断得到的结果。设置一个count进行技术，如果结果与运算得到的结果为1，那么count就加1，每计算此意，１就向向左移动一位，直到完成所有的计算，最后得到的count值就是输出。</p>
<div class="table-container">
<table>
<thead>
<tr>
<th style="text-align:center">１</th>
<th style="text-align:center">０</th>
<th style="text-align:center">０</th>
<th style="text-align:center">１</th>
<th style="text-align:center">count</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
<td style="text-align:center">１</td>
<td style="text-align:center">1</td>
</tr>
<tr>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
<td style="text-align:center">1</td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
</tr>
<tr>
<td style="text-align:center"></td>
<td style="text-align:center">1</td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
<td style="text-align:center">1</td>
</tr>
<tr>
<td style="text-align:center">1</td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
<td style="text-align:center">2</td>
</tr>
</tbody>
</table>
</div>
</summary>
<category term="编程" scheme="http://yoursite.com/categories/%E7%BC%96%E7%A8%8B/"/>
<category term="编程，二进制" scheme="http://yoursite.com/tags/%E7%BC%96%E7%A8%8B%EF%BC%8C%E4%BA%8C%E8%BF%9B%E5%88%B6/"/>
</entry>
<entry>
<title>concrete_NLP</title>
<link href="http://yoursite.com/2018/01/28/concrete-NLP/"/>
<id>http://yoursite.com/2018/01/28/concrete-NLP/</id>
<published>2018-01-28T06:27:00.000Z</published>
<updated>2018-01-28T14:30:33.337Z</updated>
<content type="html"><![CDATA[<p>虽然存在丰富的精细和抽象的NLP技术，但集群和分类应始终作为处理这类数据时使用的第一种技术。 除了在生产中最容易扩展之外，它们的易用性可以迅速帮助企业解决一系列应用问题：</p><ul><li>如何自动区分不同类别的句子？</li><li>如何找到一个数据集中最相似的句子？</li><li>如何提取一个丰富而简洁的表示，然后可以用于一系列其他任务？</li><li>如何快速找到这些任务是否可以在你的数据集上？</li></ul><p>这篇文章的作用是提供一个简单方式的寻找句子表示，以便将它们分类或组合在一起。</p><a id="more"></a><h3 id="收集数据"><a href="#收集数据" class="headerlink" title="收集数据"></a>收集数据</h3><h4 id="数据集"><a href="#数据集" class="headerlink" title="数据集"></a>数据集</h4><p>每个机器学习问题都是从数据开始，例如电子邮件、帖子或推文。文本信息常见来源包括：</p><ul><li>产品评论（来自亚马逊，Yelp和各种原因商店）</li><li>用户发布的内容（推文，facebook帖子，stackOverflow问题）</li><li>故障排除（客户请求，聊天记录）</li></ul><p>本文我们使用的是由 <a href="https://www.crowdflower.com/data-for-everyone/" target="_blank" rel="external">Crowdflower</a>提供的名为“社交媒体中出现的灾难”数据集，其中：</p><p>投稿人查看了超过10000条推文，包括“着火”，“隔离”和“混乱”等各种检索，然后看推文是否是指灾难事件（排除掉用单词或电影评论的笑话， 一些非灾难性的）。</p><p>我们将尝试正确预测关于灾难的推文。 这是一个非常相关的问题，因为：</p><ul><li>任何试图从噪音中获得信号的人都可以采取行动（比如在这种情况下的警察部门）</li><li>这是棘手的，因为依赖于关键字比在大多数情况下像垃圾邮件更难</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">import</span> sys</div><div class="line">reload(sys)</div><div class="line">sys.setdefaultencoding( <span class="string">"utf-8"</span> )</div><div class="line"><span class="keyword">import</span> keras</div><div class="line"><span class="keyword">import</span> nltk</div><div class="line"><span class="keyword">import</span> pandas <span class="keyword">as</span> pd</div><div class="line"><span class="keyword">import</span> numpy <span class="keyword">as</span> np</div><div class="line"><span class="keyword">import</span> re</div><div class="line"><span class="keyword">import</span> codecs</div></pre></td></tr></table></figure><h3 id="数据清理"><a href="#数据清理" class="headerlink" title="数据清理"></a>数据清理</h3><p>让我们确保我们的推文只有我们想要的字符。 我们删除’＃’字符，但保留’＃’后的单词，因为它们可能是相关的（例如：#disaster）</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div></pre></td><td class="code"><pre><div class="line">input_file = codecs.open(<span class="string">"socialmedia_relevant_cols.csv"</span>, <span class="string">"r"</span>,encoding=<span class="string">'utf-8'</span>, errors=<span class="string">'replace'</span>)</div><div class="line">output_file = open(<span class="string">"socialmedia_relevant_cols_clean.csv"</span>, <span class="string">"w"</span>)</div><div class="line"><span class="function"><span class="keyword">def</span> <span class="title">sanitize_characters</span><span class="params">(raw, clean)</span>:</span> </div><div class="line"> <span class="keyword">for</span> line <span class="keyword">in</span> input_file:</div><div class="line"> out = line</div><div class="line"> output_file.write(line)</div><div class="line">sanitize_characters(input_file, output_file)</div></pre></td></tr></table></figure><h4 id="检查数据"><a href="#检查数据" class="headerlink" title="检查数据"></a>检查数据</h4><p>它看起来很稳固，但我们并不需要网址，我们希望我们的文字都是小写字母（Hello和HELLO对我们的任务来说非常相似）</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div></pre></td><td class="code"><pre><div class="line">questions = pd.read_csv(<span class="string">"socialmedia_relevant_cols_clean.csv"</span>)</div><div class="line">questions.columns=[<span class="string">'text'</span>, <span class="string">'choose_one'</span>, <span class="string">'class_label'</span>]</div><div class="line">questions.head()</div></pre></td></tr></table></figure><div class="table-container"><table><thead><tr><th style="text-align:center"></th><th style="text-align:center">text</th><th style="text-align:center">choose_one</th><th style="text-align:center">class_label</th></tr></thead><tbody><tr><td style="text-align:center">0</td><td style="text-align:center">Just happened a terrible car crash</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">1</td><td style="text-align:center">Our Deeds are the Reason of this #earthquake M…</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">2</td><td style="text-align:center">Heard about #earthquake is different cities, s…</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">3</td><td style="text-align:center">there is a forest fire at spot pond, geese are…</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">4</td><td style="text-align:center">Forest fire near La Ronge Sask. Canada</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr></tbody></table></div><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">questions.tail()</div></pre></td></tr></table></figure><div class="table-container"><table><thead><tr><th style="text-align:center"></th><th style="text-align:center">text</th><th style="text-align:center">choose_one</th><th style="text-align:center">class_label</th></tr></thead><tbody><tr><td style="text-align:center">10871</td><td style="text-align:center">M1.94 [01:04 UTC]?5km S of Volcano Hawaii. htt…</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">10872</td><td style="text-align:center">Police investigating after an e-bike collided …</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">10873</td><td style="text-align:center">The Latest: More Homes Razed by Northern Calif…</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">10874</td><td style="text-align:center">MEG issues Hazardous Weather Outlook (HWO)</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">10875</td><td style="text-align:center">CityofCalgary has activated its Muni</td><td style="text-align:center">NaN</td><td style="text-align:center">NaN</td></tr></tbody></table></div><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">questions.describe()</div></pre></td></tr></table></figure><div class="table-container"><table><thead><tr><th style="text-align:center"></th><th style="text-align:center">class_label</th></tr></thead><tbody><tr><td style="text-align:center">count</td><td style="text-align:center">10875.000000</td></tr><tr><td style="text-align:center">mean</td><td style="text-align:center">0.432552</td></tr><tr><td style="text-align:center">std</td><td style="text-align:center">0.498414</td></tr><tr><td style="text-align:center">min</td><td style="text-align:center">0.000000</td></tr><tr><td style="text-align:center">25%</td><td style="text-align:center">0.000000</td></tr><tr><td style="text-align:center">50%</td><td style="text-align:center">0.000000</td></tr><tr><td style="text-align:center">75%</td><td style="text-align:center">1.000000</td></tr><tr><td style="text-align:center">max</td><td style="text-align:center">2.000000</td></tr></tbody></table></div><p>让我们使用一些正则表达式来清理不必要的数据，并将其保存回csv文件供将来使用</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">def</span> <span class="title">standardize_text</span><span class="params">(ques, text_field)</span>:</span></div><div class="line"> ques[text_field] = ques[text_field].str.replace(<span class="string">r"http\S+"</span>, <span class="string">""</span>)</div><div class="line"> ques[text_field] = ques[text_field].str.replace(<span class="string">r"http"</span>, <span class="string">""</span>)</div><div class="line"> ques[text_field] = ques[text_field].str.replace(<span class="string">r"@\S+"</span>, <span class="string">""</span>)</div><div class="line"> ques[text_field] = ques[text_field].str.replace(<span class="string">r"[^A-Za-z0-9(),!?@\'\`\"\_\n]"</span>, <span class="string">" "</span>)</div><div class="line"> ques[text_field] = ques[text_field].str.replace(<span class="string">r"@"</span>, <span class="string">"at"</span>)</div><div class="line"> ques[text_field] = ques[text_field].str.lower()</div><div class="line"> <span class="keyword">return</span> ques</div><div class="line">questions = standardize_text(questions, <span class="string">"text"</span>)</div><div class="line">questions.to_csv(<span class="string">"clean_data.csv"</span>)</div><div class="line">questions.head()</div></pre></td></tr></table></figure><div class="table-container"><table><thead><tr><th style="text-align:center"></th><th style="text-align:center">text</th><th style="text-align:center">choose_one</th><th style="text-align:center">class_label</th></tr></thead><tbody><tr><td style="text-align:center">0</td><td style="text-align:center">just happened a terrible car crash</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">1</td><td style="text-align:center">our deeds are the reason of this earthquake m…</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">2</td><td style="text-align:center">heard about earthquake is different cities, s…</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">3</td><td style="text-align:center">there is a forest fire at spot pond, geese are…</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">4</td><td style="text-align:center">forest fire near la ronge sask canada</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr></tbody></table></div><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div></pre></td><td class="code"><pre><div class="line">clean_questions = pd.read_csv(<span class="string">"clean_data.csv"</span>)</div><div class="line">clean_questions.tail()</div></pre></td></tr></table></figure><div class="table-container"><table><thead><tr><th style="text-align:center"></th><th style="text-align:center">text</th><th style="text-align:center">choose_one</th><th style="text-align:center">class_label</th></tr></thead><tbody><tr><td style="text-align:center">10871</td><td style="text-align:center">m1 94 01 04 utc ?5km s of volcano hawaii</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">10872</td><td style="text-align:center">police investigating after an e bike collided …</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">10873</td><td style="text-align:center">the latest more homes razed by northern calif…</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">10874</td><td style="text-align:center">meg issues hazardous weather outlook (hwo)</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td></tr><tr><td style="text-align:center">10875</td><td style="text-align:center">cityofcalgary has activated its muni</td><td style="text-align:center">NaN</td><td style="text-align:center">NaN</td></tr></tbody></table></div><h3 id="数据概述"><a href="#数据概述" class="headerlink" title="数据概述"></a>数据概述</h3><p>让我们来看看我们的class_label</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">clean_questions.groupby(<span class="string">"class_label"</span>).count()</div></pre></td></tr></table></figure><div class="table-container"><table><thead><tr><th style="text-align:center"></th><th style="text-align:center">Unnamed: 0</th><th style="text-align:center">text</th><th style="text-align:center">choose_one</th></tr></thead><tbody><tr><td style="text-align:center">class_label</td><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center"></td></tr><tr><td style="text-align:center">0.0</td><td style="text-align:center">6187</td><td style="text-align:center">6187</td><td style="text-align:center">6187</td></tr><tr><td style="text-align:center">1.0</td><td style="text-align:center">4672</td><td style="text-align:center">4672</td><td style="text-align:center">4672</td></tr><tr><td style="text-align:center">2.0</td><td style="text-align:center">16</td><td style="text-align:center">16</td><td style="text-align:center">16</td></tr></tbody></table></div><p>我们可以看到我们的类非常平衡，对“不相关的”类稍加过度抽样。</p><p><strong>我们的数据很干净，现在需要做好准备</strong></p><p>现在我们的输入数据是更合理的，让我们以我们的模型可以理解的方式来改变我们的输入数据。</p><p>这意味着：</p><ul><li>将句子标记为单独的单词列表</li><li>创建训练集好测试集</li><li>仔细检查我们的数据来验证结果</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">from</span> nltk.tokenize <span class="keyword">import</span> RegexpTokenizer</div><div class="line">tokenizer = RegexpTokenizer(<span class="string">r'\w+'</span>)</div><div class="line">clean_questions[<span class="string">"tokens"</span>] = clean_questions[<span class="string">"text"</span>].apply(tokenizer.tokenize)</div><div class="line">clean_questions.head()</div></pre></td></tr></table></figure><div class="table-container"><table><thead><tr><th style="text-align:center"></th><th style="text-align:center">Unnamed: 0</th><th style="text-align:center">text</th><th style="text-align:center">choose_one</th><th style="text-align:center">class_label</th><th>tokens</th></tr></thead><tbody><tr><td style="text-align:center">0</td><td style="text-align:center">0</td><td style="text-align:center">just happened a terrible car crash</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td><td>[just, happened, a, terrible, car, crash]</td></tr><tr><td style="text-align:center">1</td><td style="text-align:center">1</td><td style="text-align:center">our deeds are the reason of this earthquake m…</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td><td>[our, deeds, are, the, reason, of, this, earth…</td></tr><tr><td style="text-align:center">2</td><td style="text-align:center">2</td><td style="text-align:center">heard about earthquake is different cities, s…</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td><td>[heard, about, earthquake, is, different, citi…</td></tr><tr><td style="text-align:center">3</td><td style="text-align:center">3</td><td style="text-align:center">there is a forest fire at spot pond, geese are…</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td><td>[there, is, a, forest, fire, at, spot, pond, g…</td></tr><tr><td style="text-align:center">4</td><td style="text-align:center">4</td><td style="text-align:center">forest fire near la ronge sask canada</td><td style="text-align:center">Relevant</td><td style="text-align:center">1.0</td><td>[forest, fire, near, la, ronge, sask, canada]</td></tr></tbody></table></div><h4 id="深入挖掘数据"><a href="#深入挖掘数据" class="headerlink" title="深入挖掘数据"></a>深入挖掘数据</h4><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">from</span> keras.preprocessing.text <span class="keyword">import</span> Tokenizer</div><div class="line"><span class="keyword">from</span> keras.preprocessing.sequence <span class="keyword">import</span> pad_sequences</div><div class="line"><span class="keyword">from</span> keras.utils <span class="keyword">import</span> to_categorical</div><div class="line">all_words = [word <span class="keyword">for</span> tokens <span class="keyword">in</span> clean_questions[<span class="string">'tokens'</span>] <span class="keyword">for</span> word <span class="keyword">in</span> tokens]</div><div class="line">sentence_lengths = [len(tokens) <span class="keyword">for</span> tokens <span class="keyword">in</span> clean_questions[<span class="string">"tokens"</span>]]</div><div class="line">VOCAB = sorted(list(set(all_words)))</div><div class="line">print(<span class="string">"%s words total, with a vocabulary size of %s"</span> % (len(all_words), len(VOCAB)))</div><div class="line">print(<span class="string">"Max sentence length is %s"</span> % max(sentence_lengths))</div></pre></td></tr></table></figure><blockquote><p>154721 words total, with a vocabulary size of 18102<br>Max sentence length is 34</p></blockquote><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">import</span> matplotlib.pyplot <span class="keyword">as</span> plt</div><div class="line"></div><div class="line">fig = plt.figure(figsize=(<span class="number">10</span>, <span class="number">10</span>)) </div><div class="line">plt.xlabel(<span class="string">'Sentence length'</span>)</div><div class="line">plt.ylabel(<span class="string">'Number of sentences'</span>)</div><div class="line">plt.hist(sentence_lengths)</div><div class="line">plt.show()</div></pre></td></tr></table></figure><p><img 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/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%0ARK5CYII=%0A" alt=""></p><p>现在我们的数据是干净的，准备好了，让我们进入机器学习部分</p><h3 id="Embeddings"><a href="#Embeddings" class="headerlink" title="Embeddings"></a>Embeddings</h3><p>机器学习中图像可以使用原始像素作为输入，那么NLP可以使用什么？</p><p>为计算机表示文本的一种自然方式是对每个字符进行单独编码，这似乎不足以表示和理解语言。我们的目标是首先为我们的数据集中的每个句子（或推文）创建一个有用的嵌入，然后使用这些嵌入来准确地预测相关类别。</p><p>我们可以从最简单的方法开始，使用一袋文字模型，并在上面应用逻辑回归。一袋单词只是将一个索引与我们词汇表中的每个单词相关联，并且将每个句子嵌入一个0的列表，每个索引中的每个索引对应于该句子中出现的单词。</p><h4 id="Bag-of-Words-Counts"><a href="#Bag-of-Words-Counts" class="headerlink" title="Bag of Words Counts"></a>Bag of Words Counts</h4><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div></pre></td><td class="code"><pre><div class="line">rom sklearn.model_selection <span class="keyword">import</span> train_test_split</div><div class="line"><span class="keyword">from</span> sklearn.feature_extraction.text <span class="keyword">import</span> CountVectorizer, TfidfVectorizer</div><div class="line"><span class="function"><span class="keyword">def</span> <span class="title">cv</span><span class="params">(data)</span>:</span></div><div class="line"> count_vectorizer = CountVectorizer()</div><div class="line"> emb = count_vectorizer.fit_transform(data)</div><div class="line"> <span class="keyword">return</span> emb, count_vectorizer</div><div class="line">list_corpus = clean_questions[<span class="string">"text"</span>].tolist()</div><div class="line">list_labels = clean_questions[<span class="string">"class_label"</span>].tolist()</div><div class="line">x_train, x_test, y_train, y_test = train_test_split(list_corpus, list_labels, test_size=<span class="number">0.2</span>, random_state=<span class="number">40</span>)</div><div class="line">x_train_count, count_vectorizer = cv(x_train)</div><div class="line">x_test_count = count_vectorizer.transform(x_test)</div></pre></td></tr></table></figure><h4 id="可视化embeddings"><a href="#可视化embeddings" class="headerlink" title="可视化embeddings"></a>可视化embeddings</h4><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">from</span> sklearn.decomposition <span class="keyword">import</span> PCA, TruncatedSVD</div><div class="line"><span class="keyword">import</span> matplotlib</div><div class="line"><span class="keyword">import</span> matplotlib.patches <span class="keyword">as</span> patches</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">def</span> <span class="title">plot_LSA</span><span class="params">(test_data, test_labels, savepath=<span class="string">"PCA_demo.csv"</span>, plot=True)</span>:</span></div><div class="line"> lsa = TruncatedSVD(n_components=<span class="number">2</span>)</div><div class="line"> lsa.fit(test_data)</div><div class="line"> lsa_scores = lsa.transform(test_data)</div><div class="line"> color_mapper = {label: idx <span class="keyword">for</span> idx, label <span class="keyword">in</span> enumerate(set(test_labels))}</div><div class="line"> color_column = [color_mapper[label] <span class="keyword">for</span> label <span class="keyword">in</span> test_labels]</div><div class="line"> colors = [<span class="string">'orange'</span>, <span class="string">'blue'</span>, <span class="string">'blue'</span>]</div><div class="line"> <span class="keyword">if</span> plot:</div><div class="line"> plt.scatter(lsa_scores[:, <span class="number">0</span>], lsa_scores[:, <span class="number">1</span>], s=<span class="number">8</span>, alpha=<span class="number">.8</span>, c=test_labels,</div><div class="line"> cmap=matplotlib.colors.ListedColormap(colors))</div><div class="line"> red_patch = patches.Patch(color=<span class="string">'orange'</span>, label=<span class="string">'Irrelevant'</span>)</div><div class="line"> blue_patch = patches.Patch(color=<span class="string">'blue'</span>, label=<span class="string">'Disaster'</span>)</div><div class="line"> plt.legend(handles=[red_patch, blue_patch], prop={<span class="string">'size'</span>: <span class="number">30</span>})</div><div class="line"></div><div class="line">fig = plt.figure(figsize=(<span class="number">20</span>, <span class="number">20</span>)) </div><div class="line">plot_LSA(X_train_counts, y_train)</div><div class="line">plt.show()</div></pre></td></tr></table></figure><p><img src="../img/raw_distribution.png" alt="raw_distribution"></p>]]></content>
<summary type="html">
<p>虽然存在丰富的精细和抽象的NLP技术，但集群和分类应始终作为处理这类数据时使用的第一种技术。 除了在生产中最容易扩展之外，它们的易用性可以迅速帮助企业解决一系列应用问题：</p>
<ul>
<li>如何自动区分不同类别的句子？</li>
<li>如何找到一个数据集中最相似的句子？</li>
<li>如何提取一个丰富而简洁的表示，然后可以用于一系列其他任务？</li>
<li>如何快速找到这些任务是否可以在你的数据集上？</li>
</ul>
<p>这篇文章的作用是提供一个简单方式的寻找句子表示，以便将它们分类或组合在一起。</p>
</summary>
<category term="工具资源" scheme="http://yoursite.com/categories/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90/"/>
<category term="工具资源，NLP" scheme="http://yoursite.com/tags/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90%EF%BC%8CNLP/"/>
</entry>
<entry>
<title>动态规划与贪婪算法</title>
<link href="http://yoursite.com/2018/01/28/CuttingRope/"/>
<id>http://yoursite.com/2018/01/28/CuttingRope/</id>
<published>2018-01-28T03:18:13.000Z</published>
<updated>2018-03-04T08:14:17.913Z</updated>
<content type="html"><![CDATA[<h3 id="动态规划"><a href="#动态规划" class="headerlink" title="动态规划"></a>动态规划</h3><p>动态规划算法的基本思想与分治法类似，也是将待求解的问题分解为若干个子问题（阶段），按顺序求解子阶段，前一子问题的解，为后一子问题的求解提供了有用的信息。在求解任一子问题时，列出各种可能的局部解，通过决策保留那些有可能达到最优的局部解，丢弃其他局部解。依次解决各子问题，最后一个子问题就是初始问题的解。由于动态规划解决的问题多数有重叠子问题这个特点，为减少重复计算，对每一个子问题只解一次，将其不同阶段的不同状态保存在一个二维数组中。</p><p>能采用动态规划求解的问题的特点：</p><ul><li>最优化原理：如果问题的最优解所包含的子问题的解也是最优的，就称该问题具有最优子结构，即满足最优化原理。</li><li>无后效性：即某阶段状态一旦确定，就不受这个状态以后决策的影响。也就是说，某状态以后的过程不会影响以前的状态，只与当前状态有关。</li><li>有重叠子问题：即子问题之间是不独立的，一个子问题在下一阶段决策中可能被多次使用到。（该性质并不是动态规划适用的必要条件，但是如果没有这条性质，动态规划算法同其他算法相比就不具备优势）</li><li>从上往下分析问题，从下往上求解问题。</li></ul><a id="more"></a><h3 id="贪婪算法"><a href="#贪婪算法" class="headerlink" title="贪婪算法"></a>贪婪算法</h3><p>贪心算法是指在对问题求解时，总是做出在当前看来是最好的选择。也就是说，不从整体最优上加以考虑，只做出在某种意义上的局部最优解。贪心算法不是对所有问题都能得到整体最优解，关键是贪心策略的选择，选择的贪心策略必须具备无后效性，即某个状态以前的过程不会影响以后的状态，只与当前状态有关。</p><p>解题的一般步骤是：</p><ul><li>建立数学模型来描述问题；</li><li>把求解的问题分成若干个子问题；</li><li>对每一子问题求解，得到子问题的局部最优解；</li><li>把子问题的解局部最优解合成原来解问题的一个解。</li></ul><h3 id="面试题：剪绳子"><a href="#面试题：剪绳子" class="headerlink" title="面试题：剪绳子"></a>面试题：剪绳子</h3><p><strong>题目</strong>：给你一根长度为n绳子，请把绳子剪成m段（m、n都是整数，n>1并且m≥1）。每段的绳子的长度记为k[0]、k[1]、……、k[m]。k[0]<em>k[1]</em>…*k[m]可能的最大乘积是多少？例如当绳子的长度是8时，我们把它剪成长度分别为2、3、3的三段，此时得到最大的乘积18。</p><p><strong>动态规划思路</strong>：首先定义函数f(n)把长度为n的绳子剪成若干段后各段长度乘积的最大值。在剪第一刀的时候，我们有n-1种可能的选择，也就是剪出来的第一段绳子的科能长度分别为1,2,….,n-1。因此我们可以得到f(n)=max(f(i)*f(n-i))，其中0<i<n。</p><p>这是一个从上至下的递归公式。由于递归会有很多重复的子问题，从而有大量不必要的计算。一个更好的办法是按照从下而上的顺序计算，也就是说我们先得到f(2),f(3)，再得到f(4),f(5)，直到得到f(n)。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><iostream></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><cmath></span></span></div><div class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</div><div class="line"><span class="comment">//==============动态规划============</span></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">maxProductAfterCutting_solution1</span><span class="params">(<span class="keyword">int</span> length)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(length < <span class="number">2</span>)</div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line"> <span class="keyword">if</span>(length == <span class="number">2</span>)</div><div class="line"> <span class="keyword">return</span> <span class="number">1</span>;</div><div class="line"> <span class="keyword">if</span>(length == <span class="number">3</span>)</div><div class="line"> <span class="keyword">return</span> <span class="number">2</span>;</div><div class="line"></div><div class="line"> <span class="keyword">int</span>* products = <span class="keyword">new</span> <span class="keyword">int</span>[length+<span class="number">1</span>];</div><div class="line"> <span class="keyword">int</span> Max = <span class="number">0</span>;</div><div class="line"></div><div class="line"> products[<span class="number">0</span>] = <span class="number">0</span>;</div><div class="line"> products[<span class="number">1</span>] = <span class="number">1</span>;</div><div class="line"> products[<span class="number">2</span>] = <span class="number">2</span>;</div><div class="line"> products[<span class="number">3</span>] = <span class="number">3</span>;</div><div class="line"></div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> n=<span class="number">4</span>; n<=length; ++n)</div><div class="line"> {</div><div class="line"> Max = <span class="number">0</span>;</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>; i<=n/<span class="number">2</span>; ++i)</div><div class="line"> {</div><div class="line"> <span class="keyword">int</span> product = products[i] * products[n-i];</div><div class="line"> <span class="keyword">if</span>(Max<product)</div><div class="line"> Max = product;</div><div class="line"> products[n] = Max;</div><div class="line"> }</div><div class="line"> }</div><div class="line"> Max = products[length];</div><div class="line"> <span class="keyword">delete</span>[] products;</div><div class="line"></div><div class="line"> <span class="keyword">return</span> Max;</div><div class="line">}</div></pre></td></tr></table></figure><p><strong>贪婪算法思路</strong>：如果我们按照以下策略来剪绳子，则得到的各段长度的绳子的长度的乘积将最大：当n>=5时，我们尽量多地剪去长度为３的绳子；当剩下的绳子长度为４时，把绳子剪成两段长度为2的绳子。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div></pre></td><td class="code"><pre><div class="line"><span class="comment">//==============贪婪算法============</span></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">maxProductAfterCutting_solution2</span><span class="params">(<span class="keyword">int</span> length)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(length < <span class="number">2</span>)</div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line"> <span class="keyword">if</span>(length == <span class="number">2</span>)</div><div class="line"> <span class="keyword">return</span> <span class="number">1</span>;</div><div class="line"> <span class="keyword">if</span>(length == <span class="number">3</span>)</div><div class="line"> <span class="keyword">return</span> <span class="number">2</span>;</div><div class="line"></div><div class="line"> <span class="comment">// 尽可能多地减去长度为3的绳子段</span></div><div class="line"> <span class="keyword">int</span> timesOf3 = length / <span class="number">3</span>;</div><div class="line"></div><div class="line"> <span class="comment">// 当绳子最后剩下的长度为4的时候，不能再剪去长度为3的绳子段。</span></div><div class="line"> <span class="comment">// 此时更好的方法是把绳子剪成长度为2的两段，因为2*2 > 3*1。</span></div><div class="line"> <span class="keyword">if</span>(length - timesOf3*<span class="number">3</span> == <span class="number">1</span>)</div><div class="line"> timesOf3-=<span class="number">1</span>;</div><div class="line"></div><div class="line"> <span class="keyword">int</span> timesOf2 = (length - timesOf3 * <span class="number">3</span>)/<span class="number">2</span>;</div><div class="line"></div><div class="line"> <span class="keyword">return</span> (<span class="keyword">long</span> <span class="keyword">int</span>)<span class="built_in">pow</span>(<span class="number">3</span>, timesOf3) *(<span class="keyword">long</span> <span class="keyword">int</span>) <span class="built_in">pow</span>(<span class="number">2</span>, timesOf2);</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> length = <span class="number">58</span>;</div><div class="line"> <span class="built_in">cout</span><<maxProductAfterCutting_solution1(length)<<<span class="built_in">endl</span>;</div><div class="line"> <span class="built_in">cout</span><<maxProductAfterCutting_solution2(length)<<<span class="built_in">endl</span>;</div><div class="line"></div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">}</div></pre></td></tr></table></figure><p>发现一个有趣的现象，当n>58时，贪婪算法失效了，大家觉得这是什么原因呢？</p>]]></content>
<summary type="html">
<h3 id="动态规划"><a href="#动态规划" class="headerlink" title="动态规划"></a>动态规划</h3><p>动态规划算法的基本思想与分治法类似，也是将待求解的问题分解为若干个子问题（阶段），按顺序求解子阶段，前一子问题的解，为后一子问题的求解提供了有用的信息。在求解任一子问题时，列出各种可能的局部解，通过决策保留那些有可能达到最优的局部解，丢弃其他局部解。依次解决各子问题，最后一个子问题就是初始问题的解。由于动态规划解决的问题多数有重叠子问题这个特点，为减少重复计算，对每一个子问题只解一次，将其不同阶段的不同状态保存在一个二维数组中。</p>
<p>能采用动态规划求解的问题的特点：</p>
<ul>
<li>最优化原理：如果问题的最优解所包含的子问题的解也是最优的，就称该问题具有最优子结构，即满足最优化原理。</li>
<li>无后效性：即某阶段状态一旦确定，就不受这个状态以后决策的影响。也就是说，某状态以后的过程不会影响以前的状态，只与当前状态有关。</li>
<li>有重叠子问题：即子问题之间是不独立的，一个子问题在下一阶段决策中可能被多次使用到。（该性质并不是动态规划适用的必要条件，但是如果没有这条性质，动态规划算法同其他算法相比就不具备优势）</li>
<li>从上往下分析问题，从下往上求解问题。</li>
</ul>
</summary>
<category term="编程" scheme="http://yoursite.com/categories/%E7%BC%96%E7%A8%8B/"/>
<category term="编程，动态规划与贪婪算法" scheme="http://yoursite.com/tags/%E7%BC%96%E7%A8%8B%EF%BC%8C%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92%E4%B8%8E%E8%B4%AA%E5%A9%AA%E7%AE%97%E6%B3%95/"/>
</entry>
<entry>
<title>回溯法</title>
<link href="http://yoursite.com/2018/01/27/StringPath/"/>
<id>http://yoursite.com/2018/01/27/StringPath/</id>
<published>2018-01-27T08:50:20.000Z</published>
<updated>2018-01-27T12:51:40.380Z</updated>
<content type="html"><![CDATA[<h3 id="回溯法"><a href="#回溯法" class="headerlink" title="回溯法"></a>回溯法</h3><p>回溯法可以看成蛮力法的升级版，主要是在搜索过程中寻找问题的解，当发现已经不满足求解条件时，就“回溯”返回，尝试别的路径。回溯法是一种选优搜索法，按选优条件向前搜索，以达到目标。但当搜索到某一步时，发现原先选择并不优或达不到目标，就退回一步进行选择，这种走不通就退回再走的技术为回溯法，而满足回溯条件的某个状态的点称为回溯点。</p><p>在包含问题的所有解的解空间树中，按照<strong>深度优先搜索的策略</strong>，从根结点出发深度探索解空间树。当探索到某一结点时，要先判断该结点是否包含问题的解，如果包含，就从该结点出发继续探索下去，如果该结点不包含问题的解，则逐层向其祖先结点回溯。（其实回溯法就是对隐式图的深度优先搜索法）。</p><p>若用回溯法求问题的所有解时，要回溯到根，且根结点的所有可行的子树都要已被搜索遍才结束。 而若使用回溯法求任一个解时，只要搜索到问题的一个解就可以结束。</p><p>回溯法过程：</p><ul><li>针对所给问题，确定问题的解空间：首先应明确定义问题的解空间，问题的解空间应至少包含问题的一个（最优）解。</li><li>确定结点的扩展搜索规则。</li><li>以深度优先方式搜索解空间，并在搜索过程中用剪枝函数避免无效搜索。</li></ul><a id="more"></a><h3 id="面试题：矩阵中的路径"><a href="#面试题：矩阵中的路径" class="headerlink" title="面试题：矩阵中的路径"></a>面试题：矩阵中的路径</h3><p><strong>题目</strong>：请设计一个函数，用来判断在一个矩阵中是否存在一条包含某字符串所有字符的路径。路径可以从矩阵中任意一格开始，每一步可以在矩阵中向左、右、上、下移动一格。如果一条路径经过了矩阵的某一格，那么该路径不能再次进入该格子。例如在下面的3×4的矩阵中包含一条字符串“bfce”的路径（路径中的字母用下划线标出）。但矩阵中不包含字符串“abfb”的路径，因为字符串的第一个字符b占据了矩阵中的第一行第二个格子之后，路径不能再次进入这个格子。</p><div class="table-container"><table><thead><tr><th style="text-align:center">A</th><th style="text-align:center">B</th><th style="text-align:center">T</th><th style="text-align:center">G</th></tr></thead><tbody><tr><td style="text-align:center">C</td><td style="text-align:center">F</td><td style="text-align:center">C</td><td style="text-align:center">S</td></tr><tr><td style="text-align:center">J</td><td style="text-align:center">D</td><td style="text-align:center">E</td><td style="text-align:center">H</td></tr></tbody></table></div><p><strong>思路</strong>：由于矩阵的第一行第二个字母’b’的路径’bfce’的第一个字符相等，我们就从这里开始分析。根据题目要求，我们此时有3个选项，分别是向左边到达字母’a’,向右边到达字母’t’，向下到达字母’f’。我们先尝试选项’a’,由于此时不能得到路径’bfce’，因此不得不回到结点’b’尝试下一个选项’t’，同样，经过结点也不能得到路径’bfce’，因此再次回到结点’b’尝试下一个选项’f’。</p><p>在结点’f’我们也有三个选项，向左右都能到达’c’，向下到达子字母‘d’。我们先选择向左到达字母’c’,由于只有一个选择，即向下到达字母’j’。但是无法到达路径’bfce’，我们只好回溯到上一个结点’f’尝试下一个选项，即向右到达结点’c’。</p><p>根据这个规则，一直寻找，知道满足约束条件。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><iostream></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><stdio.h></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string"><string.h></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><stack></span></span></div><div class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">bool</span> <span class="title">hasPathCore</span><span class="params">(<span class="keyword">const</span> <span class="keyword">char</span>* matrix, <span class="keyword">int</span> rows, <span class="keyword">int</span> cols, <span class="keyword">int</span> row, <span class="keyword">int</span> col,</span></span></div><div class="line"><span class="function"><span class="params"> <span class="keyword">const</span> <span class="keyword">char</span>* str, <span class="keyword">int</span>& pathLength, <span class="keyword">bool</span> *visited)</span></span>;</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">bool</span> <span class="title">hasPath</span><span class="params">(<span class="keyword">const</span> <span class="keyword">char</span>* matrix, <span class="keyword">int</span> rows, <span class="keyword">int</span> cols, <span class="keyword">const</span> <span class="keyword">char</span>* str)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(matrix == <span class="literal">nullptr</span> || rows<<span class="number">1</span> || cols<<span class="number">1</span> || str == <span class="literal">nullptr</span>)</div><div class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</div><div class="line"></div><div class="line"> <span class="keyword">bool</span> *visited = <span class="keyword">new</span> <span class="keyword">bool</span>[rows * cols];</div><div class="line"> <span class="built_in">memset</span>(visited, <span class="number">0</span>, rows*cols);</div><div class="line"></div><div class="line"> <span class="keyword">int</span> pathLength = <span class="number">0</span>;</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> row=<span class="number">0</span>; row<rows; ++row)</div><div class="line"> {</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> col=<span class="number">0</span>; col<cols; ++col)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(hasPathCore(matrix, rows, cols, row, col, str, pathLength, visited))</div><div class="line"> {</div><div class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</div><div class="line"> }</div><div class="line"> }</div><div class="line"> }</div><div class="line"> <span class="keyword">delete</span>[] visited;</div><div class="line"></div><div class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">bool</span> <span class="title">hasPathCore</span><span class="params">(<span class="keyword">const</span> <span class="keyword">char</span>* matrix, <span class="keyword">int</span> rows, <span class="keyword">int</span> cols, <span class="keyword">int</span> row, <span class="keyword">int</span> col,</span></span></div><div class="line"><span class="function"><span class="params"> <span class="keyword">const</span> <span class="keyword">char</span>* str, <span class="keyword">int</span>& pathLength, <span class="keyword">bool</span> *visited)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(str[pathLength] == <span class="string">'\0'</span>)</div><div class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</div><div class="line"></div><div class="line"> <span class="keyword">bool</span> hasPath = <span class="literal">false</span>;</div><div class="line"> <span class="keyword">if</span>(row>=<span class="number">0</span> && row<rows && col>=<span class="number">0</span> && col<cols && matrix[row*cols+col] == str[pathLength] && !visited[row*cols+col])</div><div class="line"> {</div><div class="line"> ++pathLength;</div><div class="line"></div><div class="line"> visited[row*cols+col] = <span class="literal">true</span>;</div><div class="line"> hasPath = hasPathCore(matrix, rows, cols, row, col<span class="number">-1</span>,</div><div class="line"> str, pathLength, visited)</div><div class="line"> ||hasPathCore(matrix, rows, cols, row, col+<span class="number">1</span>,</div><div class="line"> str, pathLength, visited)</div><div class="line"> ||hasPathCore(matrix, rows, cols, row<span class="number">-1</span>, col,</div><div class="line"> str, pathLength, visited)</div><div class="line"> ||hasPathCore(matrix, rows, cols, row+<span class="number">1</span>, col,</div><div class="line"> str, pathLength, visited);</div><div class="line"></div><div class="line"> <span class="keyword">if</span>(!hasPath)</div><div class="line"> {</div><div class="line"> --pathLength;</div><div class="line"> visited[row*cols+col] = <span class="literal">false</span>;</div><div class="line"> }</div><div class="line"></div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> hasPath;</div><div class="line"></div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div><div class="line">42</div><div class="line">43</div><div class="line">44</div><div class="line">45</div><div class="line">46</div><div class="line">47</div><div class="line">48</div><div class="line">49</div><div class="line">50</div><div class="line">51</div><div class="line">52</div><div class="line">53</div><div class="line">54</div><div class="line">55</div><div class="line">56</div><div class="line">57</div><div class="line">58</div><div class="line">59</div><div class="line">60</div><div class="line">61</div><div class="line">62</div><div class="line">63</div><div class="line">64</div><div class="line">65</div><div class="line">66</div><div class="line">67</div><div class="line">68</div><div class="line">69</div><div class="line">70</div><div class="line">71</div><div class="line">72</div><div class="line">73</div></pre></td><td class="code"><pre><div class="line"><span class="comment">//===============测试代码=============</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test</span><span class="params">(<span class="keyword">const</span> <span class="keyword">char</span>* testName, <span class="keyword">const</span> <span class="keyword">char</span>* matrix, <span class="keyword">int</span> rows, <span class="keyword">int</span> cols, <span class="keyword">const</span> <span class="keyword">char</span>* str, <span class="keyword">bool</span> expected)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(testName != <span class="literal">nullptr</span>)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"%s begins: "</span>, testName);</div><div class="line"></div><div class="line"> <span class="keyword">if</span>(hasPath(matrix, rows, cols, str) == expected)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Passed.\n"</span>);</div><div class="line"> <span class="keyword">else</span></div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Failed.\n"</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">//ABTG</span></div><div class="line"><span class="comment">//CFCS</span></div><div class="line"><span class="comment">//JDEH</span></div><div class="line"></div><div class="line"><span class="comment">//BFCE</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test1</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">const</span> <span class="keyword">char</span>* matrix = <span class="string">"ABTGCFCSJDEH"</span>;</div><div class="line"> <span class="keyword">const</span> <span class="keyword">char</span>* str = <span class="string">"BFCE"</span>;</div><div class="line"></div><div class="line"> Test(<span class="string">"Test1"</span>, matrix, <span class="number">3</span>, <span class="number">4</span>, str, <span class="literal">true</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">//ABCE</span></div><div class="line"><span class="comment">//SFCS</span></div><div class="line"><span class="comment">//ADEE</span></div><div class="line"></div><div class="line"><span class="comment">//SEE</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test2</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">const</span> <span class="keyword">char</span>* matrix = <span class="string">"ABCESFCSADEE"</span>;</div><div class="line"> <span class="keyword">const</span> <span class="keyword">char</span>* str = <span class="string">"SEE"</span>;</div><div class="line"></div><div class="line"> Test(<span class="string">"Test2"</span>, matrix, <span class="number">3</span>, <span class="number">4</span>, str, <span class="literal">true</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">//AAAA</span></div><div class="line"><span class="comment">//AAAA</span></div><div class="line"><span class="comment">//AAAA</span></div><div class="line"></div><div class="line"><span class="comment">//AAAAAAAAAAAA</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test3</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">const</span> <span class="keyword">char</span>* matrix = <span class="string">"AAAAAAAAAAAA"</span>;</div><div class="line"> <span class="keyword">const</span> <span class="keyword">char</span>* str = <span class="string">"AAAAAAAAAAAA"</span>;</div><div class="line"></div><div class="line"> Test(<span class="string">"Test3"</span>, (<span class="keyword">const</span> <span class="keyword">char</span>*) matrix, <span class="number">3</span>, <span class="number">4</span>, str, <span class="literal">true</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">//ABCE</span></div><div class="line"><span class="comment">//SFCS</span></div><div class="line"><span class="comment">//ADEE</span></div><div class="line"></div><div class="line"><span class="comment">//SEE</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test4</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">const</span> <span class="keyword">char</span>* matrix = <span class="string">"ABCESFCSADEE"</span>;</div><div class="line"> <span class="keyword">const</span> <span class="keyword">char</span>* str = <span class="string">"ABFB"</span>;</div><div class="line"></div><div class="line"> Test(<span class="string">"Test4"</span>, matrix, <span class="number">3</span>, <span class="number">4</span>, str, <span class="literal">false</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> Test1();</div><div class="line"> Test2();</div><div class="line"> Test3();</div><div class="line"> Test4();</div><div class="line"></div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">}</div></pre></td></tr></table></figure><h3 id="面试题：机器人的运动范围"><a href="#面试题：机器人的运动范围" class="headerlink" title="面试题：机器人的运动范围"></a>面试题：机器人的运动范围</h3><p><strong>题目</strong>：地上有m行n列的方格。一个机器人一个机器人从坐标(0, 0)的格子开始移动，它每一次可以向左、右、上、下移动一格，但不能进入行坐标和列坐标的数位之和大于k的格子。例如，当k为18时，机器人能够进入方格(35, 37)，因为3+5+3+7=18。但它不能进入方格(35, 38)，因为3+5+3+8=19。请问该机器人能够到达多少个格子？</p><p><strong>思路</strong>：和上一道题类似，这个方格也可以看做是一个m*n的矩阵。同样在这个矩阵中，除了边界上的格子外，其他格子都有四个相邻的格子。机器人的坐标从(0,0)开始移动。当它准备进入坐标为(i,j)的格子时，通过检查坐标的位数来判断机器人能否进入。如果机器人能够进入坐标为(i, j)的格子，则再判断他能否进入4个相邻的格子(i, j-1),(i-1, j). (i, j+1)和(i+1, j)。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><iostream></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><stdio.h></span></span></div><div class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">movingCountCore</span><span class="params">(<span class="keyword">int</span> threshold, <span class="keyword">int</span> rows, <span class="keyword">int</span> cols, <span class="keyword">int</span> row, <span class="keyword">int</span> col, <span class="keyword">bool</span>* visited)</span></span>;</div><div class="line"><span class="function"><span class="keyword">bool</span> <span class="title">check</span><span class="params">(<span class="keyword">int</span> threshold, <span class="keyword">int</span> rows, <span class="keyword">int</span> cols, <span class="keyword">int</span> row, <span class="keyword">int</span> col, <span class="keyword">bool</span>* visited)</span></span>;</div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">getSum</span><span class="params">(<span class="keyword">int</span> number)</span></span>;</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">movingCount</span><span class="params">(<span class="keyword">int</span> threshold, <span class="keyword">int</span> rows, <span class="keyword">int</span> cols)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(threshold<<span class="number">0</span> || rows<<span class="number">1</span> || cols<<span class="number">1</span>)</div><div class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</div><div class="line"></div><div class="line"> <span class="keyword">bool</span>* visited = <span class="keyword">new</span> <span class="keyword">bool</span>[rows*cols];</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>; i<rows*cols; ++i)</div><div class="line"> visited[i] = <span class="literal">false</span>;</div><div class="line"></div><div class="line"> <span class="keyword">int</span> count = movingCountCore(threshold, rows, cols, <span class="number">0</span>, <span class="number">0</span>, visited);</div><div class="line"></div><div class="line"> <span class="keyword">delete</span>[] visited;</div><div class="line"> <span class="keyword">return</span> count;</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">movingCountCore</span><span class="params">(<span class="keyword">int</span> threshold, <span class="keyword">int</span> rows, <span class="keyword">int</span> cols, <span class="keyword">int</span> row, <span class="keyword">int</span> col, <span class="keyword">bool</span>* visited)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> count = <span class="number">0</span>;</div><div class="line"></div><div class="line"> <span class="keyword">if</span>(check(threshold, rows, cols, row, col, visited))</div><div class="line"> {</div><div class="line"> visited[row*cols+col] = <span class="literal">true</span>;</div><div class="line"></div><div class="line"> count =<span class="number">1</span>+movingCountCore(threshold, rows, cols,</div><div class="line"> row, col<span class="number">-1</span>, visited)</div><div class="line"> + movingCountCore(threshold, rows, cols,</div><div class="line"> row<span class="number">-1</span>, col, visited)</div><div class="line"> + movingCountCore(threshold, rows, cols,</div><div class="line"> row, col+<span class="number">1</span>, visited)</div><div class="line"> + movingCountCore(threshold, rows, cols,</div><div class="line"> row+<span class="number">1</span>, col, visited);</div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> count;</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">bool</span> <span class="title">check</span><span class="params">(<span class="keyword">int</span> threshold, <span class="keyword">int</span> rows, <span class="keyword">int</span> cols, <span class="keyword">int</span> row, <span class="keyword">int</span> col,</span></span></div><div class="line"><span class="function"><span class="params"> <span class="keyword">bool</span>* visited)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(row >= <span class="number">0</span> && row < rows && col >= <span class="number">0</span> && col < cols</div><div class="line"> && getSum(row) + getSum(col) <= threshold</div><div class="line"> && !visited[row* cols + col])</div><div class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</div><div class="line"></div><div class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">getSum</span><span class="params">(<span class="keyword">int</span> number)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> sum = <span class="number">0</span>;</div><div class="line"> <span class="keyword">while</span>(number><span class="number">0</span>)</div><div class="line"> {</div><div class="line"> sum += number % <span class="number">10</span>;</div><div class="line"> number = number/<span class="number">10</span>;</div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> sum;</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div><div class="line">42</div><div class="line">43</div><div class="line">44</div><div class="line">45</div><div class="line">46</div><div class="line">47</div><div class="line">48</div><div class="line">49</div><div class="line">50</div><div class="line">51</div><div class="line">52</div><div class="line">53</div><div class="line">54</div><div class="line">55</div><div class="line">56</div><div class="line">57</div><div class="line">58</div><div class="line">59</div><div class="line">60</div><div class="line">61</div><div class="line">62</div><div class="line">63</div><div class="line">64</div><div class="line">65</div><div class="line">66</div><div class="line">67</div><div class="line">68</div><div class="line">69</div><div class="line">70</div><div class="line">71</div><div class="line">72</div><div class="line">73</div><div class="line">74</div><div class="line">75</div><div class="line">76</div><div class="line">77</div><div class="line">78</div><div class="line">79</div><div class="line">80</div><div class="line">81</div><div class="line">82</div><div class="line">83</div><div class="line">84</div><div class="line">85</div><div class="line">86</div><div class="line">87</div><div class="line">88</div><div class="line">89</div><div class="line">90</div></pre></td><td class="code"><pre><div class="line"><span class="comment">// ====================测试代码====================</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test</span><span class="params">(<span class="keyword">char</span>* testName, <span class="keyword">int</span> threshold, <span class="keyword">int</span> rows, <span class="keyword">int</span> cols, <span class="keyword">int</span> excepted)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(testName != <span class="literal">nullptr</span>)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"%s begins: "</span>, testName);</div><div class="line"></div><div class="line"> <span class="keyword">if</span>(movingCount(threshold, rows, cols) == excepted)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Test Passed.\n"</span>);</div><div class="line"> <span class="keyword">else</span></div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Test Failed.\n"</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 方格多行多列</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test1</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> Test(<span class="string">"Test1"</span>, <span class="number">5</span>, <span class="number">10</span>, <span class="number">10</span>, <span class="number">21</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 方格多行多列</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test2</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> Test(<span class="string">"Test2"</span>, <span class="number">15</span>, <span class="number">20</span>, <span class="number">20</span>, <span class="number">359</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 方格只有一行，机器人只能到达部分方格</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test3</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> Test(<span class="string">"Test3"</span>, <span class="number">10</span>, <span class="number">1</span>, <span class="number">100</span>, <span class="number">29</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 方格只有一行，机器人能到达所有方格</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test4</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> Test(<span class="string">"Test4"</span>, <span class="number">10</span>, <span class="number">1</span>, <span class="number">10</span>, <span class="number">10</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 方格只有一列，机器人只能到达部分方格</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test5</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> Test(<span class="string">"Test5"</span>, <span class="number">15</span>, <span class="number">100</span>, <span class="number">1</span>, <span class="number">79</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 方格只有一列，机器人能到达所有方格</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test6</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> Test(<span class="string">"Test6"</span>, <span class="number">15</span>, <span class="number">10</span>, <span class="number">1</span>, <span class="number">10</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 方格只有一行一列</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test7</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> Test(<span class="string">"Test7"</span>, <span class="number">15</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 方格只有一行一列</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test8</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> Test(<span class="string">"Test8"</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 机器人不能进入任意一个方格</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test9</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> Test(<span class="string">"Test9"</span>, <span class="number">-10</span>, <span class="number">10</span>, <span class="number">10</span>, <span class="number">0</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="comment">/**</span></div><div class="line"><span class="comment"> int threshold, rows, cols;</span></div><div class="line"><span class="comment"> cin>>threshold;</span></div><div class="line"><span class="comment"> cin>>rows;</span></div><div class="line"><span class="comment"> cin>>cols;</span></div><div class="line"><span class="comment"> cout<<movingCount(threshold, rows, cols);</span></div><div class="line"><span class="comment"> int n;</span></div><div class="line"><span class="comment"> cin>>n;</span></div><div class="line"><span class="comment"> cout<<getSum(n)<<ends;</span></div><div class="line"><span class="comment"> **/</span></div><div class="line"> Test1();</div><div class="line"> Test2();</div><div class="line"> Test3();</div><div class="line"> Test4();</div><div class="line"> Test5();</div><div class="line"> Test6();</div><div class="line"> Test7();</div><div class="line"> Test8();</div><div class="line"> test9();</div><div class="line"></div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">}</div></pre></td></tr></table></figure>]]></content>
<summary type="html">
<h3 id="回溯法"><a href="#回溯法" class="headerlink" title="回溯法"></a>回溯法</h3><p>回溯法可以看成蛮力法的升级版，主要是在搜索过程中寻找问题的解，当发现已经不满足求解条件时，就“回溯”返回，尝试别的路径。回溯法是一种选优搜索法，按选优条件向前搜索，以达到目标。但当搜索到某一步时，发现原先选择并不优或达不到目标，就退回一步进行选择，这种走不通就退回再走的技术为回溯法，而满足回溯条件的某个状态的点称为回溯点。</p>
<p>在包含问题的所有解的解空间树中，按照<strong>深度优先搜索的策略</strong>，从根结点出发深度探索解空间树。当探索到某一结点时，要先判断该结点是否包含问题的解，如果包含，就从该结点出发继续探索下去，如果该结点不包含问题的解，则逐层向其祖先结点回溯。（其实回溯法就是对隐式图的深度优先搜索法）。</p>
<p>若用回溯法求问题的所有解时，要回溯到根，且根结点的所有可行的子树都要已被搜索遍才结束。 而若使用回溯法求任一个解时，只要搜索到问题的一个解就可以结束。</p>
<p>回溯法过程：</p>
<ul>
<li>针对所给问题，确定问题的解空间：首先应明确定义问题的解空间，问题的解空间应至少包含问题的一个（最优）解。</li>
<li>确定结点的扩展搜索规则。</li>
<li>以深度优先方式搜索解空间，并在搜索过程中用剪枝函数避免无效搜索。</li>
</ul>
</summary>
<category term="编程" scheme="http://yoursite.com/categories/%E7%BC%96%E7%A8%8B/"/>
<category term="编程，回溯法" scheme="http://yoursite.com/tags/%E7%BC%96%E7%A8%8B%EF%BC%8C%E5%9B%9E%E6%BA%AF%E6%B3%95/"/>
</entry>
<entry>
<title>旋转数组的最小数字</title>
<link href="http://yoursite.com/2018/01/27/MinInOrder/"/>
<id>http://yoursite.com/2018/01/27/MinInOrder/</id>
<published>2018-01-27T03:44:35.000Z</published>
<updated>2018-01-27T04:02:50.128Z</updated>
<content type="html"><![CDATA[<h3 id="面试题：旋转数组的最小数字"><a href="#面试题：旋转数组的最小数字" class="headerlink" title="面试题：旋转数组的最小数字"></a>面试题：旋转数组的最小数字</h3><p><strong>题目</strong>：把一个数组最开始的若干个元素搬到数组的末尾，我们称之为数组的旋转。输入一个递增排序的数组的一个旋转，输出旋转数组的最小元素。例如数组{3, 4, 5, 1, 2}为{1, 2, 3, 4, 5}的一个旋转，该数组的最小值为1。</p><p><strong>思路</strong>：我们注意到旋转之后的数组实际上可以划分为两个排序的子数组，而且前面的子数组的元素都大于或者等于后面子数组的元素。我们还注意到最小的元素刚好是这两个子数组的分界线。在排序的数组中没我们可以用二分法实现O(logn)的查找。我们用两个指针分别指向数组的第一个元素和最后一个元素，按照旋转规则，第一个元素大于或者等于最后一个元素。</p><p>接着我们可以找到数组中间的元素。如果该中间元素位于前面的递增子数组，那么它应该大于或者等于第一个指针指向的元素。此时数组中最小的元素位于该之间元素的后面。我们可以把第一个指针指向该之间元素，这样就可以缩小寻找范围，移动之后的第一个指针仍然位于前面的递增数组。</p><p>同样，如果该中间元素位于后面的递增子数组，那么它应该小于或者等于第二个指针指向的元素。此时数组中最小的元素位于该之间元素的前面。我们可以把第二个指针指向该之间元素，这样就可以缩小寻找范围，移动之后的第二个指针仍然位于前面的递增数组。</p><p>对于特殊情况，如下面的情况，就需要利用顺序查找。对于数组{0,1,1,1,1}的旋转。</p><a id="more"></a><div class="table-container"><table><thead><tr><th style="text-align:center">１</th><th style="text-align:center">０</th><th style="text-align:center">１</th><th style="text-align:center">１</th><th style="text-align:center">１</th></tr></thead><tbody><tr><td style="text-align:center">p1</td><td style="text-align:center"></td><td style="text-align:center">Mid</td><td style="text-align:center"></td><td style="text-align:center">p2</td></tr></tbody></table></div><div class="table-container"><table><thead><tr><th style="text-align:center">１</th><th style="text-align:center">1</th><th style="text-align:center">１</th><th style="text-align:center">0</th><th style="text-align:center">１</th></tr></thead><tbody><tr><td style="text-align:center">p1</td><td style="text-align:center"></td><td style="text-align:center">Mid</td><td style="text-align:center"></td><td style="text-align:center">p2</td></tr></tbody></table></div><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><iostream></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><cstdio></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><exception></span></span></div><div class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">MinInOrder</span><span class="params">(<span class="keyword">int</span>* numbers, <span class="keyword">int</span> index1, <span class="keyword">int</span> index2)</span></span>;</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">Min</span><span class="params">(<span class="keyword">int</span>* numbers, <span class="keyword">int</span> length)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(numbers == <span class="literal">nullptr</span> || length <= <span class="number">0</span>)</div><div class="line"> <span class="keyword">throw</span> <span class="built_in">std</span>::exception();</div><div class="line"></div><div class="line"> <span class="keyword">int</span> index1 = <span class="number">0</span>;</div><div class="line"> <span class="keyword">int</span> index2 = length<span class="number">-1</span>;</div><div class="line"> <span class="keyword">int</span> Mid = index1;</div><div class="line"> <span class="keyword">while</span>(numbers[index1] >= numbers[index2])</div><div class="line"> {</div><div class="line"> <span class="comment">// 如果index1和index2指向相邻的两个数，</span></div><div class="line"> <span class="comment">// 则index1指向第一个递增子数组的最后一个数字，</span></div><div class="line"> <span class="comment">// index2指向第二个子数组的第一个数字，也就是数组中的最小数字</span></div><div class="line"> <span class="keyword">if</span>(index2 - index1 == <span class="number">1</span>)</div><div class="line"> {</div><div class="line"> <span class="comment">//index2指向的是最小的数字</span></div><div class="line"> Mid = index2;</div><div class="line"> <span class="keyword">break</span>;</div><div class="line"> }</div><div class="line"> Mid = (index1 + index2)/<span class="number">2</span>;</div><div class="line"></div><div class="line"> <span class="comment">// 如果下标为index1、index2和indexMid指向的三个数字相等，</span></div><div class="line"> <span class="comment">// 则只能顺序查找</span></div><div class="line"> <span class="keyword">if</span>(numbers[index1] == numbers[index2] && numbers[index1] == numbers[Mid])</div><div class="line"> <span class="keyword">return</span> MinInOrder(numbers, index1, index2);</div><div class="line"></div><div class="line"> <span class="keyword">if</span>(numbers[Mid] >= numbers[index1])</div><div class="line"> index1 = Mid;</div><div class="line"> <span class="keyword">else</span> <span class="keyword">if</span>(numbers[Mid] <= numbers[index2])</div><div class="line"> index2 = Mid;</div><div class="line"></div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> numbers[Mid];</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">MinInOrder</span><span class="params">(<span class="keyword">int</span>* numbers, <span class="keyword">int</span> index1, <span class="keyword">int</span> index2)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> reslut = <span class="number">0</span>;</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=index1+<span class="number">1</span>; i<=index2; i++)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(numbers[reslut]>numbers[i])</div><div class="line"> reslut = numbers[i];</div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> reslut;</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div></pre></td><td class="code"><pre><div class="line"><span class="comment">// ====================测试代码====================</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test</span><span class="params">(<span class="keyword">int</span>* numbers, <span class="keyword">int</span> length, <span class="keyword">int</span> excepted)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> result = <span class="number">0</span>;</div><div class="line"> <span class="keyword">try</span></div><div class="line"> {</div><div class="line"> result = Min(numbers, length);</div><div class="line"></div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>; i<length; i++)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"%d "</span>, numbers[i]);</div><div class="line"></div><div class="line"> <span class="keyword">if</span>(result == excepted)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"\tPassed.\n"</span>);</div><div class="line"> <span class="keyword">else</span></div><div class="line"> <span class="built_in">printf</span>(<span class="string">"\tFailed.\n"</span>);</div><div class="line"> }</div><div class="line"> <span class="keyword">catch</span>(...)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(numbers == <span class="literal">nullptr</span>)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Test Passed.\n"</span>);</div><div class="line"> <span class="keyword">else</span></div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Test Failed.\n"</span>);</div><div class="line"> }</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="comment">// 典型输入，单调升序的数组的一个旋转</span></div><div class="line"> <span class="keyword">int</span> array1[] = { <span class="number">3</span>, <span class="number">4</span>, <span class="number">5</span>, <span class="number">1</span>, <span class="number">2</span> };</div><div class="line"> Test(array1, <span class="keyword">sizeof</span>(array1) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), <span class="number">1</span>);</div><div class="line"></div><div class="line"> <span class="comment">// 有重复数字，并且重复的数字刚好的最小的数字</span></div><div class="line"> <span class="keyword">int</span> array2[] = { <span class="number">3</span>, <span class="number">4</span>, <span class="number">5</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">2</span> };</div><div class="line"> Test(array2, <span class="keyword">sizeof</span>(array2) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), <span class="number">1</span>);</div><div class="line"></div><div class="line"> <span class="comment">// 有重复数字，但重复的数字不是第一个数字和最后一个数字</span></div><div class="line"> <span class="keyword">int</span> array3[] = { <span class="number">3</span>, <span class="number">4</span>, <span class="number">5</span>, <span class="number">1</span>, <span class="number">2</span>, <span class="number">2</span> };</div><div class="line"> Test(array3, <span class="keyword">sizeof</span>(array3) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), <span class="number">1</span>);</div><div class="line"></div><div class="line"> <span class="comment">// 有重复的数字，并且重复的数字刚好是第一个数字和最后一个数字</span></div><div class="line"> <span class="keyword">int</span> array4[] = { <span class="number">1</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="number">1</span>, <span class="number">1</span> };</div><div class="line"> Test(array4, <span class="keyword">sizeof</span>(array4) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), <span class="number">0</span>);</div><div class="line"></div><div class="line"> <span class="comment">// 单调升序数组，旋转0个元素，也就是单调升序数组本身</span></div><div class="line"> <span class="keyword">int</span> array5[] = { <span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">4</span>, <span class="number">5</span> };</div><div class="line"> Test(array5, <span class="keyword">sizeof</span>(array5) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), <span class="number">1</span>);</div><div class="line"></div><div class="line"> <span class="comment">// 数组中只有一个数字</span></div><div class="line"> <span class="keyword">int</span> array6[] = { <span class="number">2</span> };</div><div class="line"> Test(array6, <span class="keyword">sizeof</span>(array6) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), <span class="number">2</span>);</div><div class="line"></div><div class="line"> <span class="comment">// 输入nullptr</span></div><div class="line"> Test(<span class="literal">nullptr</span>, <span class="number">0</span>, <span class="number">0</span>);</div><div class="line"></div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">}</div></pre></td></tr></table></figure>]]></content>
<summary type="html">
<h3 id="面试题：旋转数组的最小数字"><a href="#面试题：旋转数组的最小数字" class="headerlink" title="面试题：旋转数组的最小数字"></a>面试题：旋转数组的最小数字</h3><p><strong>题目</strong>：把一个数组最开始的若干个元素搬到数组的末尾，我们称之为数组的旋转。输入一个递增排序的数组的一个旋转，输出旋转数组的最小元素。例如数组{3, 4, 5, 1, 2}为{1, 2, 3, 4, 5}的一个旋转，该数组的最小值为1。</p>
<p><strong>思路</strong>：我们注意到旋转之后的数组实际上可以划分为两个排序的子数组，而且前面的子数组的元素都大于或者等于后面子数组的元素。我们还注意到最小的元素刚好是这两个子数组的分界线。在排序的数组中没我们可以用二分法实现O(logn)的查找。我们用两个指针分别指向数组的第一个元素和最后一个元素，按照旋转规则，第一个元素大于或者等于最后一个元素。</p>
<p>接着我们可以找到数组中间的元素。如果该中间元素位于前面的递增子数组，那么它应该大于或者等于第一个指针指向的元素。此时数组中最小的元素位于该之间元素的后面。我们可以把第一个指针指向该之间元素，这样就可以缩小寻找范围，移动之后的第一个指针仍然位于前面的递增数组。</p>
<p>同样，如果该中间元素位于后面的递增子数组，那么它应该小于或者等于第二个指针指向的元素。此时数组中最小的元素位于该之间元素的前面。我们可以把第二个指针指向该之间元素，这样就可以缩小寻找范围，移动之后的第二个指针仍然位于前面的递增数组。</p>
<p>对于特殊情况，如下面的情况，就需要利用顺序查找。对于数组{0,1,1,1,1}的旋转。</p>
</summary>
<category term="编程" scheme="http://yoursite.com/categories/%E7%BC%96%E7%A8%8B/"/>
<category term="编程，数组" scheme="http://yoursite.com/tags/%E7%BC%96%E7%A8%8B%EF%BC%8C%E6%95%B0%E7%BB%84/"/>
</entry>
<entry>
<title>斐波那契数列</title>
<link href="http://yoursite.com/2018/01/26/Fibonacci/"/>
<id>http://yoursite.com/2018/01/26/Fibonacci/</id>
<published>2018-01-26T12:25:00.000Z</published>
<updated>2018-01-26T12:39:17.247Z</updated>
<content type="html"><![CDATA[<h3 id="面试题：斐波那契数列"><a href="#面试题：斐波那契数列" class="headerlink" title="面试题：斐波那契数列"></a>面试题：斐波那契数列</h3><p><strong>题目</strong>：写一个函数，输入n，求斐波那契（Fibonacci）数列的第n项。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div></pre></td><td class="code"><pre><div class="line"><span class="comment">// ====================方法1：递归====================</span></div><div class="line"><span class="function"><span class="keyword">long</span> <span class="keyword">long</span> <span class="title">Fibonacci_soultion1</span><span class="params">(<span class="keyword">unsigned</span> <span class="keyword">int</span> n)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(n<= <span class="number">0</span>)</div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line"></div><div class="line"> <span class="keyword">if</span>(n == <span class="number">1</span>)</div><div class="line"> <span class="keyword">return</span> <span class="number">1</span>;</div><div class="line"></div><div class="line"> <span class="keyword">return</span> Fibonacci_soultion1(n<span class="number">-1</span>)+Fibonacci_soultion1(n<span class="number">-2</span>);</div><div class="line">}</div></pre></td></tr></table></figure><a id="more"></a><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div></pre></td><td class="code"><pre><div class="line"><span class="comment">// ====================方法2：循环====================</span></div><div class="line"><span class="function"><span class="keyword">long</span> <span class="keyword">long</span> <span class="title">Fibonacci_soultion2</span><span class="params">(<span class="keyword">unsigned</span> n)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> result[<span class="number">2</span>] = {<span class="number">0</span>, <span class="number">1</span>};</div><div class="line"> <span class="keyword">if</span>(n<<span class="number">2</span>)</div><div class="line"> <span class="keyword">return</span> result[n];</div><div class="line"></div><div class="line"> <span class="keyword">long</span> <span class="keyword">long</span> fibNOne = <span class="number">1</span>;</div><div class="line"> <span class="keyword">long</span> <span class="keyword">long</span> fibNTwo = <span class="number">0</span>;</div><div class="line"> <span class="keyword">long</span> <span class="keyword">long</span> fibN = <span class="number">0</span>;</div><div class="line"></div><div class="line"> <span class="keyword">for</span>(<span class="keyword">unsigned</span> <span class="keyword">int</span> i=<span class="number">2</span>; i<=n; i++)</div><div class="line"> {</div><div class="line"> fibN = fibNOne + fibNTwo;</div><div class="line"></div><div class="line"> fibNTwo = fibNOne;</div><div class="line"> fibNOne = fibN;</div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> fibN;</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> n=<span class="number">0</span>;</div><div class="line"> <span class="built_in">cin</span>>>n;</div><div class="line"> <span class="built_in">cout</span><<Fibonacci_soultion1(n)<<<span class="built_in">endl</span>;</div><div class="line"> <span class="comment">// Fibonacci_soultion1(100) 3.495s</span></div><div class="line"> <span class="comment">// Fibonacci_soultion1(100) 3.380s</span></div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">}</div></pre></td></tr></table></figure><p>通常基于递归实现的代码比基于循环实现的代码要简洁很多，但同时也有显著的缺点，递归由于是调用自身，而函数调用是有时间和空间消耗的：每一次函数调用都需要在内存堆栈中分配空间以保存参数、返回地址及临时变量，而且往堆栈里压入数据和弹出数据都需要时间。这就不难理解例子中递归效率不如循环。</p>]]></content>
<summary type="html">
<h3 id="面试题：斐波那契数列"><a href="#面试题：斐波那契数列" class="headerlink" title="面试题：斐波那契数列"></a>面试题：斐波那契数列</h3><p><strong>题目</strong>：写一个函数，输入n，求斐波那契（Fibonacci）数列的第n项。</p>
<figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div></pre></td><td class="code"><pre><div class="line"><span class="comment">// ====================方法1：递归====================</span></div><div class="line"><span class="function"><span class="keyword">long</span> <span class="keyword">long</span> <span class="title">Fibonacci_soultion1</span><span class="params">(<span class="keyword">unsigned</span> <span class="keyword">int</span> n)</span></span></div><div class="line"><span class="function"></span>&#123;</div><div class="line"> <span class="keyword">if</span>(n&lt;= <span class="number">0</span>)</div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line"></div><div class="line"> <span class="keyword">if</span>(n == <span class="number">1</span>)</div><div class="line"> <span class="keyword">return</span> <span class="number">1</span>;</div><div class="line"></div><div class="line"> <span class="keyword">return</span> Fibonacci_soultion1(n<span class="number">-1</span>)+Fibonacci_soultion1(n<span class="number">-2</span>);</div><div class="line">&#125;</div></pre></td></tr></table></figure>
</summary>
<category term="编程" scheme="http://yoursite.com/categories/%E7%BC%96%E7%A8%8B/"/>
<category term="编程，Fibonacci" scheme="http://yoursite.com/tags/%E7%BC%96%E7%A8%8B%EF%BC%8CFibonacci/"/>
</entry>
<entry>
<title>替换空格</title>
<link href="http://yoursite.com/2018/01/24/Replacespace/"/>
<id>http://yoursite.com/2018/01/24/Replacespace/</id>
<published>2018-01-24T12:23:45.000Z</published>
<updated>2018-01-27T04:06:07.545Z</updated>
<content type="html"><![CDATA[<h3 id="替换空格"><a href="#替换空格" class="headerlink" title="替换空格"></a>替换空格</h3><p>题目：请实现一个函数，把字符串中的每个空格替换成”%20”。例如输入“We are happy.”，则输出“We%20are%20happy.”。</p><p><strong>思路</strong>: 首先准备两个指针：p1和p2。p1指向原始字符串的末尾，p2指向替换之后的字符串的末尾。接下来我们向前移动p1，逐个把它指向的字符串复制到p2指向的位置，知道遇到第一个空格为止。此时p1向前移动一格，在p2之前插入字符串”%20”，同时p2向前移动三格。</p><div class="table-container"><table><thead><tr><th style="text-align:center">I</th><th style="text-align:center"></th><th style="text-align:center">a</th><th style="text-align:center"></th><th style="text-align:center"></th></tr></thead><tbody><tr><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center">p1(indexofOriginal)</td><td style="text-align:center"></td><td style="text-align:center">p2(indexofNew)</td></tr><tr><td style="text-align:center">I</td><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center">a</td></tr><tr><td style="text-align:center"></td><td style="text-align:center">p1</td><td style="text-align:center"></td><td style="text-align:center">p2</td><td style="text-align:center"></td></tr><tr><td style="text-align:center">I</td><td style="text-align:center">%</td><td style="text-align:center">2</td><td style="text-align:center">0</td><td style="text-align:center">a</td></tr><tr><td style="text-align:center">p1,p2</td><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center"></td></tr></tbody></table></div><a id="more"></a><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div><div class="line">42</div><div class="line">43</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><iostream></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><cstring></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><cstdio></span></span></div><div class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">ReplaceBlank</span><span class="params">(<span class="keyword">char</span> str[], <span class="keyword">int</span> length)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(str == <span class="literal">nullptr</span> || length <= <span class="number">0</span>)</div><div class="line"> <span class="keyword">return</span> ;</div><div class="line"></div><div class="line"> <span class="keyword">int</span> OriginalLength = <span class="number">0</span>;</div><div class="line"> <span class="keyword">int</span> numberofBlank = <span class="number">0</span>;</div><div class="line"> <span class="keyword">int</span> i = <span class="number">0</span>;</div><div class="line"></div><div class="line"> <span class="keyword">while</span>(str[i] != <span class="string">'\0'</span>)</div><div class="line"> {</div><div class="line"> ++OriginalLength;</div><div class="line"> <span class="keyword">if</span>(str[i] == <span class="string">' '</span>)</div><div class="line"> ++numberofBlank;</div><div class="line"> ++i;</div><div class="line"> }</div><div class="line"></div><div class="line"> <span class="keyword">int</span> newLength = OriginalLength + numberofBlank * <span class="number">2</span>;</div><div class="line"> <span class="keyword">if</span>(newLength > length)</div><div class="line"> <span class="keyword">return</span> ;</div><div class="line"></div><div class="line"> <span class="keyword">int</span> indexofOriginal = OriginalLength; <span class="comment">//p1</span></div><div class="line"> <span class="keyword">int</span> indexofNew = newLength; <span class="comment">//p2</span></div><div class="line"></div><div class="line"> <span class="keyword">while</span>(indexofOriginal >= <span class="number">0</span> && indexofNew > indexofOriginal)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(str[indexofOriginal] == <span class="string">' '</span>)</div><div class="line"> {</div><div class="line"> str[indexofNew--] = <span class="string">'0'</span>;</div><div class="line"> str[indexofNew--] = <span class="string">'2'</span>;</div><div class="line"> str[indexofNew--] = <span class="string">'%'</span>;</div><div class="line"> }</div><div class="line"> <span class="keyword">else</span></div><div class="line"> str[indexofNew--] = str[indexofOriginal];</div><div class="line"></div><div class="line"> --indexofOriginal;</div><div class="line"> }</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div></pre></td><td class="code"><pre><div class="line"><span class="comment">// ====================测试代码====================</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test</span><span class="params">(<span class="keyword">char</span>* testname, <span class="keyword">char</span> str[], <span class="keyword">int</span> length, <span class="keyword">char</span> expected[])</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(testname != <span class="literal">nullptr</span>)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"%s begins: "</span>, testname);</div><div class="line"></div><div class="line"> ReplaceBlank(str, length);</div><div class="line"></div><div class="line"> <span class="keyword">if</span>(expected == <span class="literal">nullptr</span> && str == <span class="literal">nullptr</span>)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Passed. \n"</span>);</div><div class="line"> <span class="keyword">else</span> <span class="keyword">if</span>(expected == <span class="literal">nullptr</span> && str != <span class="literal">nullptr</span>)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Failed. \n"</span>);</div><div class="line"> <span class="keyword">else</span> <span class="keyword">if</span>(<span class="built_in">strcmp</span>(str, expected) == <span class="number">0</span>)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Passed. \n"</span>);</div><div class="line"> <span class="keyword">else</span></div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Failed. \n"</span>);</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div><div class="line">42</div><div class="line">43</div><div class="line">44</div><div class="line">45</div><div class="line">46</div><div class="line">47</div><div class="line">48</div><div class="line">49</div><div class="line">50</div><div class="line">51</div><div class="line">52</div><div class="line">53</div><div class="line">54</div><div class="line">55</div><div class="line">56</div><div class="line">57</div><div class="line">58</div><div class="line">59</div><div class="line">60</div><div class="line">61</div><div class="line">62</div><div class="line">63</div><div class="line">64</div><div class="line">65</div><div class="line">66</div><div class="line">67</div><div class="line">68</div><div class="line">69</div><div class="line">70</div><div class="line">71</div><div class="line">72</div><div class="line">73</div><div class="line">74</div><div class="line">75</div><div class="line">76</div><div class="line">77</div><div class="line">78</div><div class="line">79</div><div class="line">80</div><div class="line">81</div><div class="line">82</div><div class="line">83</div><div class="line">84</div><div class="line">85</div><div class="line">86</div><div class="line">87</div><div class="line">88</div><div class="line">89</div><div class="line">90</div><div class="line">91</div><div class="line">92</div><div class="line">93</div></pre></td><td class="code"><pre><div class="line"></div><div class="line"><span class="comment">//空格在句子中间</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test1</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">const</span> <span class="keyword">int</span> length = <span class="number">50</span>;</div><div class="line"></div><div class="line"> <span class="keyword">char</span> str[length] = <span class="string">"hello world"</span>;</div><div class="line"> Test(<span class="string">"test1"</span>, str, length, <span class="string">"hello%20world"</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 空格在句子开头</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test2</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">const</span> <span class="keyword">int</span> length = <span class="number">50</span>;</div><div class="line"></div><div class="line"> <span class="keyword">char</span> str[length] = <span class="string">" helloworld"</span>;</div><div class="line"> Test(<span class="string">"Test2"</span>, str, length, <span class="string">"%20helloworld"</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 空格在句子末尾</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test3</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">const</span> <span class="keyword">int</span> length = <span class="number">50</span>;</div><div class="line"></div><div class="line"> <span class="keyword">char</span> str[length] = <span class="string">"helloworld "</span>;</div><div class="line"> Test(<span class="string">"Test3"</span>, str, length, <span class="string">"helloworld%20"</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 连续有两个空格</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test4</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">const</span> <span class="keyword">int</span> length = <span class="number">50</span>;</div><div class="line"></div><div class="line"> <span class="keyword">char</span> str[length] = <span class="string">"hello world"</span>;</div><div class="line"> Test(<span class="string">"Test4"</span>, str, length, <span class="string">"hello%20%20world"</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 传入nullptr</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test5</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> Test(<span class="string">"Test5"</span>, <span class="literal">nullptr</span>, <span class="number">0</span>, <span class="literal">nullptr</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 传入内容为空的字符串</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test6</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">const</span> <span class="keyword">int</span> length = <span class="number">50</span>;</div><div class="line"></div><div class="line"> <span class="keyword">char</span> str[length] = <span class="string">""</span>;</div><div class="line"> Test(<span class="string">"Test6"</span>, str, length, <span class="string">""</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">//传入内容为一个空格的字符串</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test7</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">const</span> <span class="keyword">int</span> length = <span class="number">50</span>;</div><div class="line"></div><div class="line"> <span class="keyword">char</span> str[length] = <span class="string">" "</span>;</div><div class="line"> Test(<span class="string">"Test7"</span>, str, length, <span class="string">"%20"</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 传入的字符串没有空格</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test8</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">const</span> <span class="keyword">int</span> length = <span class="number">50</span>;</div><div class="line"></div><div class="line"> <span class="keyword">char</span> str[length] = <span class="string">"helloworld"</span>;</div><div class="line"> Test(<span class="string">"Test8"</span>, str, length, <span class="string">"helloworld"</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 传入的字符串全是空格</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test9</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">const</span> <span class="keyword">int</span> length = <span class="number">50</span>;</div><div class="line"></div><div class="line"> <span class="keyword">char</span> str[length] = <span class="string">" "</span>;</div><div class="line"> Test(<span class="string">"Test9"</span>, str, length, <span class="string">"%20%20%20"</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> Test1();</div><div class="line"> Test2();</div><div class="line"> Test3();</div><div class="line"> Test4();</div><div class="line"> Test5();</div><div class="line"> Test6();</div><div class="line"> Test7();</div><div class="line"> Test8();</div><div class="line"> Test9();</div><div class="line"></div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">}</div></pre></td></tr></table></figure>]]></content>
<summary type="html">
<h3 id="替换空格"><a href="#替换空格" class="headerlink" title="替换空格"></a>替换空格</h3><p>题目：请实现一个函数，把字符串中的每个空格替换成”%20”。例如输入“We are happy.”，则输出“We%20are%20happy.”。</p>
<p><strong>思路</strong>: 首先准备两个指针：p1和p2。p1指向原始字符串的末尾，p2指向替换之后的字符串的末尾。接下来我们向前移动p1，逐个把它指向的字符串复制到p2指向的位置，知道遇到第一个空格为止。此时p1向前移动一格，在p2之前插入字符串”%20”，同时p2向前移动三格。</p>
<div class="table-container">
<table>
<thead>
<tr>
<th style="text-align:center">I</th>
<th style="text-align:center"></th>
<th style="text-align:center">a</th>
<th style="text-align:center"></th>
<th style="text-align:center"></th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
<td style="text-align:center">p1(indexofOriginal)</td>
<td style="text-align:center"></td>
<td style="text-align:center">p2(indexofNew)</td>
</tr>
<tr>
<td style="text-align:center">I</td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
<td style="text-align:center">a</td>
</tr>
<tr>
<td style="text-align:center"></td>
<td style="text-align:center">p1</td>
<td style="text-align:center"></td>
<td style="text-align:center">p2</td>
<td style="text-align:center"></td>
</tr>
<tr>
<td style="text-align:center">I</td>
<td style="text-align:center">%</td>
<td style="text-align:center">2</td>
<td style="text-align:center">0</td>
<td style="text-align:center">a</td>
</tr>
<tr>
<td style="text-align:center">p1,p2</td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
</tr>
</tbody>
</table>
</div>
</summary>
<category term="编程" scheme="http://yoursite.com/categories/%E7%BC%96%E7%A8%8B/"/>
<category term="编程，字符" scheme="http://yoursite.com/tags/%E7%BC%96%E7%A8%8B%EF%BC%8C%E5%AD%97%E7%AC%A6/"/>
</entry>
<entry>
<title>深度学习常用数据集介绍</title>
<link href="http://yoursite.com/2018/01/24/dataset-introduction/"/>
<id>http://yoursite.com/2018/01/24/dataset-introduction/</id>
<published>2018-01-24T02:47:23.000Z</published>
<updated>2018-01-25T12:15:06.442Z</updated>
<content type="html"><![CDATA[<p>深度学习在计算机视觉领域取得了十分重大的突破，许多研究也是如雨后春笋般。而模型的训练离不开数据集的支持，因此有必要对常用的数据集进行了解。接下来主要对计算机视觉和自然语言处理这两个领域的常用数据集进行介绍。</p><h2 id="计算机视觉"><a href="#计算机视觉" class="headerlink" title="计算机视觉"></a>计算机视觉</h2><h3 id="MNIST"><a href="#MNIST" class="headerlink" title="MNIST"></a>MNIST</h3><p>MNIST数据集被称为深度学习领域的“Hello World!”，入门必备！它有<strong>60000</strong>个训练样本集和<strong>10000</strong>个测试样本集，每个样本图像的宽高为<strong>28*28</strong>。此数据集是以二进制存储的，不能直接以图像格式查看，不过很容易找到将其转换成图像格式的工具。</p><p>该数据集可在<a href="http://yann.lecun.com/exdb/mnist/" target="_blank" rel="external">http://yann.lecun.com/exdb/mnist/</a> 获取，主要包含以下四部分：</p><blockquote><p><code>train-images-idx3-ubyte.gz: training set images (9912422 bytes)</code><br><code>train-labels-idx1-ubyte.gz: training set labels (28881 bytes)</code><br><code>t10k-images-idx3-ubyte.gz: test set images (1648877 bytes)</code><br><code>t10k-labels-idx1-ubyte.gz: test set labels (4542 bytes)</code></p></blockquote><a id="more"></a><h3 id="CIFAR"><a href="#CIFAR" class="headerlink" title="CIFAR"></a>CIFAR</h3><h4 id="CIFAR-10"><a href="#CIFAR-10" class="headerlink" title="CIFAR-10"></a>CIFAR-10</h4><p>CIFAR-10包含<strong>10</strong>个类别，<strong>50000</strong>个训练图像，彩色图像大小：<strong>32x32</strong>，<strong>10000</strong>个测试图像。</p><p>该数据集可在<a href="http://www.cs.toronto.edu/~kriz/cifar.html" target="_blank" rel="external">http://www.cs.toronto.edu/~kriz/cifar.html</a> 获取，主要包含以下类别：</p><p><img src="https://upload-images.jianshu.io/upload_images/669323-4c48aff1693a078d?imageMogr2/auto-orient/strip%7CimageView2/2/w/580" alt=""></p><h4 id="CIFAR-100"><a href="#CIFAR-100" class="headerlink" title="CIFAR-100"></a>CIFAR-100</h4><p>CIFAR-100与CIFAR-10类似，包含<strong>100</strong>个类，每类有<strong>600</strong>张图片，其中<strong>500</strong>张用于训练，<strong>100</strong>张用于测试；这<strong>100</strong>个类分组成<strong>20</strong>个超类。图像类别均有明确标注。</p><div class="table-container"><table><thead><tr><th style="text-align:left">Superclass</th><th>Classes</th></tr></thead><tbody><tr><td style="text-align:left">aquatic mammals</td><td>beaver, dolphin, otter, seal, whale</td></tr><tr><td style="text-align:left">fish</td><td>aquarium fish, flatfish, ray, shark, trout</td></tr><tr><td style="text-align:left">flowers</td><td>orchids, poppies, roses, sunflowers, tulips</td></tr><tr><td style="text-align:left">food containers</td><td>bottles, bowls, cans, cups, plates</td></tr><tr><td style="text-align:left">fruit and vegetables</td><td>apples, mushrooms, oranges, pears, sweet peppers</td></tr><tr><td style="text-align:left">household electrical devices</td><td>clock, computer keyboard, lamp, telephone, television</td></tr><tr><td style="text-align:left">household furniture</td><td>bed, chair, couch, table, wardrobe</td></tr><tr><td style="text-align:left">insects</td><td>bee, beetle, butterfly, caterpillar, cockroach</td></tr><tr><td style="text-align:left">large carnivores</td><td>bear, leopard, lion, tiger, wolf</td></tr><tr><td style="text-align:left">large man-made outdoor things</td><td>bridge, castle, house, road, skyscraper</td></tr><tr><td style="text-align:left">large natural outdoor scenes</td><td>cloud, forest, mountain, plain, sea</td></tr><tr><td style="text-align:left">large omnivores and herbivores</td><td>camel, cattle, chimpanzee, elephant, kangaroo</td></tr><tr><td style="text-align:left">medium-sized mammals</td><td>fox, porcupine, possum, raccoon, skunk</td></tr><tr><td style="text-align:left">non-insect invertebrates</td><td>crab, lobster, snail, spider, worm</td></tr><tr><td style="text-align:left">people</td><td>baby, boy, girl, man, woman</td></tr><tr><td style="text-align:left">reptiles</td><td>crocodile, dinosaur, lizard, snake, turtle</td></tr><tr><td style="text-align:left">small mammals</td><td>hamster, mouse, rabbit, shrew, squirrel</td></tr><tr><td style="text-align:left">trees</td><td>maple, oak, palm, pine, willow</td></tr><tr><td style="text-align:left">vehicles 1</td><td>bicycle, bus, motorcycle, pickup truck, train</td></tr><tr><td style="text-align:left">vehicles 2</td><td>lawn-mower, rocket, streetcar, tank, tractor</td></tr></tbody></table></div><h3 id="Imagenet"><a href="#Imagenet" class="headerlink" title="Imagenet"></a>Imagenet</h3><p>MNIST将初学者领进了深度学习领域，而Imagenet数据集对深度学习的浪潮起了巨大的推动作用。深度学习大牛Hinton在2012年发表的论文《ImageNet Classification with Deep Convolutional Neural Networks》在计算机视觉领域带来了一场“革命”，此论文的工作正是基于Imagenet数据集。</p><p><img src="https://upload-images.jianshu.io/upload_images/669323-8155cd4456504709?imageMogr2/auto-orient/strip%7CimageView2/2/w/640" alt=""></p><p>Imagenet数据集有<strong>1400多万</strong>幅图片，涵盖<strong>2万</strong>多个类别；其中有超过百万的图片有明确的类别标注和图像中物体位置的标注，具体信息如下：</p><ul><li>Total number of non-empty synsets: 21841</li><li>Total number of images: 14,197,122</li><li>Number of images with bounding box annotations: 1,034,908</li><li>Number of synsets with SIFT features: 1000</li><li>Number of images with SIFT features: 1.2 million</li></ul><p>Imagenet数据集是目前深度学习图像领域应用得非常多的一个领域，关于图像分类、定位、检测等研究工作大多基于此数据集展开。Imagenet数据集文档详细，有专门的团队维护，使用非常方便，在计算机视觉领域研究论文中应用非常广，几乎成为了目前深度学习图像领域算法性能检验的“标准”数据集。</p><h2 id="自然语言处理"><a href="#自然语言处理" class="headerlink" title="自然语言处理"></a>自然语言处理</h2><h3 id="语言模型"><a href="#语言模型" class="headerlink" title="语言模型"></a>语言模型</h3><h4 id="Penn-Treebank-Dataset（PTB）"><a href="#Penn-Treebank-Dataset（PTB）" class="headerlink" title="Penn Treebank Dataset（PTB）"></a>Penn Treebank Dataset（PTB）</h4><p>PTB（Penn Treebank Dataset）文本数据集是语言模型学习中目前最广泛使用的数据集。语言建模(LM)是自然语言处理和自然理解模型任务的一个核心任务，能对句子结构分步进行表示，它展示的不仅是语言的复杂内容，比如语法结构，还能提取语料库可能包含的一定数量信息。PTB是一个较小的数据集，PTB数据集由华尔街日报的文章组成，包含<unk>字符，<strong>929k</strong>个训练tokens，词汇量为<strong>10k</strong>。</unk></p><h4 id="wikitext2"><a href="#wikitext2" class="headerlink" title="wikitext2"></a>wikitext2</h4><p>wikitext2数据集源自维基百科文章，包含2M训练tokens，词汇量为33k。PTB数据集一样wikitext2数据集包含非混洗文档，因此需要模型来捕获句间依赖性才能很好地执行。</p><h4 id="text8-amp-amp-wikitext103"><a href="#text8-amp-amp-wikitext103" class="headerlink" title="text8&&wikitext103"></a>text8&&wikitext103</h4><p>text8数据集包含17M的训练标记，词汇量为44k字；而wikitext103数据集的训练集大小为103M，词汇量为267k字。这是两个中等规模的数据集。</p><h4 id="LAMBADA"><a href="#LAMBADA" class="headerlink" title="LAMBADA"></a>LAMBADA</h4><p>LAMBADA 数据集是从小说中提取的短段落的数据集。$lambada $数据集包含大约200M tokens,词汇量大小为93215。</p><h3 id="文本分类"><a href="#文本分类" class="headerlink" title="文本分类"></a>文本分类</h3><h4 id="IMDB"><a href="#IMDB" class="headerlink" title="IMDB"></a>IMDB</h4><p>这个数据包括3个部分，训练集，测试集和未标记的数据集。训练集和测试集用于训练和测试文本分类模型，未标记的数据集用于训练词向量。IMDB电影数据集含有50000个电影评论，分为正反两类。训练集包中包含25000个正反类评论用于训练，测试集中包含25000个评论用于测试。</p><h4 id="MR"><a href="#MR" class="headerlink" title="MR"></a>MR</h4><p>MR数据集是“电影评论”中的情绪极性数据集。主要包括：</p><ul><li>document-level: polarity dataset v2.0: 1000 positive and 1000 negative processed reviews.</li><li>sentence-level: sentence polarity dataset v1.0: 5331 positive and 5331 negative processed sentences/snippets.</li><li>Sentiment-scale datasets: scale dataset v1.0: a collection of documents whose labels come from a rating scale.</li><li>Subjectivity dataset v1.0: 5000 subjective and 5000 objective processed sentences.</li></ul><h4 id="Google-Snippets"><a href="#Google-Snippets" class="headerlink" title="Google Snippets"></a>Google Snippets</h4><p>Google Snippets数据集包括10060个训练样本和2280个测试样本，分为8个类。平均下来每个snippet有18.07个词。</p><h4 id="TREC"><a href="#TREC" class="headerlink" title="TREC"></a>TREC</h4><p>TREC数据集包括6个不同的问题类型，训练集有5452个标注了的问题，测试集有500个问题。</p>]]></content>
<summary type="html">
<p>深度学习在计算机视觉领域取得了十分重大的突破，许多研究也是如雨后春笋般。而模型的训练离不开数据集的支持，因此有必要对常用的数据集进行了解。接下来主要对计算机视觉和自然语言处理这两个领域的常用数据集进行介绍。</p>
<h2 id="计算机视觉"><a href="#计算机视觉" class="headerlink" title="计算机视觉"></a>计算机视觉</h2><h3 id="MNIST"><a href="#MNIST" class="headerlink" title="MNIST"></a>MNIST</h3><p>MNIST数据集被称为深度学习领域的“Hello World!”，入门必备！它有<strong>60000</strong>个训练样本集和<strong>10000</strong>个测试样本集，每个样本图像的宽高为<strong>28*28</strong>。此数据集是以二进制存储的，不能直接以图像格式查看，不过很容易找到将其转换成图像格式的工具。</p>
<p>该数据集可在<a href="http://yann.lecun.com/exdb/mnist/" target="_blank" rel="external">http://yann.lecun.com/exdb/mnist/</a> 获取，主要包含以下四部分：</p>
<blockquote>
<p><code>train-images-idx3-ubyte.gz: training set images (9912422 bytes)</code><br><code>train-labels-idx1-ubyte.gz: training set labels (28881 bytes)</code><br><code>t10k-images-idx3-ubyte.gz: test set images (1648877 bytes)</code><br><code>t10k-labels-idx1-ubyte.gz: test set labels (4542 bytes)</code></p>
</blockquote>
</summary>
<category term="工具资源" scheme="http://yoursite.com/categories/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90/"/>
<category term="工具资源，DL数据集" scheme="http://yoursite.com/tags/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90%EF%BC%8CDL%E6%95%B0%E6%8D%AE%E9%9B%86/"/>
</entry>
<entry>
<title>二维数组中的查找</title>
<link href="http://yoursite.com/2018/01/22/findinsortedmatrix/"/>
<id>http://yoursite.com/2018/01/22/findinsortedmatrix/</id>
<published>2018-01-22T11:39:25.000Z</published>
<updated>2018-01-27T04:04:50.577Z</updated>
<content type="html"><![CDATA[<h3 id="二维数组中的查找"><a href="#二维数组中的查找" class="headerlink" title="二维数组中的查找"></a>二维数组中的查找</h3><p>题目：在一个二维数组中，每一行都按照从左到右递增的顺序排序，每一列都按照从上到下递增的顺序排序。请完成一个函数，输入这样的一个二维数组和一个整数，判断数组中是否含有该整数。</p><p><strong>思路</strong>:首先选取数组右上角的数字。如果该数字等于要查找的数字，则查找过程结束；如果该数字大于要查找的数字，则剔除这个数字所在的列；如果该数字小于要查找的数字，则剔除这个数字所在的行。</p><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div></pre></td><td class="code"><pre><div class="line">1 2 8 9 1 2 8 1 2</div><div class="line">2 4 9 12 2 4 9 2 4 2 4</div><div class="line">4 7 10 13 4 7 10 4 7 4 7 4 7</div><div class="line">6 8 11 15 6 8 11 7 8 7 8 7 8</div></pre></td></tr></table></figure><a id="more"></a><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><iostream></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><cstdio></span></span></div><div class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">bool</span> <span class="title">Find</span><span class="params">(<span class="keyword">int</span>* matrix, <span class="keyword">int</span> rows, <span class="keyword">int</span> columns, <span class="keyword">int</span> number)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">bool</span> found = <span class="literal">false</span>;</div><div class="line"></div><div class="line"> <span class="keyword">if</span>(matrix != <span class="literal">nullptr</span> && rows><span class="number">0</span> && columns><span class="number">0</span>)</div><div class="line"> {</div><div class="line"> <span class="keyword">int</span> row = <span class="number">0</span>;</div><div class="line"> <span class="keyword">int</span> column = columns<span class="number">-1</span>;</div><div class="line"> <span class="keyword">while</span>(row<rows && column>=<span class="number">0</span>)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(matrix[row*columns + column] == number)</div><div class="line"> {</div><div class="line"> found = <span class="literal">true</span>;</div><div class="line"> <span class="keyword">break</span>;</div><div class="line"> }</div><div class="line"> <span class="keyword">else</span> <span class="keyword">if</span>(matrix[row*columns + column] > number)</div><div class="line"> {</div><div class="line"> --column;</div><div class="line"> }</div><div class="line"> <span class="keyword">else</span></div><div class="line"> ++row;</div><div class="line"> }</div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> found;</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div></pre></td><td class="code"><pre><div class="line"><span class="comment">// ====================测试代码====================</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Test</span><span class="params">(<span class="keyword">char</span>* testname, <span class="keyword">int</span>* matrix, <span class="keyword">int</span> rows, <span class="keyword">int</span> columns, <span class="keyword">int</span> number, <span class="keyword">bool</span> expected)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(testname != <span class="literal">nullptr</span>)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"%s begins: "</span>, testname);</div><div class="line"> <span class="keyword">bool</span> result = Find(matrix, rows, columns, number);</div><div class="line"> <span class="keyword">if</span>(result == expected)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Passed.\n"</span>);</div><div class="line"> <span class="keyword">else</span></div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Failed.\n"</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 1 2 8 9</span></div><div class="line"><span class="comment">// 2 4 9 12</span></div><div class="line"><span class="comment">// 4 7 10 13</span></div><div class="line"><span class="comment">// 6 8 11 15</span></div><div class="line"><span class="comment">// 要查找的数在数组中</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test1</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> matrix[<span class="number">4</span>][<span class="number">4</span>] = {{<span class="number">1</span>, <span class="number">2</span>, <span class="number">8</span>, <span class="number">9</span>}, {<span class="number">2</span>, <span class="number">4</span>, <span class="number">9</span>, <span class="number">12</span>}, {<span class="number">4</span>, <span class="number">7</span>, <span class="number">10</span>, <span class="number">13</span>}, {<span class="number">6</span>, <span class="number">8</span>, <span class="number">11</span>, <span class="number">15</span>}};</div><div class="line"> Test(<span class="string">"test1"</span>, (<span class="keyword">int</span>*)matrix, <span class="number">4</span>, <span class="number">4</span>, <span class="number">7</span>, <span class="literal">true</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test2</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> Test(<span class="string">"test2"</span>, <span class="literal">nullptr</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">1</span>, <span class="literal">false</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> test1();</div><div class="line"> test2();</div><div class="line"></div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">}</div></pre></td></tr></table></figure>]]></content>
<summary type="html">
<h3 id="二维数组中的查找"><a href="#二维数组中的查找" class="headerlink" title="二维数组中的查找"></a>二维数组中的查找</h3><p>题目：在一个二维数组中，每一行都按照从左到右递增的顺序排序，每一列都按照从上到下递增的顺序排序。请完成一个函数，输入这样的一个二维数组和一个整数，判断数组中是否含有该整数。</p>
<p><strong>思路</strong>:首先选取数组右上角的数字。如果该数字等于要查找的数字，则查找过程结束；如果该数字大于要查找的数字，则剔除这个数字所在的列；如果该数字小于要查找的数字，则剔除这个数字所在的行。</p>
<figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div></pre></td><td class="code"><pre><div class="line">1 2 8 9 1 2 8 1 2</div><div class="line">2 4 9 12 2 4 9 2 4 2 4</div><div class="line">4 7 10 13 4 7 10 4 7 4 7 4 7</div><div class="line">6 8 11 15 6 8 11 7 8 7 8 7 8</div></pre></td></tr></table></figure>
</summary>
<category term="编程" scheme="http://yoursite.com/categories/%E7%BC%96%E7%A8%8B/"/>
<category term="编程，" scheme="http://yoursite.com/tags/%E7%BC%96%E7%A8%8B%EF%BC%8C/"/>
</entry>
<entry>
<title>数组找出重复的数字</title>
<link href="http://yoursite.com/2018/01/20/findduplicationNoEdit/"/>
<id>http://yoursite.com/2018/01/20/findduplicationNoEdit/</id>
<published>2018-01-20T13:17:35.000Z</published>
<updated>2018-01-27T04:03:46.792Z</updated>
<content type="html"><![CDATA[<h3 id="面试题：找出数组中重复的数字"><a href="#面试题：找出数组中重复的数字" class="headerlink" title="面试题：找出数组中重复的数字"></a>面试题：找出数组中重复的数字</h3><p> 题目：在一个长度为n的数组里的所有数字都在0到n-1的范围内。数组中某些数字是重复的，但不知道有几个数字重复了，也不知道每个数字重复了几次。请找出数组中任意一个重复的数字。例如，如果输入长度为7的数组{2, 3, 1, 0, 2, 5, 3}，那么对应的输出是重复的数字2或者3。</p><p><strong>思路</strong>：排序一个长度为n的数组需要O(nlogn)的时间，我们选择利用哈希表来解决这个问题。从头到尾顺序扫描数组的每个数字，每扫描到一个数字的时候，都可以用O(1)的时间来判断哈希表里是否包含了该数字。如果哈希表没有这个数字，就把它加入哈希表。如果哈希表已经存在该数字，就找到一个重复数字。这个算法的时间复杂度是O(n),他是以创建一个大小O(n)的哈希表为代价。现在我们重排这个数组，从头到尾依次扫描这个数组。当扫描到下标为i的数组时，首先比较这个数字（用m表示）是不是等于i。如果是，则扫描下一个数字；如果不是，则再拿它和第m个数字进行比较。如果他和地ｍ个数字相等，就找到一个重复的数字；如果他和第m个数字不相等，就把第i个数字和地ｍ个数字作交换，把Ｍ放到属于他的位置。重复比较交换这个过程，知道发现一个重复数字。</p><a id="more"></a><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><cstdio></span></span></div><div class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</div><div class="line"></div><div class="line"><span class="comment">// 参数:</span></div><div class="line"><span class="comment">// numbers: 一个整数数组</span></div><div class="line"><span class="comment">// length: 数组的长度</span></div><div class="line"><span class="comment">// duplication: (输出) 数组中的一个重复的数字</span></div><div class="line"><span class="comment">// 返回值:</span></div><div class="line"><span class="comment">// true - 输入有效，并且数组中存在重复的数字</span></div><div class="line"><span class="comment">// false - 输入无效，或者数组中没有重复的数字</span></div><div class="line"><span class="function"><span class="keyword">bool</span> <span class="title">duplicate</span><span class="params">(<span class="keyword">int</span> numbers[], <span class="keyword">int</span> length, <span class="keyword">int</span>* duplication)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(numbers == <span class="literal">nullptr</span> || length<=<span class="number">0</span>)</div><div class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</div><div class="line"></div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>; i<length; ++i)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(numbers[i]<<span class="number">0</span> || numbers[i]> length<span class="number">-1</span>)</div><div class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</div><div class="line"> }</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>; i<length; ++i)</div><div class="line"> {</div><div class="line"> <span class="keyword">while</span>(numbers[i] != i)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(numbers[i] == numbers[numbers[i]])</div><div class="line"> {</div><div class="line"> *duplication = numbers[i];</div><div class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</div><div class="line"> }</div><div class="line"></div><div class="line"> <span class="keyword">int</span> temp = numbers[i];</div><div class="line"> numbers[i] = numbers[temp];</div><div class="line"> numbers[temp] = temp;</div><div class="line"> }</div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</div><div class="line">}</div></pre></td></tr></table></figure><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div><div class="line">42</div><div class="line">43</div><div class="line">44</div><div class="line">45</div><div class="line">46</div><div class="line">47</div><div class="line">48</div><div class="line">49</div><div class="line">50</div><div class="line">51</div><div class="line">52</div><div class="line">53</div><div class="line">54</div><div class="line">55</div><div class="line">56</div><div class="line">57</div><div class="line">58</div><div class="line">59</div><div class="line">60</div><div class="line">61</div><div class="line">62</div><div class="line">63</div><div class="line">64</div><div class="line">65</div><div class="line">66</div><div class="line">67</div><div class="line">68</div><div class="line">69</div><div class="line">70</div><div class="line">71</div><div class="line">72</div><div class="line">73</div><div class="line">74</div><div class="line">75</div><div class="line">76</div></pre></td><td class="code"><pre><div class="line"><span class="comment">// ====================测试代码====================</span></div><div class="line"><span class="function"><span class="keyword">bool</span> <span class="title">contains</span><span class="params">(<span class="keyword">int</span> <span class="built_in">array</span>[], <span class="keyword">int</span> length, <span class="keyword">int</span> number)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">0</span>; i < length; ++i)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(<span class="built_in">array</span>[i] == number)</div><div class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</div><div class="line"> }</div><div class="line"></div><div class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test</span><span class="params">(<span class="keyword">char</span>* testName, <span class="keyword">int</span> numbers[], <span class="keyword">int</span> lengthNumbers, <span class="keyword">int</span> expected[], <span class="keyword">int</span> expectedExpected, <span class="keyword">bool</span> validArgument)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"%s begins: "</span>, testName);</div><div class="line"></div><div class="line"> <span class="keyword">int</span> duplication;</div><div class="line"> <span class="keyword">bool</span> validInput = duplicate(numbers, lengthNumbers, &duplication);</div><div class="line"></div><div class="line"> <span class="keyword">if</span>(validArgument == validInput)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(validArgument)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(contains(expected, expectedExpected, duplication))</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Passed.\n"</span>);</div><div class="line"> <span class="keyword">else</span></div><div class="line"> <span class="built_in">printf</span>(<span class="string">"FAILED.\n"</span>);</div><div class="line"> }</div><div class="line"> <span class="keyword">else</span></div><div class="line"> <span class="built_in">printf</span>(<span class="string">"Passed.\n"</span>);</div><div class="line"> }</div><div class="line"> <span class="keyword">else</span></div><div class="line"> <span class="built_in">printf</span>(<span class="string">"FAILED.\n"</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 重复的数字是数组中最小的数字</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test1</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> numbers[] = { <span class="number">2</span>, <span class="number">1</span>, <span class="number">3</span>, <span class="number">1</span>, <span class="number">4</span> };</div><div class="line"> <span class="keyword">int</span> duplications[] = { <span class="number">1</span> };</div><div class="line"> test(<span class="string">"test1"</span>, numbers, <span class="keyword">sizeof</span>(numbers) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), duplications, <span class="keyword">sizeof</span>(duplications) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), <span class="literal">true</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 重复的数字是数组中最大的数字</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test2</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> numbers[] = { <span class="number">2</span>, <span class="number">4</span>, <span class="number">3</span>, <span class="number">1</span>, <span class="number">4</span> };</div><div class="line"> <span class="keyword">int</span> duplications[] = { <span class="number">4</span> };</div><div class="line"> test(<span class="string">"test2"</span>, numbers, <span class="keyword">sizeof</span>(numbers) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), duplications, <span class="keyword">sizeof</span>(duplications) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), <span class="literal">true</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 数组中存在多个重复的数字</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test3</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> numbers[] = { <span class="number">2</span>, <span class="number">4</span>, <span class="number">2</span>, <span class="number">1</span>, <span class="number">4</span> };</div><div class="line"> <span class="keyword">int</span> duplications[] = { <span class="number">2</span>, <span class="number">4</span> };</div><div class="line"> test(<span class="string">"test3"</span>, numbers, <span class="keyword">sizeof</span>(numbers) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), duplications, <span class="keyword">sizeof</span>(duplications) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), <span class="literal">true</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 数组中不存在重复的数字</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test4</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> numbers[] = { <span class="number">0</span>, <span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">4</span> };</div><div class="line"> <span class="keyword">int</span> duplications[] = { <span class="number">-1</span> };</div><div class="line"> test(<span class="string">"test4"</span>, numbers, <span class="keyword">sizeof</span>(numbers) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), duplications, <span class="keyword">sizeof</span>(duplications) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), <span class="literal">false</span>);</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> test1();</div><div class="line"> test2();</div><div class="line"> test3();</div><div class="line"> test4();</div><div class="line"></div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">}</div></pre></td></tr></table></figure><h3 id="面试题：不修改数组找出重复的数字"><a href="#面试题：不修改数组找出重复的数字" class="headerlink" title="面试题：不修改数组找出重复的数字"></a>面试题：不修改数组找出重复的数字</h3><p> 在一个长度为n+1的数组里的所有数字都在1到n的范围内，所以数组中至少有一个数字是重复的。请找出数组中任意一个重复的数字，但不能修改输入的数组。例如，如果输入长度为8的数组{2, 3, 5, 4, 3, 2, 6, 7}，那么对应的输出是重复的数字2或者3。</p><p><strong>思路</strong>：如果没有重复的数字，那么1~n的范围内只有n个数字。有余数组里包含n个数字，所以一定包含了重复的数字。我们把从1~n的数字把中间的数字m分为两部分，前一半为1~m，后一半为m+1~n．如果1~m的数字的数目超过m，那么这一半的区间里一定包含重复数字；否则另外一半m+1~n的区间里一定包含重复的数字。我么可以继续把包含重复的数字的区间一分为二，直到找到一个重复的数字。</p><!-- more --><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div 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class="line">121</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><iostream></span></span></div><div class="line"></div><div class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">countRange</span><span class="params">(<span class="keyword">const</span> <span class="keyword">int</span>* numbers, <span class="keyword">int</span> length, <span class="keyword">int</span> start, <span class="keyword">int</span> end)</span></span>;</div><div class="line"></div><div class="line"><span class="comment">// 参数:</span></div><div class="line"><span class="comment">// numbers: 一个整数数组</span></div><div class="line"><span class="comment">// length: 数组的长度</span></div><div class="line"><span class="comment">// 返回值:</span></div><div class="line"><span class="comment">// 正数 - 输入有效，并且数组中存在重复的数字，返回值为重复的数字</span></div><div class="line"><span class="comment">// 负数 - 输入无效，或者数组中没有重复的数字</span></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">getDuplication</span><span class="params">(<span class="keyword">const</span> <span class="keyword">int</span>* numbers, <span class="keyword">int</span> length)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(numbers == <span class="literal">nullptr</span> || length <= <span class="number">0</span>)</div><div class="line"> <span class="keyword">return</span> <span class="number">-1</span>;</div><div class="line"></div><div class="line"> <span class="keyword">int</span> start = <span class="number">1</span>;</div><div class="line"> <span class="keyword">int</span> end = length <span class="number">-1</span>;</div><div class="line"></div><div class="line"> <span class="keyword">while</span>(start <= end)</div><div class="line"> {</div><div class="line"> <span class="keyword">int</span> middle = ((end - start) >> <span class="number">1</span>) + start;</div><div class="line"> <span class="keyword">int</span> count = countRange(numbers, length, start, middle);</div><div class="line"></div><div class="line"> <span class="keyword">if</span>(start == end)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(count > <span class="number">1</span>)</div><div class="line"> <span class="keyword">return</span> start;</div><div class="line"> <span class="keyword">else</span></div><div class="line"> <span class="keyword">break</span>;</div><div class="line"> }</div><div class="line"></div><div class="line"> <span class="keyword">if</span>((middle-start+<span class="number">1</span>) < count)</div><div class="line"> {</div><div class="line"> end = middle;</div><div class="line"> }</div><div class="line"> <span class="keyword">else</span></div><div class="line"> start = middle+<span class="number">1</span>;</div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> <span class="number">-1</span>;</div><div class="line"></div><div class="line">}</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">countRange</span><span class="params">(<span class="keyword">const</span> <span class="keyword">int</span>* numbers, <span class="keyword">int</span> length, <span class="keyword">int</span> start, <span class="keyword">int</span> end)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(numbers == <span class="literal">nullptr</span>)</div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line"> <span class="keyword">int</span> count = <span class="number">0</span>;</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>; i<length; i++)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(numbers[i]>=start && numbers[i]<=end)</div><div class="line"> ++count;</div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> count;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// ====================测试代码====================</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test</span><span class="params">(<span class="keyword">const</span> <span class="keyword">char</span>* testName, <span class="keyword">int</span>* numbers, <span class="keyword">int</span> length, <span class="keyword">int</span>* duplications, <span class="keyword">int</span> dupLength)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> result = getDuplication(numbers, length);</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">0</span>; i < dupLength; ++i)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(result == duplications[i])</div><div class="line"> {</div><div class="line"> <span class="built_in">std</span>::<span class="built_in">cout</span> << testName << <span class="string">" passed."</span> << <span class="built_in">std</span>::<span class="built_in">endl</span>;</div><div class="line"> <span class="keyword">return</span>;</div><div class="line"> }</div><div class="line"> }</div><div class="line"> <span class="built_in">std</span>::<span class="built_in">cout</span> << testName << <span class="string">" FAILED."</span> << <span class="built_in">std</span>::<span class="built_in">endl</span>;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 一个重复的数字</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test1</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> numbers[] = { <span class="number">3</span>, <span class="number">2</span>, <span class="number">1</span>, <span class="number">4</span>, <span class="number">4</span>, <span class="number">5</span>, <span class="number">6</span>, <span class="number">7</span> };</div><div class="line"> <span class="keyword">int</span> duplications[] = { <span class="number">4</span> };</div><div class="line"> test(<span class="string">"test1"</span>, numbers, <span class="keyword">sizeof</span>(numbers) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), duplications, <span class="keyword">sizeof</span>(duplications) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>));</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 多个重复的数字</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test2</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> numbers[] = { <span class="number">2</span>, <span class="number">3</span>, <span class="number">5</span>, <span class="number">4</span>, <span class="number">3</span>, <span class="number">2</span>, <span class="number">6</span>, <span class="number">7</span> };</div><div class="line"> <span class="keyword">int</span> duplications[] = { <span class="number">2</span>, <span class="number">3</span> };</div><div class="line"> test(<span class="string">"test2"</span>, numbers, <span class="keyword">sizeof</span>(numbers) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), duplications, <span class="keyword">sizeof</span>(duplications) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>));</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 数组中只有两个数字</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test3</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> numbers[] = { <span class="number">1</span>, <span class="number">1</span> };</div><div class="line"> <span class="keyword">int</span> duplications[] = { <span class="number">1</span> };</div><div class="line"> test(<span class="string">"test3"</span>, numbers, <span class="keyword">sizeof</span>(numbers) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), duplications, <span class="keyword">sizeof</span>(duplications) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>));</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 数组中没有重复的数字</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test4</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> numbers[] = { <span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>, <span class="number">4</span>, <span class="number">5</span> };</div><div class="line"> <span class="keyword">int</span> duplications[] = { <span class="number">1</span> };</div><div class="line"> test(<span class="string">"test4"</span>, numbers, <span class="keyword">sizeof</span>(numbers) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), duplications, <span class="keyword">sizeof</span>(duplications) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>));</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">// 无效的输入</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test5</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span>* numbers = <span class="literal">nullptr</span>;</div><div class="line"> <span class="keyword">int</span> duplications[] = { <span class="number">1</span> };</div><div class="line"> test(<span class="string">"test5"</span>, numbers, <span class="keyword">sizeof</span>(numbers) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>), duplications, <span class="keyword">sizeof</span>(duplications) / <span class="keyword">sizeof</span>(<span class="keyword">int</span>));</div><div class="line"></div><div class="line">}</div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> test1();</div><div class="line"> test2();</div><div class="line"> test3();</div><div class="line"> test4();</div><div class="line"> test5();</div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">}</div></pre></td></tr></table></figure>]]></content>
<summary type="html">
<h3 id="面试题：找出数组中重复的数字"><a href="#面试题：找出数组中重复的数字" class="headerlink" title="面试题：找出数组中重复的数字"></a>面试题：找出数组中重复的数字</h3><p> 题目：在一个长度为n的数组里的所有数字都在0到n-1的范围内。数组中某些数字是重复的，但不知道有几个数字重复了，也不知道每个数字重复了几次。请找出数组中任意一个重复的数字。例如，如果输入长度为7的数组{2, 3, 1, 0, 2, 5, 3}，那么对应的输出是重复的数字2或者3。</p>
<p><strong>思路</strong>：排序一个长度为n的数组需要O(nlogn)的时间，我们选择利用哈希表来解决这个问题。从头到尾顺序扫描数组的每个数字，每扫描到一个数字的时候，都可以用O(1)的时间来判断哈希表里是否包含了该数字。如果哈希表没有这个数字，就把它加入哈希表。如果哈希表已经存在该数字，就找到一个重复数字。这个算法的时间复杂度是O(n),他是以创建一个大小O(n)的哈希表为代价。现在我们重排这个数组，从头到尾依次扫描这个数组。当扫描到下标为i的数组时，首先比较这个数字（用m表示）是不是等于i。如果是，则扫描下一个数字；如果不是，则再拿它和第m个数字进行比较。如果他和地ｍ个数字相等，就找到一个重复的数字；如果他和第m个数字不相等，就把第i个数字和地ｍ个数字作交换，把Ｍ放到属于他的位置。重复比较交换这个过程，知道发现一个重复数字。</p>
</summary>
<category term="编程" scheme="http://yoursite.com/categories/%E7%BC%96%E7%A8%8B/"/>
<category term="编程，数组" scheme="http://yoursite.com/tags/%E7%BC%96%E7%A8%8B%EF%BC%8C%E6%95%B0%E7%BB%84/"/>
</entry>
<entry>
<title>Pytorch</title>
<link href="http://yoursite.com/2018/01/16/torch/"/>
<id>http://yoursite.com/2018/01/16/torch/</id>
<published>2018-01-16T05:57:07.000Z</published>
<updated>2018-01-19T13:25:49.201Z</updated>
<content type="html"><![CDATA[<h3 id="Torch"><a href="#Torch" class="headerlink" title="Torch"></a>Torch</h3><p><code>torch</code>包含了多维的数据结构以及基于其上的数学运算。它提供了多种实用工具，具有CUDA对应的实现</p><h2 id="张量-Tensors"><a href="#张量-Tensors" class="headerlink" title="张量 Tensors"></a>张量 Tensors</h2><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.is_tensor(obj)</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">b = np.random.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">torch.is_tensor(a)</div><div class="line">Out[<span class="number">1</span>]: <span class="keyword">True</span></div><div class="line">torch.is_tensor(b)</div><div class="line">Out[<span class="number">2</span>]: <span class="keyword">False</span></div></pre></td></tr></table></figure><p>判断是否为张量，如果是pytorch张量，则返回True</p><a id="more"></a><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.is_storage(obj)</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">x = torch.FloatTensor(a)</div><div class="line">y = x.storage()</div><div class="line">torch.is_storage(x)</div><div class="line">Out[<span class="number">1</span>]: <span class="keyword">False</span></div><div class="line">torch.is_storage(y)</div><div class="line">Out[<span class="number">2</span>]: <span class="keyword">True</span></div></pre></td></tr></table></figure><p>判断是否为pytorch Storage，如何是，则返回True</p><figure class="highlight"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.numel(input)->int</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">torch.numel(a)</div><div class="line">Out[<span class="number">1</span>]: <span class="number">12</span></div></pre></td></tr></table></figure><p>返回<code>input</code> 张量中的元素个数 参数: input (<a href="http://pytorch.org/docs/tensors.html#torch.Tensor" target="_blank" rel="external">Tensor</a>) – 输入张量</p><h2 id="创建操作-Creation-Ops"><a href="#创建操作-Creation-Ops" class="headerlink" title="创建操作 Creation Ops"></a>创建操作 Creation Ops</h2><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.eye(n, m=<span class="keyword">None</span>, out=<span class="keyword">None</span>)</div></pre></td></tr></table></figure><p>参数: </p><ul><li><code>n</code> (int) – 行数</li><li><code>m</code> (int, 可选) – 列数.如果为None,则默认为<em>n</em> </li><li><code>out</code> (Tensor,可选) - 输出张量</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div></pre></td><td class="code"><pre><div class="line">torch.eye(<span class="number">3</span>)</div><div class="line">Out[<span class="number">1</span>]: [torch.FloatTensor of size <span class="number">3</span>x3]</div><div class="line"> </div><div class="line">torch.eye(<span class="number">3</span>, m=<span class="number">4</span>)</div><div class="line">torch.eye(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">Out[<span class="number">2</span>]:</div><div class="line"><span class="number">1</span> <span class="number">0</span> <span class="number">0</span> <span class="number">0</span></div><div class="line"><span class="number">0</span> <span class="number">1</span> <span class="number">0</span> <span class="number">0</span></div><div class="line"><span class="number">0</span> <span class="number">0</span> <span class="number">1</span> <span class="number">0</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x4]</div><div class="line"></div><div class="line">torch.eye(<span class="number">3</span>,<span class="number">3</span>,out=torch.LongTensor())</div><div class="line">Out[<span class="number">3</span>]:[torch.LongTensor of size <span class="number">3</span>x4]</div></pre></td></tr></table></figure><p>返回一个2维张量，对角线数字为1，其它位置为0</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.from_numpy(ndarray) → Tensor</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div></pre></td><td class="code"><pre><div class="line">x = np.array([<span class="number">1</span>,<span class="number">2</span>,<span class="number">3</span>])</div><div class="line">torch.from_numpy(x)</div><div class="line">Out[<span class="number">1</span>]: [torch.LongTensor of size <span class="number">3</span>]</div><div class="line">x</div><div class="line">Out[<span class="number">13</span>]: array([<span class="number">1</span>, <span class="number">2</span>, <span class="number">3</span>])</div></pre></td></tr></table></figure><p>将<code>numpy.ndarray</code>转换为<code>Tensor</code>。返回的张量tensor和numpy的ndarray共享一个内存空间。修改一个会导致另外一个也被修改。返回的张量不能调整大小。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.linspace(start, end, steps=<span class="number">100</span>, ut=<span class="keyword">None</span>) → Tensor</div></pre></td></tr></table></figure><p>参数: </p><ul><li><code>start</code> (float) – 点集的开始值</li><li><code>end</code> (float) – 点集的最终值</li><li><code>steps</code> (int) - 在<code>start</code>和<code>end</code>之间的采样数</li><li><code>out (Tensor, 可选的)</code> – 结果张量</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div></pre></td><td class="code"><pre><div class="line">torch.linspace(<span class="number">1</span>, <span class="number">10</span>, <span class="number">4</span>)</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"> <span class="number">1</span></div><div class="line"> <span class="number">4</span></div><div class="line"> <span class="number">7</span></div><div class="line"> <span class="number">10</span></div><div class="line">[torch.FloatTensor of size <span class="number">4</span>]</div></pre></td></tr></table></figure><p>返回start和end之间长度为<code>steps</code>的一维张量</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.ones(*sizes, out=<span class="keyword">None</span>) → Tensor</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">m = a.size()</div><div class="line">torch.ones(*m)</div><div class="line">Out[<span class="number">1</span>]:</div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x4]</div></pre></td></tr></table></figure><p>返回一个全为1的张量，形状由可变参数<code>sizes</code>定义。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.randperm(n, out=<span class="keyword">None</span>) → LongTensor</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div></pre></td><td class="code"><pre><div class="line">torch.randperm(<span class="number">3</span>)</div><div class="line">Out[<span class="number">25</span>]: </div><div class="line"> <span class="number">1</span></div><div class="line"> <span class="number">2</span></div><div class="line"> <span class="number">0</span></div><div class="line">[torch.LongTensor of size <span class="number">3</span>]</div></pre></td></tr></table></figure><p>输入参数<code>n</code>，返回一个从<code>0</code> 到<code>n -1</code>的随机整数排列。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.arange(start, end, step=<span class="number">1</span>, out=<span class="keyword">None</span>) → Tensor</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div></pre></td><td class="code"><pre><div class="line">torch.arange(<span class="number">1</span>, <span class="number">10</span>, step=<span class="number">4</span>)</div><div class="line">Out[<span class="number">27</span>]: </div><div class="line"> <span class="number">1</span></div><div class="line"> <span class="number">5</span></div><div class="line"> <span class="number">9</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>]</div></pre></td></tr></table></figure><p>返回一个1维张量，长度为floor((end−start)/step),floor代表向下取整。包含从<code>start</code>到<code>end</code>，以<code>step</code>为步长的一组序列值(默认步长为1)。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.zeros(*sizes, out=<span class="keyword">None</span>) → Tensor</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">m = a.size()</div><div class="line">torch.zeros(*m)</div><div class="line">Out[<span class="number">1</span>]:</div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x4]</div></pre></td></tr></table></figure><p>返回一个全0的张量，形状由可变参数<code>sizes</code>定义。</p><h2 id="索引-切片-连接-变异操作"><a href="#索引-切片-连接-变异操作" class="headerlink" title="索引,切片,连接,变异操作"></a>索引,切片,连接,变异操作</h2><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.cat(seq, dim=0, out=None) → Tensor</div></pre></td></tr></table></figure><p>参数:</p><ul><li><code>seq</code>（Tensors的序列） - 可以是相同类型的Tensor的任何python序列。</li><li><code>dim</code>（int，可选） - 张量连接的尺寸</li><li><code>out</code>（Tensor，可选） - 输出参数</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">torch.cat((a, a, a),<span class="number">0</span>)</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line">[torch.FloatTensor of size <span class="number">9</span>x4]</div><div class="line"></div><div class="line">torch.cat((a, a, a),<span class="number">1</span>) & torch.cat((a, a, a),<span class="number">-1</span>)</div><div class="line">Out[<span class="number">2</span>]: </div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x12]</div></pre></td></tr></table></figure><p>在给定维度上对输入的张量序列<code>seq</code> 进行连接操作。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.chunk(tensor, chunks, dim=<span class="number">0</span>)</div></pre></td></tr></table></figure><p>参数:</p><ul><li><code>tensor</code> (Tensor) – 待分块的输入张量</li><li><code>chunks</code> (int) – 分块的个数</li><li><code>dim</code>(int) – 沿着此维度进行分块</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div></pre></td><td class="code"><pre><div class="line">b = torch.randn(<span class="number">3</span>,<span class="number">6</span>)</div><div class="line">torch.chunk(b, <span class="number">3</span>, <span class="number">0</span>)</div><div class="line">Out[<span class="number">46</span>]: </div><div class="line">(</div><div class="line"> <span class="number">-1.2120</span> <span class="number">0.0617</span> <span class="number">0.2106</span> <span class="number">-0.3776</span> <span class="number">-2.2615</span> <span class="number">1.2279</span></div><div class="line"> [torch.FloatTensor of size <span class="number">1</span>x6], </div><div class="line"> <span class="number">0.1425</span> <span class="number">1.3961</span> <span class="number">-0.6864</span> <span class="number">0.7581</span> <span class="number">0.5757</span> <span class="number">-0.7915</span></div><div class="line"> [torch.FloatTensor of size <span class="number">1</span>x6], </div><div class="line"> <span class="number">0.5075</span> <span class="number">-1.8589</span> <span class="number">-0.5447</span> <span class="number">-0.6180</span> <span class="number">0.2896</span> <span class="number">0.1451</span></div><div class="line"> [torch.FloatTensor of size <span class="number">1</span>x6])</div><div class="line"></div><div class="line">torch.chunk(b, <span class="number">3</span>, <span class="number">1</span>)</div><div class="line">Out[<span class="number">47</span>]: </div><div class="line">(</div><div class="line"> <span class="number">-1.2120</span> <span class="number">0.0617</span></div><div class="line"> <span class="number">0.1425</span> <span class="number">1.3961</span></div><div class="line"> <span class="number">0.5075</span> <span class="number">-1.8589</span></div><div class="line"> [torch.FloatTensor of size <span class="number">3</span>x2], </div><div class="line"> <span class="number">0.2106</span> <span class="number">-0.3776</span></div><div class="line"> <span class="number">-0.6864</span> <span class="number">0.7581</span></div><div class="line"> <span class="number">-0.5447</span> <span class="number">-0.6180</span></div><div class="line"> [torch.FloatTensor of size <span class="number">3</span>x2], </div><div class="line"> <span class="number">-2.2615</span> <span class="number">1.2279</span></div><div class="line"> <span class="number">0.5757</span> <span class="number">-0.7915</span></div><div class="line"> <span class="number">0.2896</span> <span class="number">0.1451</span></div><div class="line"> [torch.FloatTensor of size <span class="number">3</span>x2])</div></pre></td></tr></table></figure><p>将张量沿着给定维度分解成的多个块。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.gather(input, dim, index, out=<span class="keyword">None</span>) → Tensor</div></pre></td></tr></table></figure><p>参数： </p><ul><li><code>input</code>(Tensor) - 源张量</li><li><code>dim</code>(int) - 要索引的轴</li><li><code>index</code>(LongTensor) - 要收集的元素的索引</li><li><code>out</code>(Tensor，可选) - 目的张量</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div></pre></td><td class="code"><pre><div class="line">x = torch.FloatTensor([[<span class="number">1</span>,<span class="number">2</span>,<span class="number">3</span>],[<span class="number">4</span>,<span class="number">5</span>,<span class="number">6</span>],[<span class="number">7</span>,<span class="number">8</span>,<span class="number">9</span>]])</div><div class="line">Out[<span class="number">50</span>]: </div><div class="line"> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span></div><div class="line"> <span class="number">4</span> <span class="number">5</span> <span class="number">6</span></div><div class="line"> <span class="number">7</span> <span class="number">8</span> <span class="number">9</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x3]</div><div class="line"></div><div class="line">torch.gather(x, <span class="number">0</span>, torch.LongTensor([[<span class="number">0</span>,<span class="number">0</span>,<span class="number">0</span>],[<span class="number">0</span>,<span class="number">0</span>,<span class="number">0</span>],[<span class="number">0</span>,<span class="number">0</span>,<span class="number">0</span>]]))</div><div class="line">Out[<span class="number">58</span>]: </div><div class="line"> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span></div><div class="line"> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span></div><div class="line"> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x3]</div><div class="line"></div><div class="line">torch.gather(x, <span class="number">1</span>, torch.LongTensor([[<span class="number">0</span>,<span class="number">0</span>,<span class="number">0</span>],[<span class="number">0</span>,<span class="number">0</span>,<span class="number">0</span>],[<span class="number">0</span>,<span class="number">0</span>,<span class="number">0</span>]]))</div><div class="line">Out[<span class="number">60</span>]: </div><div class="line"> <span class="number">1</span> <span class="number">1</span> <span class="number">1</span></div><div class="line"> <span class="number">4</span> <span class="number">4</span> <span class="number">4</span></div><div class="line"> <span class="number">7</span> <span class="number">7</span> <span class="number">7</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x3]</div><div class="line"></div><div class="line">torch.gather(x, <span class="number">0</span>, torch.LongTensor([[<span class="number">0</span>,<span class="number">0</span>,<span class="number">0</span>],[<span class="number">1</span>,<span class="number">0</span>,<span class="number">1</span>],[<span class="number">0</span>,<span class="number">0</span>,<span class="number">0</span>]]))</div><div class="line">Out[<span class="number">59</span>]: </div><div class="line"> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span></div><div class="line"> <span class="number">4</span> <span class="number">2</span> <span class="number">6</span></div><div class="line"> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x3]</div></pre></td></tr></table></figure><p>沿给定轴<code>dim</code>，将输入索引张量<code>index</code>指定位置的值进行聚合。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.index_select(input, dim, index, out=<span class="keyword">None</span>) → Tensor</div></pre></td></tr></table></figure><p>参数:</p><ul><li><code>input</code> (Tensor) – 输入张量</li><li><code>dim</code> (int) – 索引的轴</li><li><code>index</code> (LongTensor) – 包含索引下标的一维张量</li><li><code>out</code> (Tensor, 可选的) – 目标张量</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">index = torch.LongTensor([<span class="number">0</span>,<span class="number">1</span>])</div><div class="line">torch.index_select(a, <span class="number">0</span>, index)</div><div class="line">Out[<span class="number">66</span>]: </div><div class="line"> <span class="number">0.6552</span> <span class="number">1.2615</span> <span class="number">-1.8676</span> <span class="number">-1.3015</span></div><div class="line"><span class="number">-0.6448</span> <span class="number">-0.0267</span> <span class="number">0.6535</span> <span class="number">-0.2193</span></div><div class="line">[torch.FloatTensor of size <span class="number">2</span>x4]</div><div class="line"></div><div class="line">torch.index_select(a, <span class="number">1</span>, index)</div><div class="line">Out[<span class="number">67</span>]: </div><div class="line"> <span class="number">0.6552</span> <span class="number">1.2615</span></div><div class="line"><span class="number">-0.6448</span> <span class="number">-0.0267</span></div><div class="line"><span class="number">-0.0179</span> <span class="number">-0.2577</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x2]</div></pre></td></tr></table></figure><p>返回一个新的张量，其索引input 张量沿尺寸 dim使用的条目中index这是一个LongTensor。</p><p>返回的Tensor具有与原始Tensor相同数量的尺寸。注意： 返回的张量不与原始张量共享内存空间。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"> <span class="number">0.6552</span> <span class="number">1.2615</span> <span class="number">-1.8676</span> <span class="number">-1.3015</span></div><div class="line"><span class="number">-0.6448</span> <span class="number">-0.0267</span> <span class="number">0.6535</span> <span class="number">-0.2193</span></div><div class="line"><span class="number">-0.0179</span> <span class="number">-0.2577</span> <span class="number">0.0076</span> <span class="number">0.2455</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x4]</div><div class="line"></div><div class="line">mask = a.ge(<span class="number">0.5</span>)</div><div class="line">a.ge(<span class="number">0.5</span>)</div><div class="line">Out[<span class="number">2</span>]: </div><div class="line"> <span class="number">1</span> <span class="number">1</span> <span class="number">0</span> <span class="number">0</span></div><div class="line"> <span class="number">0</span> <span class="number">0</span> <span class="number">1</span> <span class="number">0</span></div><div class="line"> <span class="number">0</span> <span class="number">0</span> <span class="number">0</span> <span class="number">0</span></div><div class="line">[torch.ByteTensor of size <span class="number">3</span>x4]</div><div class="line"></div><div class="line">torch.masked_select(a, mask)</div><div class="line">Out[<span class="number">3</span>]: </div><div class="line"> <span class="number">0.6552</span></div><div class="line"> <span class="number">1.2615</span></div><div class="line"> <span class="number">0.6535</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>]</div></pre></td></tr></table></figure><p>根据掩码张量<code>mask</code>中的二元值，取输入张量中的指定项( <code>mask</code>为一个 <em>ByteTensor</em>)，将取值返回到一个新的1D张量，张量 <code>mask</code>须跟<code>input</code>张量有相同数量的元素数目，但形状或维度不需要相同。注意： 返回的张量不与原始张量共享内存空间。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.nonzero(input, out=<span class="keyword">None</span>) → LongTensor</div></pre></td></tr></table></figure><p>参数:</p><ul><li><code>input</code> (Tensor) – 源张量</li><li><code>out</code> (LongTensor, 可选的) – 包含索引值的结果张量</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div></pre></td><td class="code"><pre><div class="line">b = torch.Tensor([<span class="number">1</span>,<span class="number">0</span>,<span class="number">1</span>,<span class="number">1</span>,<span class="number">0</span>])</div><div class="line">torch.nonzero(b)</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"> <span class="number">0</span></div><div class="line"> <span class="number">2</span></div><div class="line"> <span class="number">3</span></div><div class="line">[torch.LongTensor of size <span class="number">3</span>x1]</div></pre></td></tr></table></figure><p>返回一个包含输入<code>input</code>中非零元素索引的张量。输出张量中的每行包含输入中非零元素的索引。</p><p>如果输入<code>input</code>有<code>n</code>维，则输出的索引张量<code>output</code>的形状为 z x n, 这里 z 是输入张量<code>input</code>中所有非零元素的个数。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.split(tensor, split_size, dim=<span class="number">0</span>)</div></pre></td></tr></table></figure><p>参数:</p><ul><li><code>tensor</code> (Tensor) – 待分割张量</li><li><code>split_size</code> (int) – 单个分块的形状大小</li><li><code>dim</code> (int) – 沿着此维进行分割</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">torch.split(a,<span class="number">1</span>,<span class="number">0</span>)</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line">(</div><div class="line"> <span class="number">0.6552</span> <span class="number">1.2615</span> <span class="number">-1.8676</span> <span class="number">-1.3015</span></div><div class="line"> [torch.FloatTensor of size <span class="number">1</span>x4], </div><div class="line"> <span class="number">-0.6448</span> <span class="number">-0.0267</span> <span class="number">0.6535</span> <span class="number">-0.2193</span></div><div class="line"> [torch.FloatTensor of size <span class="number">1</span>x4], </div><div class="line"> <span class="number">-0.0179</span> <span class="number">-0.2577</span> <span class="number">0.0076</span> <span class="number">0.2455</span></div><div class="line"> [torch.FloatTensor of size <span class="number">1</span>x4])</div><div class="line"></div><div class="line">torch.split(a,<span class="number">1</span>,<span class="number">1</span>)</div><div class="line">Out[<span class="number">101</span>]: </div><div class="line">(</div><div class="line"> <span class="number">0.6552</span></div><div class="line"> <span class="number">-0.6448</span></div><div class="line"> <span class="number">-0.0179</span></div><div class="line"> [torch.FloatTensor of size <span class="number">3</span>x1], </div><div class="line"> <span class="number">1.2615</span></div><div class="line"> <span class="number">-0.0267</span></div><div class="line"> <span class="number">-0.2577</span></div><div class="line"> [torch.FloatTensor of size <span class="number">3</span>x1], </div><div class="line"> <span class="number">-1.8676</span></div><div class="line"> <span class="number">0.6535</span></div><div class="line"> <span class="number">0.0076</span></div><div class="line"> [torch.FloatTensor of size <span class="number">3</span>x1], </div><div class="line"> <span class="number">-1.3015</span></div><div class="line"> <span class="number">-0.2193</span></div><div class="line"> <span class="number">0.2455</span></div><div class="line"> [torch.FloatTensor of size <span class="number">3</span>x1])</div></pre></td></tr></table></figure><p>将输入张量分割成相等形状的chunks（如果可分）。 如果沿指定维的张量形状大小不能被<code>split_size</code> 整分， 则最后一个分块会小于其它分块。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.squeeze(input, dim=<span class="keyword">None</span>, out=<span class="keyword">None</span>)</div></pre></td></tr></table></figure><p>参数: </p><ul><li><code>input</code> (Tensor) – 输入张量</li><li><code>dim</code> (int, 可选的) – 如果给定，则<code>input</code>只会在给定维度挤压</li><li><code>out</code> (Tensor, 可选的) – 输出张量</li></ul><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div></pre></td><td class="code"><pre><div class="line">x = torch.zeros(2, 1, 2, 1, 2)</div><div class="line">torch.squeeze(x)</div><div class="line">Out[1]: </div><div class="line">[torch.FloatTensor of size 2x2x2]</div><div class="line"></div><div class="line">torch.squeeze(x, 0)</div><div class="line">Out[2]: </div><div class="line">[torch.FloatTensor of size 2x1x2x1x2]</div><div class="line"></div><div class="line">torch.squeeze(x,1)</div><div class="line">Out[3]:</div><div class="line">[torch.FloatTensor of size 2x2x1x2]</div></pre></td></tr></table></figure><p>将输入张量形状中的<code>1</code> 去除并返回。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.unsqueeze(input, dim, out=<span class="keyword">None</span>)</div></pre></td></tr></table></figure><p>参数:</p><ul><li><code>tensor</code> (Tensor) – 输入张量</li><li><code>dim</code> (int) – 插入维度的索引</li><li><code>out</code> (Tensor, 可选的) – 结果张量</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div></pre></td><td class="code"><pre><div class="line">x = torch.FloatTensor([<span class="number">1</span>,<span class="number">2</span>,<span class="number">3</span>],[<span class="number">4</span>,<span class="number">5</span>,<span class="number">6</span>])</div><div class="line">torch.unsqueeze(x, <span class="number">0</span>)</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line">(<span class="number">0</span> ,.,.) = </div><div class="line"> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span></div><div class="line"> <span class="number">4</span> <span class="number">5</span> <span class="number">6</span></div><div class="line">[torch.FloatTensor of size <span class="number">1</span>x2x3]</div><div class="line"></div><div class="line">torch.unsqueeze(x, <span class="number">1</span>)</div><div class="line">Out[<span class="number">2</span>]: </div><div class="line">(<span class="number">0</span> ,.,.) = </div><div class="line"> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span></div><div class="line">(<span class="number">1</span> ,.,.) = </div><div class="line"> <span class="number">4</span> <span class="number">5</span> <span class="number">6</span></div><div class="line">[torch.FloatTensor of size <span class="number">2</span>x1x3]</div><div class="line"></div><div class="line">torch.unsqueeze(x, <span class="number">2</span>)</div><div class="line">Out[<span class="number">3</span>]: </div><div class="line">(<span class="number">0</span> ,.,.) = </div><div class="line"> <span class="number">1</span></div><div class="line"> <span class="number">2</span></div><div class="line"> <span class="number">3</span></div><div class="line">(<span class="number">1</span> ,.,.) = </div><div class="line"> <span class="number">4</span></div><div class="line"> <span class="number">5</span></div><div class="line"> <span class="number">6</span></div><div class="line">[torch.FloatTensor of size <span class="number">2</span>x3x1]</div></pre></td></tr></table></figure><p>返回一个新的张量，对输入的制定位置插入维度 1</p><p>如果<code>dim</code>为负，则将会被转化dim+input.dim()+1</p><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.stack(sequence, dim=0)</div></pre></td></tr></table></figure><p>参数: </p><ul><li><code>sequence</code> (Sequence) – 待连接的张量序列</li><li><code>dim</code> (int) – 插入的维度。必须介于 0 与 待连接的张量序列数之间。</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div></pre></td><td class="code"><pre><div class="line">x = torch.FloatTensor([<span class="number">1</span>,<span class="number">2</span>,<span class="number">3</span>],[<span class="number">4</span>,<span class="number">5</span>,<span class="number">6</span>])</div><div class="line">torch.stack((x, x), <span class="number">0</span>)</div><div class="line">Out[<span class="number">115</span>]: </div><div class="line">(<span class="number">0</span> ,.,.) = </div><div class="line"> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span></div><div class="line"> <span class="number">4</span> <span class="number">5</span> <span class="number">6</span></div><div class="line">(<span class="number">1</span> ,.,.) = </div><div class="line"> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span></div><div class="line"> <span class="number">4</span> <span class="number">5</span> <span class="number">6</span></div><div class="line">[torch.FloatTensor of size <span class="number">2</span>x2x3]</div><div class="line"></div><div class="line">torch.stack((x, x), <span class="number">2</span>)</div><div class="line">Out[<span class="number">117</span>]: </div><div class="line">(<span class="number">0</span> ,.,.) = </div><div class="line"> <span class="number">1</span> <span class="number">1</span></div><div class="line"> <span class="number">2</span> <span class="number">2</span></div><div class="line"> <span class="number">3</span> <span class="number">3</span></div><div class="line">(<span class="number">1</span> ,.,.) = </div><div class="line"> <span class="number">4</span> <span class="number">4</span></div><div class="line"> <span class="number">5</span> <span class="number">5</span></div><div class="line"> <span class="number">6</span> <span class="number">6</span></div><div class="line">[torch.FloatTensor of size <span class="number">2</span>x3x2]</div></pre></td></tr></table></figure><p>沿着一个新维度对输入张量序列进行连接。序列中所有的张量都应该为相同形状。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.take(input, indices) → Tensor</div></pre></td></tr></table></figure><p>参数: </p><ul><li><code>input</code> (Tensor) – 输入张量</li><li><code>indices</code>(LongTensor) – 索引到张量</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div></pre></td><td class="code"><pre><div class="line">x = torch.FloatTensor([<span class="number">1</span>,<span class="number">2</span>,<span class="number">3</span>],[<span class="number">4</span>,<span class="number">5</span>,<span class="number">6</span>])</div><div class="line">torch.take(x, torch.LongTensor([<span class="number">0</span>,<span class="number">2</span>,<span class="number">5</span>]))</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"> <span class="number">1</span></div><div class="line"> <span class="number">3</span></div><div class="line"> <span class="number">6</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>]</div></pre></td></tr></table></figure><p>用给定索引处的输入元素返回一个新的张量， 输入张量被看作是一维张量。 结果与指数具有相同形状。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.transpose(input, dim0, dim1, out=<span class="keyword">None</span>) → Tensor</div></pre></td></tr></table></figure><p>参数: </p><ul><li><code>input</code> (Tensor) – 输入张量</li><li><code>dim0</code> (int) – 转置的第一维</li><li><code>dim1</code> (int) – 转置的第二维 </li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"> <span class="number">0.6552</span> <span class="number">1.2615</span> <span class="number">-1.8676</span> <span class="number">-1.3015</span></div><div class="line"><span class="number">-0.6448</span> <span class="number">-0.0267</span> <span class="number">0.6535</span> <span class="number">-0.2193</span></div><div class="line"><span class="number">-0.0179</span> <span class="number">-0.2577</span> <span class="number">0.0076</span> <span class="number">0.2455</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x4]</div><div class="line"></div><div class="line">torch.transpose(a, <span class="number">0</span>, <span class="number">1</span>)</div><div class="line">Out[<span class="number">2</span>]: </div><div class="line"> <span class="number">0.6552</span> <span class="number">-0.6448</span> <span class="number">-0.0179</span></div><div class="line"> <span class="number">1.2615</span> <span class="number">-0.0267</span> <span class="number">-0.2577</span></div><div class="line"><span class="number">-1.8676</span> <span class="number">0.6535</span> <span class="number">0.0076</span></div><div class="line"><span class="number">-1.3015</span> <span class="number">-0.2193</span> <span class="number">0.2455</span></div><div class="line">[torch.FloatTensor of size <span class="number">4</span>x3]</div></pre></td></tr></table></figure><p>返回输入矩阵<code>input</code>的转置。交换维度<code>dim0</code>和<code>dim1</code>。输出张量与输入张量共享内存，所以改变其中一个会导致另外一个也被修改。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.unbind(tensor, dim=<span class="number">0</span>)</div></pre></td></tr></table></figure><p>参数:</p><ul><li><code>tensor</code> (Tensor) – 输入张量</li><li><code>dim</code> (int) – 删除的维度</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">torch.unbind(a, <span class="number">1</span>)</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line">(</div><div class="line"> <span class="number">0.6552</span></div><div class="line"> <span class="number">-0.6448</span></div><div class="line"> <span class="number">-0.0179</span></div><div class="line"> [torch.FloatTensor of size <span class="number">3</span>], </div><div class="line"> <span class="number">1.2615</span></div><div class="line"> <span class="number">-0.0267</span></div><div class="line"> <span class="number">-0.2577</span></div><div class="line"> [torch.FloatTensor of size <span class="number">3</span>], </div><div class="line"> <span class="number">-1.8676</span></div><div class="line"> <span class="number">0.6535</span></div><div class="line"> <span class="number">0.0076</span></div><div class="line"> [torch.FloatTensor of size <span class="number">3</span>], </div><div class="line"> <span class="number">-1.3015</span></div><div class="line"> <span class="number">-0.2193</span></div><div class="line"> <span class="number">0.2455</span></div><div class="line"> [torch.FloatTensor of size <span class="number">3</span>])</div><div class="line"></div><div class="line">torch.unbind(a, <span class="number">0</span>)</div><div class="line">Out[<span class="number">2</span>]: </div><div class="line">(</div><div class="line"> <span class="number">0.6552</span></div><div class="line"> <span class="number">1.2615</span></div><div class="line"> <span class="number">-1.8676</span></div><div class="line"> <span class="number">-1.3015</span></div><div class="line"> [torch.FloatTensor of size <span class="number">4</span>], </div><div class="line"> <span class="number">-0.6448</span></div><div class="line"> <span class="number">-0.0267</span></div><div class="line"> <span class="number">0.6535</span></div><div class="line"> <span class="number">-0.2193</span></div><div class="line"> [torch.FloatTensor of size <span class="number">4</span>], </div><div class="line"> <span class="number">-0.0179</span></div><div class="line"> <span class="number">-0.2577</span></div><div class="line"> <span class="number">0.0076</span></div><div class="line"> <span class="number">0.2455</span></div><div class="line"> [torch.FloatTensor of size <span class="number">4</span>])</div></pre></td></tr></table></figure><p>移除指定维后，返回一个元组，包含了沿着指定维切片后的各个切片</p><h2 id="随机抽样-Random-sampling"><a href="#随机抽样-Random-sampling" class="headerlink" title="随机抽样 Random sampling"></a>随机抽样 Random sampling</h2><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.manual_seed(seed)</div></pre></td></tr></table></figure><p>设定生成随机数的种子，并返回一个 _torch.<em>C.Generator</em> 对象.</p><p>参数: seed (int or long) – 种子.</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.initial_seed()</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div></pre></td><td class="code"><pre><div class="line">torch.manual_seed(<span class="number">2</span>)</div><div class="line">Out[<span class="number">1</span>]: <torch._C.Generator at <span class="number">0x7fa4860b2370</span>></div><div class="line"> </div><div class="line">torch.initial_seed()</div><div class="line">Out[<span class="number">2</span>]: <span class="number">2L</span></div></pre></td></tr></table></figure><p>返回生成随机数的原始种子值（python long）。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.get_rng_state()</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div></pre></td><td class="code"><pre><div class="line">torch.get_rng_state()</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"> <span class="number">2</span></div><div class="line"> <span class="number">0</span></div><div class="line"> <span class="number">0</span></div><div class="line"> ⋮ </div><div class="line"> <span class="number">0</span></div><div class="line"> <span class="number">0</span></div><div class="line"> <span class="number">0</span></div><div class="line">[torch.ByteTensor of size <span class="number">5048</span>]</div></pre></td></tr></table></figure><p>返回随机生成器状态(<em>ByteTensor</em>)</p><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.set_rng_state(new_state)</div></pre></td></tr></table></figure><p>设定随机生成器状态参数: new_state (torch.ByteTensor) – 期望的状态</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.bernoulli(input, out=<span class="keyword">None</span>) → Tensor</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div></pre></td><td class="code"><pre><div class="line">b = torch.Tensor(<span class="number">3</span>,<span class="number">4</span>).uniform_(<span class="number">0</span>,<span class="number">1</span>)</div><div class="line">b</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"> <span class="number">0.5596</span> <span class="number">0.5591</span> <span class="number">0.0915</span> <span class="number">0.2100</span></div><div class="line"> <span class="number">0.0072</span> <span class="number">0.0390</span> <span class="number">0.9929</span> <span class="number">0.9131</span></div><div class="line"> <span class="number">0.6186</span> <span class="number">0.9744</span> <span class="number">0.3189</span> <span class="number">0.2148</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x4]</div><div class="line"></div><div class="line">torch.bernoulli(b)</div><div class="line">Out[<span class="number">2</span>]: </div><div class="line"> <span class="number">1</span> <span class="number">0</span> <span class="number">0</span> <span class="number">0</span></div><div class="line"> <span class="number">0</span> <span class="number">0</span> <span class="number">1</span> <span class="number">1</span></div><div class="line"> <span class="number">1</span> <span class="number">1</span> <span class="number">0</span> <span class="number">0</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x4]</div></pre></td></tr></table></figure><p>从伯努利分布中抽取二元随机数(0 或者 1)。输入张量须包含用于抽取上述二元随机值的概率。 因此，输入中的所有值都必须在［0,1］区间，即 ( 0<=input_i<=1 )输出张量的第<em>i</em>个元素值， 将会以输入张量的第<em>i</em>个概率值等于<code>1</code>。返回值将会是与输入相同大小的张量，每个值为0或者1。</p><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.multinomial(input, num_samples,replacement=False, out=None) → LongTensor</div></pre></td></tr></table></figure><p>参数:</p><ul><li><code>input</code> (Tensor) – 包含概率值的张量</li><li><code>num_samples</code> (int) – 抽取的样本数</li><li><code>replacement</code> (bool, 可选的) – 布尔值，决定是否能重复抽取</li><li><code>out</code> (Tensor, 可选的) – 结果张量</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div></pre></td><td class="code"><pre><div class="line">weights = torch.Tensor([<span class="number">0</span>, <span class="number">10</span>, <span class="number">3</span>, <span class="number">1</span>])</div><div class="line">torch.multinomial(weights, <span class="number">4</span>)</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"> <span class="number">1</span></div><div class="line"> <span class="number">2</span></div><div class="line"> <span class="number">3</span></div><div class="line"> <span class="number">0</span></div><div class="line">[torch.LongTensor of size <span class="number">4</span>]</div><div class="line"></div><div class="line">torch.multinomial(weights, <span class="number">4</span>, replacement=<span class="keyword">True</span>)</div><div class="line">Out[<span class="number">2</span>]: </div><div class="line"> <span class="number">1</span></div><div class="line"> <span class="number">1</span></div><div class="line"> <span class="number">1</span></div><div class="line"> <span class="number">1</span></div><div class="line">[torch.LongTensor of size <span class="number">4</span>]</div></pre></td></tr></table></figure><p>返回一个张量，每行包含从<code>input</code>相应行中定义的多项分布中抽取的<code>num_samples</code>个样本。 </p><p>当抽取样本时，依次从左到右排列(第一个样本对应第一列)。</p><p>如果输入<code>input</code>是一个向量，输出<code>out</code>也是一个相同长度<code>num_samples</code>的向量。如果输入<code>input</code>是有 (m )行的矩阵，输出<code>out</code>是形如( m * n )的矩阵。</p><p>如果参数<code>replacement</code> 为 <em>True</em>, 则样本抽取可以重复。否则，一个样本在每行不能被重复抽取。</p><p>参数<code>num_samples</code>必须小于<code>input</code>长度(即，<code>input</code>的列数，如果是<code>input</code>是一个矩阵)。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.normal(means, std, out=<span class="keyword">None</span>)</div></pre></td></tr></table></figure><p>参数:</p><ul><li><code>means</code> (Tensor) – 均值</li><li><code>std</code> (Tensor) – 标准差</li><li><code>out</code> (Tensor) – 可选的输出张量</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div></pre></td><td class="code"><pre><div class="line">torch.normal(means=torch.arange(<span class="number">0</span>, <span class="number">11</span>), std=torch.arange(<span class="number">1</span>, <span class="number">0</span>, <span class="number">-0.1</span>))</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"> <span class="number">0.3889</span></div><div class="line"> <span class="number">-0.1244</span></div><div class="line"> <span class="number">1.4945</span></div><div class="line"> <span class="number">3.0249</span></div><div class="line"> <span class="number">3.4251</span></div><div class="line"> <span class="number">4.1258</span></div><div class="line"> <span class="number">6.5222</span></div><div class="line"> <span class="number">7.0321</span></div><div class="line"> <span class="number">7.9798</span></div><div class="line"> <span class="number">8.9608</span></div><div class="line"> <span class="number">10.0000</span></div><div class="line">[torch.FloatTensor of size <span class="number">11</span>]</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.normal(mean=<span class="number">0.0</span>, std, out=<span class="keyword">None</span>)</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div></pre></td><td class="code"><pre><div class="line">torch.normal(mean=<span class="number">0.5</span>, std=torch.arange(<span class="number">1</span>,<span class="number">6</span>))</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"><span class="number">-0.4879</span></div><div class="line"><span class="number">-0.2523</span></div><div class="line"><span class="number">-0.3742</span></div><div class="line"><span class="number">-1.0413</span></div><div class="line"> <span class="number">2.2176</span></div><div class="line">[torch.FloatTensor of size <span class="number">5</span>]</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.normal(means, std=<span class="number">1.0</span>, out=<span class="keyword">None</span>)</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div></pre></td><td class="code"><pre><div class="line">torch.normal(means=torch.arange(<span class="number">1</span>,<span class="number">6</span>))</div><div class="line">Out[<span class="number">171</span>]: </div><div class="line"> <span class="number">1.9339</span></div><div class="line"> <span class="number">1.5494</span></div><div class="line"> <span class="number">1.9340</span></div><div class="line"> <span class="number">3.5107</span></div><div class="line"> <span class="number">3.8822</span></div><div class="line">[torch.FloatTensor of size <span class="number">5</span>]</div></pre></td></tr></table></figure><p>返回一个张量，包含从给定参数<code>means</code>,<code>std</code>的离散正态分布中抽取随机数。均值<code>means</code>是一个张量，包含每个输出元素相关的正态分布的均值。<code>std</code>是一个张量，包含每个输出元素相关的正态分布的标准差。均值和标准差的形状不须匹配，但每个张量的元素个数须相同。</p><h2 id="序列化-Serialization"><a href="#序列化-Serialization" class="headerlink" title="序列化 Serialization"></a>序列化 Serialization</h2><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.save(obj, f, pickle_module=<module <span class="string">'pickle'</span> <span class="keyword">from</span> <span class="string">'/usr/bin/python2.7/pickle.py'</span>>, pickle_protocol=<span class="number">2</span>)</div></pre></td></tr></table></figure><p>参数：</p><ul><li><code>obj</code> – 保存对象</li><li><code>f</code> － 类文件对象 (返回文件描述符)或一个保存文件名的字符串</li><li><code>pickle_module</code> – 用于pickling元数据和对象的模块</li><li><code>pickle_protocol</code> – 指定pickle protocal 可以覆盖默认参数</li></ul><p>保存一个对象到一个硬盘文件上。参见 <a href="http://pytorch.org/docs/0.3.0/notes/serialization.html#recommend-saving-models" target="_blank" rel="external">Recommended approach for saving a model</a></p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.load(f, map_location=<span class="keyword">None</span>, pickle_module=<module <span class="string">'pickle'</span> <span class="keyword">from</span> <span class="string">'/usr/bin/python2.7/pickle.py'</span>>)</div></pre></td></tr></table></figure><p>参数:</p><ul><li><code>f</code> – 类文件对象 (返回文件描述符)或一个保存文件名的字符串</li><li><code>map_location</code> – 一个函数或字典规定如何remap存储位置</li><li><code>pickle_module</code> – 用于unpickling元数据和对象的模块 (必须匹配序列化文件时的pickle_module )</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div></pre></td><td class="code"><pre><div class="line"><span class="meta">>>> </span>torch.load(<span class="string">'tensors.pt'</span>)</div><div class="line"><span class="comment"># Load all tensors onto the CPU</span></div><div class="line"><span class="meta">>>> </span>torch.load(<span class="string">'tensors.pt'</span>, map_location=<span class="keyword">lambda</span> storage, loc: storage)</div><div class="line"><span class="comment"># Map tensors from GPU 1 to GPU 0</span></div><div class="line"><span class="meta">>>> </span>torch.load(<span class="string">'tensors.pt'</span>, map_location={<span class="string">'cuda:1'</span>:<span class="string">'cuda:0'</span>})</div></pre></td></tr></table></figure><p>从磁盘文件中读取一个通过<code>torch.save()</code>保存的对象。<code>torch.load()</code> 可通过参数<code>map_location</code><br>动态地进行内存重映射，使其能从不动设备中读取文件。一般调用时，需两个参数: storage 和 location tag. 返回不同地址中的storage，或着返回None (此时地址可以通过默认方法进行解析). 如果这个参数是字典的话，意味着其是从文件的地址标记到当前系统的地址标记的映射。默认情况下， location tags中 “cpu”对应host tensors，‘cuda:device_id’ (e.g. ‘cuda:2’) 对应cuda tensors。</p><p>用户可以通过register_package进行扩展，使用自己定义的标记和反序列化方法。</p><h1 id="数学操作Math-operations"><a href="#数学操作Math-operations" class="headerlink" title="数学操作Math operations"></a>数学操作Math operations</h1><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.abs(input, out=<span class="keyword">None</span>) → Tensor</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div></pre></td><td class="code"><pre><div class="line">torch.abs(torch.FloatTensor([<span class="number">-1</span>, <span class="number">2</span>, <span class="number">-3</span>]))</div><div class="line">Out[<span class="number">8</span>]: </div><div class="line"> <span class="number">1</span></div><div class="line"> <span class="number">2</span></div><div class="line"> <span class="number">3</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>]</div></pre></td></tr></table></figure><p>计算输入张量的每个元素绝对值</p><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.add(input, value, out=None)</div></pre></td></tr></table></figure><p>参数:</p><ul><li><code>input</code> (Tensor) – 输入张量</li><li><code>value</code> (Number) – 添加到输入每个元素的数</li><li><code>out</code> (Tensor, 可选的) – 结果张量</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>, <span class="number">4</span>)</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"><span class="number">-0.5815</span> <span class="number">-1.6031</span> <span class="number">1.9077</span> <span class="number">0.0478</span></div><div class="line"> <span class="number">2.6821</span> <span class="number">1.0581</span> <span class="number">0.0966</span> <span class="number">-0.8499</span></div><div class="line"><span class="number">-0.7623</span> <span class="number">1.3194</span> <span class="number">1.4320</span> <span class="number">-0.0202</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x4]</div><div class="line"></div><div class="line">torch.add(a, <span class="number">10</span>)</div><div class="line">Out[<span class="number">2</span>]: </div><div class="line"> <span class="number">9.4185</span> <span class="number">8.3969</span> <span class="number">11.9077</span> <span class="number">10.0478</span></div><div class="line"> <span class="number">12.6821</span> <span class="number">11.0581</span> <span class="number">10.0966</span> <span class="number">9.1501</span></div><div class="line"> <span class="number">9.2377</span> <span class="number">11.3194</span> <span class="number">11.4320</span> <span class="number">9.9798</span></div><div class="line">[torch.FloatTensor of size <span class="number">3</span>x4]</div></pre></td></tr></table></figure><p>对输入张量<code>input</code>逐元素加上标量值<code>value</code>，并返回结果到一个新的张量<code>out</code>，即 ( out = tensor + value )。如果输入<code>input</code>是FloatTensor or DoubleTensor类型，则<code>value</code> 必须为实数，否则须为整数。</p><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.addcdiv(tensor, value=1, tensor1, tensor2, out=None) → Tensor</div></pre></td></tr></table></figure><p>参数：</p><ul><li>tensor (Tensor) – 张量，对 tensor1 ./ tensor 进行相加</li><li>value (Number, 可选的) – 标量，对 tensor1 ./ tensor2 进行相乘</li><li>tensor1 (Tensor) – 张量，作为被除数(分子)</li><li>tensor2 (Tensor) –张量，作为除数(分母)</li><li>out (Tensor, 可选的) – 输出张量</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>, <span class="number">4</span>)</div><div class="line">a1 = torch.randn(<span class="number">2</span>, <span class="number">6</span>)</div><div class="line">a2 = torch.randn(<span class="number">6</span>, <span class="number">2</span>)</div><div class="line">torch.addcdiv(a, <span class="number">0.1</span>, a1, a2)</div></pre></td></tr></table></figure><p>对<code>tensor2</code>对<code>tensor1</code>逐元素相除，然后乘以标量值<code>value</code> 并加到<code>tensor</code>。</p><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.addcmul(tensor, value=1, tensor1, tensor2, out=None) → Tensor</div></pre></td></tr></table></figure><p>用<code>tensor2</code>对<code>tensor1</code>逐元素相乘，并对结果乘以标量值<code>value</code>然后加到<code>tensor</code>。张量的形状不需要匹配，但元素数量必须一致。如果输入是FloatTensor or DoubleTensor类型，则<code>value</code> 必须为实数，否则须为整数。</p><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.ceil(input, out=None) → Tensor</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div></pre></td><td class="code"><pre><div class="line">b = torch.randn(<span class="number">4</span>)</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"><span class="number">-0.4149</span></div><div class="line"> <span class="number">1.1449</span></div><div class="line"><span class="number">-1.3121</span></div><div class="line"> <span class="number">1.4417</span></div><div class="line">[torch.FloatTensor of size <span class="number">4</span>]</div><div class="line"></div><div class="line">torch.ceil(b)</div><div class="line">Out[<span class="number">20</span>]: </div><div class="line"><span class="number">-0</span></div><div class="line"> <span class="number">2</span></div><div class="line"><span class="number">-1</span></div><div class="line"> <span class="number">2</span></div><div class="line">[torch.FloatTensor of size <span class="number">4</span>]</div></pre></td></tr></table></figure><p>对输入<code>input</code>张量每个元素向上取整, 即取不小于每个元素的最小整数，并返回结果到输出。</p><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.clamp(input, min, max, out=None) → Tensor</div></pre></td></tr></table></figure><p>操作定义如下：</p><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div></pre></td><td class="code"><pre><div class="line"> | min, if x_i < min</div><div class="line">y_i = | x_i, if min <= x_i <= max</div><div class="line"> | max, if x_i > max</div></pre></td></tr></table></figure><p>如果输入是FloatTensor or DoubleTensor类型，则参数<code>min</code> <code>max</code> 必须为实数，否则须为整数。</p><p>参数：</p><ul><li>input (Tensor) – 输入张量</li><li>min (Number) – 限制范围下限</li><li>max (Number) – 限制范围上限</li><li>out (Tensor, 可选的) – 输出张量</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div></pre></td><td class="code"><pre><div class="line">b = torch.randn(<span class="number">4</span>)</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"><span class="number">-0.4149</span></div><div class="line"> <span class="number">1.1449</span></div><div class="line"><span class="number">-1.3121</span></div><div class="line"> <span class="number">1.4417</span></div><div class="line">[torch.FloatTensor of size <span class="number">4</span>]</div><div class="line"></div><div class="line">torch.clamp(b, <span class="number">-1</span>, <span class="number">1</span>)</div><div class="line">Out[<span class="number">22</span>]: </div><div class="line"><span class="number">-0.4149</span></div><div class="line"> <span class="number">1.0000</span></div><div class="line"><span class="number">-1.0000</span></div><div class="line"> <span class="number">1.0000</span></div><div class="line">[torch.FloatTensor of size <span class="number">4</span>]</div></pre></td></tr></table></figure><p>将输入<code>input</code>张量每个元素的夹紧到区间 ([min, max] )，并返回结果到一个新张量。</p><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.floor(input, out=None) → Tensor</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div></pre></td><td class="code"><pre><div class="line">b = torch.randn(<span class="number">4</span>)</div><div class="line">Out[<span class="number">1</span>]: </div><div class="line"><span class="number">-0.4149</span></div><div class="line"> <span class="number">1.1449</span></div><div class="line"><span class="number">-1.3121</span></div><div class="line"> <span class="number">1.4417</span></div><div class="line">[torch.FloatTensor of size <span class="number">4</span>]</div><div class="line"></div><div class="line">torch.floor(b)</div><div class="line">Out[<span class="number">24</span>]: </div><div class="line"><span class="number">-1</span></div><div class="line"> <span class="number">1</span></div><div class="line"><span class="number">-2</span></div><div class="line"> <span class="number">1</span></div><div class="line">[torch.FloatTensor of size <span class="number">4</span>]</div></pre></td></tr></table></figure><p>床函数: 返回一个新张量，包含输入<code>input</code>张量每个元素的floor，即不小于元素的最大整数。</p>]]></content>
<summary type="html">
<h3 id="Torch"><a href="#Torch" class="headerlink" title="Torch"></a>Torch</h3><p><code>torch</code>包含了多维的数据结构以及基于其上的数学运算。它提供了多种实用工具，具有CUDA对应的实现</p>
<h2 id="张量-Tensors"><a href="#张量-Tensors" class="headerlink" title="张量 Tensors"></a>张量 Tensors</h2><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">torch.is_tensor(obj)</div></pre></td></tr></table></figure>
<figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div></pre></td><td class="code"><pre><div class="line">a = torch.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">b = np.random.randn(<span class="number">3</span>,<span class="number">4</span>)</div><div class="line">torch.is_tensor(a)</div><div class="line">Out[<span class="number">1</span>]: <span class="keyword">True</span></div><div class="line">torch.is_tensor(b)</div><div class="line">Out[<span class="number">2</span>]: <span class="keyword">False</span></div></pre></td></tr></table></figure>
<p>判断是否为张量，如果是pytorch张量，则返回True</p>
</summary>
<category term="工具资源" scheme="http://yoursite.com/categories/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90/"/>
<category term="工具资源，torch" scheme="http://yoursite.com/tags/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90%EF%BC%8Ctorch/"/>
</entry>
<entry>
<title>cache_model</title>
<link href="http://yoursite.com/2018/01/15/cache-model/"/>
<id>http://yoursite.com/2018/01/15/cache-model/</id>
<published>2018-01-15T10:02:44.000Z</published>
<updated>2018-01-15T10:13:21.500Z</updated>
<content type="html"><![CDATA[<h3 id="ABSTRACT"><a href="#ABSTRACT" class="headerlink" title="ABSTRACT"></a>ABSTRACT</h3><p>我们提出对神经网络语言模型进行的一个扩展，以使其预测适应最近的历史。我们的模型是内存增强网络的简化版本。它将过去隐藏的激活存储为内存，并通过当前隐藏激活的点积访问它们。这种机制非常有效，可以扩展到非常大的内存大小。我们还在神经网络中使用外部存储器和基于计数的语言模型使用缓存模型之间建立了联系。我们在几个语言模型数据集上进行演示，我们的方法比最近的内存扩展网络性能更好。</p><h3 id="INTRODUCTION"><a href="#INTRODUCTION" class="headerlink" title="INTRODUCTION"></a>INTRODUCTION</h3><p>语言模型是单词序列的概率分布，具有许多应用，如machine translation，speech recognition 或dialogue agents。虽然传统的神经网络语言模型已经在这个领域获得了最先进的性能，但是它们缺乏适应其最近历史的能力，这限制了它们在动态环境中的应用。最近的解决这个问题的方法是用external memory来扩充这些网络。这些模型可能会使用外部存储器来存储新的信息并适应不断变化的环境。</p><p>虽然这些网络在语言建模数据集上取得了很好的结果，但它们在计算上相当昂贵。通常，他们必须学习一个可以参数化的机制来读取或写入存储单元。这可能会限制其可用内存的大小以及可以训练的数据量。在这项工作中，我们提出了一个非常轻量级的选择，它可以共享内存扩展网络的一些特性，特别是随着时间的推移动态调整的能力。通过最小化内存的计算负担，我们可以使用更大的内存并扩展到更大的数据集。我们在实践中观察到，这使我们能够在不同的语言建模任务上超越记忆增强网络的性能。</p><a id="more"></a><p>我们的模型与Kuhn提出的模型有一些相似之处，称为缓存模型。缓存模型存储最近过去的简单表示，通常以unigrams和…的形式存储使用它们进行预测。这种上下文信息是非常容易存储并且可以有效地访问。它也不需要任何训练，可以应用在任何模型之上。这使得这个模型对领域适应尤其有意思。</p><p>我们的主要贡献是提出一个缓存模型的连续版本，称为神经缓存模型，它可以适应任何神经网络语言模型。我们存储最近隐藏的激活并将其用作上下文的表示。并和当前的隐藏激活使用简单的点积操作，结果发现获得料非常丰富的预测。我们的模型不需要训练，可以用于任何预先训练的神经网络。它也可以毫不费力地扩展到数千个存储单元。我们演示了几种语言模型任务和LAMBADA数据集的神经缓存模型的质量。</p><h3 id="LANGUAGE-MODELING"><a href="#LANGUAGE-MODELING" class="headerlink" title="LANGUAGE MODELING"></a>LANGUAGE MODELING</h3><p>语言模型是单词序列的概率分布。令词汇表的大小为$V$。每个单词由在$R^V = K$中的one-hot编码向量表示，对应于其在词汇表中的索引。使用链式规则，分配给一系列单词$x_1,…,x_T$的概率可以被分解为:</p><script type="math/tex; mode=display">p(x_1,...,x_T) = P(x1)P(x_2|x_1)P(x_3|x_2, x_1)· · · P(x_T |x_1 . . . x_{T −1})</script><script type="math/tex; mode=display">=\prod_{t-1}^{T}p(x_t|x_{t-1},...,x_1)</script><p>Language modeling通常被定义为在给定历史的情况下在单词上学习条件概率。这个条件概率传统上是用基于计数统计的非参数模型来近似的，特别是平滑的N-gram模型在实践中取得了良好的表现。参数化模型有最大熵语言模型，前馈网络语言模型或循环神经网络语言模型。特别地，循环神经网络是目前近似这个条件概率最好的解决方案，并在标准语言建模基准上 实现了state-of-the-arts的性能。</p><p><strong>Recurrent networks.</strong> 假设我们有一个向量为$h_t \in R^d$对历史单词$x_t,…,x_1$进行编码，则可以将单词w的条件概率参数化为：</p><script type="math/tex; mode=display">p_{vocab}(w|x_t,...,x_1) \propto exp(h_t^To_w)</script><p>历史向量$h_t$通过递归地应用形式的等式由循环神经网络计算</p><script type="math/tex; mode=display">h_t = \Phi(x_t,h_{t-1})</script><p>其中$\Phi$是一个取决于网络架构的函数。已经提出了几种循环神经网络的架构，例如Elman network，LSTM,GRU。Elman network是最简单的循环神经网络之一，其中：</p><script type="math/tex; mode=display">h_t = \sigma(Lx_t+Rh_{t-1})</script><p>其中$\sigma$是非线性的，例如logistic或tanh函数，$L \in R^{d\times V}$是一个word embedding 矩阵，$R \in R^{d\times d}$是隐藏层矩阵。LSTM架构在语言建模方面尤为有趣我们将读者引用Graves到了解这个架构的细节。</p><p>通过最小化训练数据的负对数似然性来学习循环神经网络语言模型的参数。这个目标函数通常通过使用随机梯度下降算法或Adagrad等变体来最小化。使用截断后向传播时间算法计算梯度。</p><p><strong>Cache model.</strong>一个单词在一个文档出现后，它很有可能再次出现。例如，在维基百科页面上单词$tiger$出现相同名字的频率是2.8％，而整个维基百科的频率是0.0037％。Cache model利用这个简单的观察来通过捕获文档中的远程依赖关系来改进n-gram语言模型。更确切地说，这些模型有一个缓存组件，其中包含近期历史中出现的单词（文档或固定数量的单词）。一个简单的语言模型，比如一个unigram或平滑的bigram模型，被放在缓存中的单词上，并用静态语言模型进行插值（在较大的数据集上进行训练）。这种技术有很多优点。首先，这是使语言模型适应新领域的一种非常有效的方法。其次，这样的模型能够预测不在词汇表中的词（OOV词），在看过一次这些词后。最后，这有助于捕获文档中的远程依赖关系，以便生成更加一致的文本。</p><p> <img src="/home/miacher/Pictures/datastructure/cache_model.png" alt="cache_model"></p><p>神经缓存模型将先前的隐藏状态存储在存储器单元中。然后将它们用作key来检索它们相应的单词，即下一个单词。在写作和阅读过程中，存储没有任何转换。</p>]]></content>
<summary type="html">
<h3 id="ABSTRACT"><a href="#ABSTRACT" class="headerlink" title="ABSTRACT"></a>ABSTRACT</h3><p>我们提出对神经网络语言模型进行的一个扩展，以使其预测适应最近的历史。我们的模型是内存增强网络的简化版本。它将过去隐藏的激活存储为内存，并通过当前隐藏激活的点积访问它们。这种机制非常有效，可以扩展到非常大的内存大小。我们还在神经网络中使用外部存储器和基于计数的语言模型使用缓存模型之间建立了联系。我们在几个语言模型数据集上进行演示，我们的方法比最近的内存扩展网络性能更好。</p>
<h3 id="INTRODUCTION"><a href="#INTRODUCTION" class="headerlink" title="INTRODUCTION"></a>INTRODUCTION</h3><p>语言模型是单词序列的概率分布，具有许多应用，如machine translation，speech recognition 或dialogue agents。虽然传统的神经网络语言模型已经在这个领域获得了最先进的性能，但是它们缺乏适应其最近历史的能力，这限制了它们在动态环境中的应用。最近的解决这个问题的方法是用external memory来扩充这些网络。这些模型可能会使用外部存储器来存储新的信息并适应不断变化的环境。</p>
<p>虽然这些网络在语言建模数据集上取得了很好的结果，但它们在计算上相当昂贵。通常，他们必须学习一个可以参数化的机制来读取或写入存储单元。这可能会限制其可用内存的大小以及可以训练的数据量。在这项工作中，我们提出了一个非常轻量级的选择，它可以共享内存扩展网络的一些特性，特别是随着时间的推移动态调整的能力。通过最小化内存的计算负担，我们可以使用更大的内存并扩展到更大的数据集。我们在实践中观察到，这使我们能够在不同的语言建模任务上超越记忆增强网络的性能。</p>
</summary>
<category term="论文" scheme="http://yoursite.com/categories/%E8%AE%BA%E6%96%87/"/>
<category term="论文，cache model" scheme="http://yoursite.com/tags/%E8%AE%BA%E6%96%87%EF%BC%8Ccache-model/"/>
</entry>
<entry>
<title>worldcloud</title>
<link href="http://yoursite.com/2018/01/13/worldcloud/"/>
<id>http://yoursite.com/2018/01/13/worldcloud/</id>
<published>2018-01-13T12:25:37.000Z</published>
<updated>2018-01-27T06:48:18.060Z</updated>
<content type="html"><![CDATA[<p> 今天介绍一个python库－－wordcloud，这个库的主要功能是对一个文本中的单词进行统计，并且以词云的方式进行展示，从生成的图片中，我们可以直观的发现哪些单词出现的频率较高，一个很有意思的用途就是统计一个会议中，提交论文的主题是哪些，从而看出当前研究的趋势。</p><h3 id="快速安装词云"><a href="#快速安装词云" class="headerlink" title="快速安装词云"></a>快速安装词云</h3><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">pip install wordcloud</div></pre></td></tr></table></figure><h3 id="快速生成词云"><a href="#快速生成词云" class="headerlink" title="快速生成词云"></a>快速生成词云</h3><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">from</span> wordcloud <span class="keyword">import</span> WordCloud</div><div class="line"></div><div class="line">f = open(<span class="string">u'moment.txt'</span>,<span class="string">'r'</span>).read()</div><div class="line">wordcloud = WordCloud(background_color=<span class="string">"white"</span>,width=<span class="number">1000</span>, height=<span class="number">860</span>, margin=<span class="number">2</span>).generate(f)</div><div class="line"></div><div class="line"><span class="comment"># width,height,margin可以设置图片属性</span></div><div class="line"><span class="comment"># generate 可以对全部文本进行自动分词,但是他对中文支持不好,对中文的分词处理请看我的下一篇文章</span></div><div class="line"><span class="comment">#wordcloud = WordCloud(font_path = r'~\Fonts\simkai.ttf').generate(f)</span></div><div class="line"><span class="comment"># 你可以通过font_path参数来设置字体集</span></div><div class="line"><span class="comment">#background_color参数为设置背景颜色,默认颜色为黑</span></div><div class="line"></div><div class="line"><span class="keyword">import</span> matplotlib.pyplot <span class="keyword">as</span> plt</div><div class="line">plt.imshow(wordcloud)</div><div class="line">plt.axis(<span class="string">"off"</span>)</div><div class="line">plt.show()</div><div class="line"></div><div class="line">wordcloud.to_file(<span class="string">'test.png'</span>)</div><div class="line"><span class="comment"># 保存图片,但是在第三模块的例子中 图片大小将会按照 mask 保存</span></div></pre></td></tr></table></figure><a id="more"></a><h2 id="利用背景图片生成词云"><a href="#利用背景图片生成词云" class="headerlink" title="利用背景图片生成词云"></a>利用背景图片生成词云</h2><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div><div class="line">42</div><div class="line">43</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">from</span> os <span class="keyword">import</span> path</div><div class="line"><span class="keyword">from</span> PIL <span class="keyword">import</span> Image</div><div class="line"><span class="keyword">import</span> numpy <span class="keyword">as</span> np</div><div class="line"><span class="keyword">import</span> matplotlib.pyplot <span class="keyword">as</span> plt</div><div class="line"><span class="keyword">from</span> wordcloud <span class="keyword">import</span> WordCloud, STOPWORDS, ImageColorGenerator</div><div class="line"></div><div class="line">d = path.dirname(__file__)</div><div class="line"></div><div class="line"><span class="comment"># Read the whole text.</span></div><div class="line">text = open(path.join(d, <span class="string">'moment.txt'</span>)).read()</div><div class="line"></div><div class="line"><span class="comment"># read the mask / color image taken from</span></div><div class="line"><span class="comment"># http://jirkavinse.deviantart.com/art/quot-Real-Life-quot-Alice-282261010</span></div><div class="line">alice_coloring = np.array(Image.open(path.join(d, <span class="string">"alice_color.png"</span>)))</div><div class="line"></div><div class="line"><span class="comment"># 设置停用词</span></div><div class="line">stopwords = set(STOPWORDS)</div><div class="line">stopwords.add(<span class="string">"life"</span>)</div><div class="line"></div><div class="line"><span class="comment"># 你可以通过 mask 参数 来设置词云形状</span></div><div class="line">wc = WordCloud(background_color=<span class="string">"white"</span>, max_words=<span class="number">2000</span>, mask=alice_coloring,</div><div class="line"> stopwords=stopwords, max_font_size=<span class="number">40</span>, random_state=<span class="number">42</span>)</div><div class="line"><span class="comment"># generate word cloud</span></div><div class="line">wc.generate(text)</div><div class="line"></div><div class="line"><span class="comment"># create coloring from image</span></div><div class="line">image_colors = ImageColorGenerator(alice_coloring)</div><div class="line"></div><div class="line"><span class="comment"># show</span></div><div class="line"><span class="comment"># 在只设置mask的情况下,你将会得到一个拥有图片形状的词云</span></div><div class="line">plt.imshow(wc, interpolation=<span class="string">"bilinear"</span>)</div><div class="line">plt.axis(<span class="string">"off"</span>)</div><div class="line">plt.figure()</div><div class="line"><span class="comment"># recolor wordcloud and show</span></div><div class="line"><span class="comment"># we could also give color_func=image_colors directly in the constructor</span></div><div class="line"><span class="comment"># 我们还可以直接在构造函数中直接给颜色</span></div><div class="line"><span class="comment"># 通过这种方式词云将会按照给定的图片颜色布局生成字体颜色策略</span></div><div class="line">plt.imshow(wc.recolor(color_func=image_colors), interpolation=<span class="string">"bilinear"</span>)</div><div class="line">plt.axis(<span class="string">"off"</span>)</div><div class="line">plt.figure()</div><div class="line">plt.imshow(alice_coloring, cmap=plt.cm.gray, interpolation=<span class="string">"bilinear"</span>)</div><div class="line">plt.axis(<span class="string">"off"</span>)</div><div class="line">plt.show()</div></pre></td></tr></table></figure>]]></content>
<summary type="html">
<p> 今天介绍一个python库－－wordcloud，这个库的主要功能是对一个文本中的单词进行统计，并且以词云的方式进行展示，从生成的图片中，我们可以直观的发现哪些单词出现的频率较高，一个很有意思的用途就是统计一个会议中，提交论文的主题是哪些，从而看出当前研究的趋势。</p>
<h3 id="快速安装词云"><a href="#快速安装词云" class="headerlink" title="快速安装词云"></a>快速安装词云</h3><figure class="highlight plain"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">pip install wordcloud</div></pre></td></tr></table></figure>
<h3 id="快速生成词云"><a href="#快速生成词云" class="headerlink" title="快速生成词云"></a>快速生成词云</h3><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">from</span> wordcloud <span class="keyword">import</span> WordCloud</div><div class="line"></div><div class="line">f = open(<span class="string">u'moment.txt'</span>,<span class="string">'r'</span>).read()</div><div class="line">wordcloud = WordCloud(background_color=<span class="string">"white"</span>,width=<span class="number">1000</span>, height=<span class="number">860</span>, margin=<span class="number">2</span>).generate(f)</div><div class="line"></div><div class="line"><span class="comment"># width,height,margin可以设置图片属性</span></div><div class="line"><span class="comment"># generate 可以对全部文本进行自动分词,但是他对中文支持不好,对中文的分词处理请看我的下一篇文章</span></div><div class="line"><span class="comment">#wordcloud = WordCloud(font_path = r'~\Fonts\simkai.ttf').generate(f)</span></div><div class="line"><span class="comment"># 你可以通过font_path参数来设置字体集</span></div><div class="line"><span class="comment">#background_color参数为设置背景颜色,默认颜色为黑</span></div><div class="line"></div><div class="line"><span class="keyword">import</span> matplotlib.pyplot <span class="keyword">as</span> plt</div><div class="line">plt.imshow(wordcloud)</div><div class="line">plt.axis(<span class="string">"off"</span>)</div><div class="line">plt.show()</div><div class="line"></div><div class="line">wordcloud.to_file(<span class="string">'test.png'</span>)</div><div class="line"><span class="comment"># 保存图片,但是在第三模块的例子中 图片大小将会按照 mask 保存</span></div></pre></td></tr></table></figure>
</summary>
<category term="工具资源" scheme="http://yoursite.com/categories/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90/"/>
<category term="工具资源，词云" scheme="http://yoursite.com/tags/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90%EF%BC%8C%E8%AF%8D%E4%BA%91/"/>
</entry>
<entry>
<title>Exploring Word Vectors with GloVe</title>
<link href="http://yoursite.com/2018/01/12/Golve/"/>
<id>http://yoursite.com/2018/01/12/Golve/</id>
<published>2018-01-12T11:25:20.000Z</published>
<updated>2018-01-12T11:28:14.006Z</updated>
<content type="html"><![CDATA[<p>在处理文字时，处理庞大但是稀少的语言是很困难的。即使对于一个晓得语料库，神经网络也需要支持数以千计的离散输入和输出。</p><p>除了原始数字外，将单词表示为one-hot向量的方法无法捕获任何有关单词之间关系的信息。</p><p>Ｗord Vector 通过在多维向量空间中表示单词来解决这个问题。这样就可以将问题的维度数十万减少到数百。而且向量空间能够从距离向量之间的夹角来捕获单词之间的语义关系。</p><p><img src="../img/analogy.png" alt="analogy"></p><p>现已有一些创建Ｗord Vector的技巧。word2vec算法可预测上下文中的单词(例如”the cat”最可能出现的单词是”the mouse”)，而Glove向量则基于整个语料库的全局计数。glove最大的特点就是可以轻松的下载多套预先训练好的词向量。</p><a id="more"></a><h3 id="Loading-word-vectors"><a href="#Loading-word-vectors" class="headerlink" title="Loading word vectors"></a>Loading word vectors</h3><p>Torchtext包括下载GloVe（和其他）嵌入的函数。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">import</span> torch</div><div class="line"><span class="keyword">import</span> torchtext.vocab <span class="keyword">as</span> vocab</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">glove = vocab.GloVe(name=<span class="string">'6B'</span>, dim=<span class="number">100</span>)</div></pre></td></tr></table></figure><blockquote><p>[out]: 98%|█████████▊| 391063/400000 [00:19<00:00, 19964.76it/s]<br> 98%|█████████▊| 393086/400000 [00:19<00:00, 19965.52it/s]<br> 99%|█████████▉| 395108/400000 [00:19<00:00, 19966.79it/s]<br> 99%|█████████▉| 397132/400000 [00:19<00:00, 19968.13it/s]<br> 100%|█████████▉| 399154/400000 [00:19<00:00, 19968.55it/s]<br> 100%|██████████| 400000/400000 [00:20<00:00, 19969.45it/s]</p></blockquote><p>返回的GloVe对象包含以下属性：</p><ul><li><code>stoi</code> <em>string-to-index</em> returns a dictionary of words to indexes</li><li><code>itos</code> <em>index-to-string</em> returns an array of words by index</li><li><code>vectors</code> returns the actual vectors. To get a word vector get the index to get the vector</li></ul><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">def</span> <span class="title">get_word</span><span class="params">(word)</span>:</span></div><div class="line"> <span class="keyword">return</span> glove.vectors[glove.stoi[word]]</div><div class="line"><span class="comment">#get_word('google') 输出size为100的向量</span></div></pre></td></tr></table></figure><h3 id="Finding-closest-vectors"><a href="#Finding-closest-vectors" class="headerlink" title="Finding closest vectors"></a>Finding closest vectors</h3><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">def</span> <span class="title">closest</span><span class="params">(vec, n=<span class="number">10</span>)</span>:</span></div><div class="line"> <span class="string">"""</span></div><div class="line"><span class="string"> Find the closest words for a given vector</span></div><div class="line"><span class="string"> """</span></div><div class="line"> all_dists = [(w, torch.dist(vec, get_word(w))) <span class="keyword">for</span> w <span class="keyword">in</span> glove.itos]</div><div class="line"> <span class="keyword">return</span> sorted(all_dists, key=<span class="keyword">lambda</span> t: t[<span class="number">1</span>])[:n]</div><div class="line"><span class="function"><span class="keyword">def</span> <span class="title">print_tuples</span><span class="params">(tuples)</span>:</span></div><div class="line"> <span class="keyword">for</span> tuple <span class="keyword">in</span> tuples:</div><div class="line"> print(<span class="string">'(%.4f) %s'</span> % (tuple[<span class="number">1</span>], tuple[<span class="number">0</span>]))</div><div class="line">print_tuples(closest(get_word(<span class="string">'google'</span>)))</div></pre></td></tr></table></figure><blockquote><p>[out]: (0.0000) google<br> (3.0772) yahoo<br> (3.8836) microsoft<br> (4.1048) web<br> (4.1082) aol<br> (4.1165) facebook<br> (4.3917) ebay<br> (4.4122) msn<br> (4.4540) internet<br> (4.4651) netscape</p></blockquote><h3 id="Word-analogies-with-vector-arithmetic"><a href="#Word-analogies-with-vector-arithmetic" class="headerlink" title="Word analogies with vector arithmetic"></a>Word analogies with vector arithmetic</h3><p>训练有素的单词向量空间的最有趣的特征是可以用正则向量算法来捕捉某些语义关系（不仅仅是单词的紧密性）。</p><p><img src="../../Pictures/datastructure/anology_ex.png" alt="anology_ex"></p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div></pre></td><td class="code"><pre><div class="line"><span class="comment"># In the form w1 : w2 :: w3 : ?</span></div><div class="line"><span class="function"><span class="keyword">def</span> <span class="title">analogy</span><span class="params">(w1, w2, w3, n=<span class="number">5</span>, filter_given=True)</span>:</span></div><div class="line"> print(<span class="string">'\n[%s : %s :: %s : ?]'</span> % (w1, w2, w3))</div><div class="line"> </div><div class="line"> <span class="comment"># w2 - w1 + w3 = w4</span></div><div class="line"> closest_words = closest(get_word(w2) - get_word(w1) + get_word(w3))</div><div class="line"> </div><div class="line"> <span class="comment"># Optionally filter out given words</span></div><div class="line"> <span class="keyword">if</span> filter_given:</div><div class="line"> closest_words = [t <span class="keyword">for</span> t <span class="keyword">in</span> closest_words <span class="keyword">if</span> t[<span class="number">0</span>] <span class="keyword">not</span> <span class="keyword">in</span> [w1, w2, w3]]</div><div class="line"> </div><div class="line"> print_tuples(closest_words[:n])</div></pre></td></tr></table></figure><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div></pre></td><td class="code"><pre><div class="line">analogy(<span class="string">'king'</span>, <span class="string">'man'</span>, <span class="string">'queen'</span>)</div></pre></td></tr></table></figure><blockquote><p>[out]: [king : man :: queen : ?]<br> (4.0811) woman<br> (4.6916) girl<br> (5.2703) she<br> (5.2788) teenager<br> (5.3084) boy</p></blockquote>]]></content>
<summary type="html">
<p>在处理文字时，处理庞大但是稀少的语言是很困难的。即使对于一个晓得语料库，神经网络也需要支持数以千计的离散输入和输出。</p>
<p>除了原始数字外，将单词表示为one-hot向量的方法无法捕获任何有关单词之间关系的信息。</p>
<p>Ｗord Vector 通过在多维向量空间中表示单词来解决这个问题。这样就可以将问题的维度数十万减少到数百。而且向量空间能够从距离向量之间的夹角来捕获单词之间的语义关系。</p>
<p><img src="../img/analogy.png" alt="analogy"></p>
<p>现已有一些创建Ｗord Vector的技巧。word2vec算法可预测上下文中的单词(例如”the cat”最可能出现的单词是”the mouse”)，而Glove向量则基于整个语料库的全局计数。glove最大的特点就是可以轻松的下载多套预先训练好的词向量。</p>
</summary>
<category term="工具资源" scheme="http://yoursite.com/categories/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90/"/>
<category term="工具资源" scheme="http://yoursite.com/tags/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90/"/>
<category term="Glove词向量" scheme="http://yoursite.com/tags/Glove%E8%AF%8D%E5%90%91%E9%87%8F/"/>
</entry>
<entry>
<title>An Empirical Study of Language CNN for Image Captioning</title>
<link href="http://yoursite.com/2018/01/10/language-CNN/"/>
<id>http://yoursite.com/2018/01/10/language-CNN/</id>
<published>2018-01-10T13:16:39.000Z</published>
<updated>2018-01-10T13:22:53.769Z</updated>
<content type="html"><![CDATA[<h3 id="Abstract"><a href="#Abstract" class="headerlink" title="Abstract"></a>Abstract</h3><p>In contrast to previous models which predict next word based on one previous word and hidden state, our language CNN is fed with all the previous words and can model the long-range dependencies in history words, which are critical for image captioning.</p><h3 id="Introduction"><a href="#Introduction" class="headerlink" title="Introduction"></a>Introduction</h3><p>Image captioning model should be capable of capturing implicit semantic information of an im-age and generating humanlike sentences. Most image captioning models follow the encoder-decoder pipeline.</p><p>Although models like LSTM networks have memory cells which aim to memorize history information for long-term, they are still limited to several time steps because long-term information is gradually diluted at every time step</p><p>To better model the hierarchical structure and long-term dependencies in word sequences we adopt a language CNN which applies temporal convolution to extract features from sequences.</p><p>To summarize, our primary contribution lies in incorporating a language CNN, which is capable of capturing long-range dependencies in sequences, with RNNs for image captioning.</p><a id="more"></a><h3 id="Model-Architecture"><a href="#Model-Architecture" class="headerlink" title="Model Architecture"></a>Model Architecture</h3><h4 id="Overall-Framework"><a href="#Overall-Framework" class="headerlink" title="Overall Framework"></a>Overall Framework</h4><p><img src="../img/language_CNN.png" alt="language_CNN"></p><p>Given an image I, we take the widely-used CNN architecture VGGNet (16-layer) pre-trained on ImageNet to extract the image features $V \in R^K$ .</p><script type="math/tex; mode=display">V = CNN_L(I)</script><h4 id="CNN-L-Layer"><a href="#CNN-L-Layer" class="headerlink" title="$CNN_L$ Layer"></a>$CNN_L$ Layer</h4><p>The $CNN_L$ is designed to represent words and their hierarchical structure in word sequences. It takes a sequence of t generated words (each word is encoded as a one-hot representation) as inputs and generates a bottom-up representation of these words.</p><p>The first layer of $CNN_L$ is a word embedding layer.Suppose we have t input words$S = ${$ {S^{[0]}, S^{[1]}, … , S^{[t-1]}}$ }, $S^{[i]}$ is the one-of-V( one-hot ) encoding.</p><p>We map each word $S^{[t]}$ in the sentence into a K-dimensional vector $x^{[t]} = W_{e}S^{[t]}$, $W_e \in R^{K \times V}$ is word embedding matrix. Those embedding are concatenated to produce a matrix:</p><script type="math/tex; mode=display">x = [x^{[0]}, x^{[1]}, ... , x^{[t-1]}]^{T} x \in R^{t \times K}</script><p>We use the temporal convolution to model the sentence. Given an input feature map $y^{(\ell-1)} \in R^{M_{\ell-1}\times K}$of Layer-$\ell$-1,the output feature map $y^{(\ell)} \in R^{M_{\ell}\times K}$of the temporal convolution layer-$\ell$ will be:</p><script type="math/tex; mode=display">y_i^{(l)}(x) = \delta (w_L^{(l)}y_i^{(\ell -1)}+b_L^{\ell})</script><p>here $y_i^{(l)}(x)$ dives the output feature map for location $i$ in Layer-$\ell$ , $w_L^{(l)}$denotes the parameters on Layer-$\ell$. The input feature map $y_i^{(\ell -1)}$ is the segment of Layer-$\ell$-1 for the convolution at location $i$.</p><p>While $y^{[0]}$ is the concatenation of $t$ word embeddings from the sequence input $S^{[0:t-1]}$.</p><p><img src="../img/sentence_modeling.png" alt="sentence_modeling"></p><p>The output features of the final convolution layer are fed into a fully connected layer that projects the extracted words features into a low-dimensional representation. Next, the projected features will be fed to a highway connection which controls flows of information in the layer and improves the gradient flow. The final output of the highway connection is a K-dimensional vector $y^{[t]}$.</p><h4 id="Multimodal-Fusion-Layer"><a href="#Multimodal-Fusion-Layer" class="headerlink" title="Multimodal Fusion Layer"></a>Multimodal Fusion Layer</h4><script type="math/tex; mode=display">m^{[t]} = f_{multimodal}(y^{[t]},V) = \delta (f_y; W_Y,b_Y)+g_v(V; W_V,b_V)</script><h4 id="Recurrent-Networks"><a href="#Recurrent-Networks" class="headerlink" title="Recurrent Networks"></a>Recurrent Networks</h4><p>RHN has directly gated connections between previous state $r^{[t-1]}$and current input $z^{[t]}$ to modulate the flow of information. The transition equations of RHN can be formulated as follows:</p><p><img src="../img/RHN.png" alt="RHN"></p><p><img src="../img/highway_net.png" alt="highway_net"></p><p>where $c^{[t]}$ is the carry gate, $t^{[t]}$is the transform gate, $h^{[t]}$ denotes the modulated input, M:$R^{2K+d} \rightarrow R^{3d}$ is an affine trandformation. $z^{[t]} \in R^{[2k]}$ denotes the concatenation of two vectors: $m^{[t]}$ and $x^{[t-1]}$.</p><script type="math/tex; mode=display">z^{[t]} = [f_{multimodal}(CNN_L(x^{[0,...,t-1]}),V);x^{[t-1]}]</script><h4 id="Training"><a href="#Training" class="headerlink" title="Training"></a>Training</h4><p>During training, given the ground truth words S and corresponding image I, the loss function for a single training instance (S, I) is defined as a sum of the negative log likelihood of the words. The loss can be written as:</p><script type="math/tex; mode=display">L(S,I) = - \sum_{T=0}^{N-1}log P(S^{[t]}|S^{[0]},...,S^{[t-1]},I)</script><p>where N is the sequence length, and $S^{[t]}$ denotes a word in the sentence S. The training objective is to minimize the cost function.</p><h3 id="Experiment"><a href="#Experiment" class="headerlink" title="Experiment"></a>Experiment</h3><h4 id="Datasets-and-Evaluation-Metrics"><a href="#Datasets-and-Evaluation-Metrics" class="headerlink" title="Datasets and Evaluation Metrics"></a>Datasets and Evaluation Metrics</h4><p><strong>BLEU</strong>-n is a precision-based metric. It measures how many words are shared by the generated captions and ground truth captions.</p><p><strong>METEOR</strong> is based on the explicit word to word matches between generated captions and ground-truth captions.</p><p><strong>CIDEr</strong> is a metric developed specifically for evaluating image captions. It measures consensus in image caption by performing a Term Frequency-Inverse Document Frequency weighting for each n-gram.</p><p><strong>SPICE</strong> is a more recent metric which has been shown to correlate better with the human judgment<br>of semantic quality than previous metrics.</p><h4 id="Results-Using-CNN-L-on-MS-COCO-and-Filcker30k"><a href="#Results-Using-CNN-L-on-MS-COCO-and-Filcker30k" class="headerlink" title="Results Using CNN L on MS COCO and Filcker30k"></a>Results Using CNN L on MS COCO and Filcker30k</h4><p><img src="../img/ms_coco.png" alt="ms_coco"></p><p><img src="../img/flicker30k.png" alt="flicker30k"></p><p><img src="../img/MS_coco.png" alt="MS_coco"></p><h3 id="Conclusion"><a href="#Conclusion" class="headerlink" title="Conclusion"></a>Conclusion</h3><p>In this work, we present an image captioning model with language CNN to explore both hierarchical and temporal information in sequence for image caption generation. Experiments conducted on MS COCO and Flickr30K image captioning datasets validate our proposal and analysis. Performance improvements are clearly observed when compared with other image captioning methods. Future research directions will go towards integrating extra attributes learning into image captioning, and how to apply a single language CNN for image caption generation is worth trying.</p>]]></content>
<summary type="html">
<h3 id="Abstract"><a href="#Abstract" class="headerlink" title="Abstract"></a>Abstract</h3><p>In contrast to previous models which predict next word based on one previous word and hidden state, our language CNN is fed with all the previous words and can model the long-range dependencies in history words, which are critical for image captioning.</p>
<h3 id="Introduction"><a href="#Introduction" class="headerlink" title="Introduction"></a>Introduction</h3><p>Image captioning model should be capable of capturing implicit semantic information of an im-age and generating humanlike sentences. Most image captioning models follow the encoder-decoder pipeline.</p>
<p>Although models like LSTM networks have memory cells which aim to memorize history information for long-term, they are still limited to several time steps because long-term information is gradually diluted at every time step</p>
<p>To better model the hierarchical structure and long-term dependencies in word sequences we adopt a language CNN which applies temporal convolution to extract features from sequences.</p>
<p>To summarize, our primary contribution lies in incorporating a language CNN, which is capable of capturing long-range dependencies in sequences, with RNNs for image captioning.</p>
</summary>
<category term="论文" scheme="http://yoursite.com/categories/%E8%AE%BA%E6%96%87/"/>
<category term="论文，image caption model" scheme="http://yoursite.com/tags/%E8%AE%BA%E6%96%87%EF%BC%8Cimage-caption-model/"/>
</entry>
<entry>
<title>Exploring the Limits of Language Modeling</title>
<link href="http://yoursite.com/2018/01/09/language-modeling-limit/"/>
<id>http://yoursite.com/2018/01/09/language-modeling-limit/</id>
<published>2018-01-09T02:46:00.000Z</published>
<updated>2018-01-09T02:49:01.917Z</updated>
<content type="html"><![CDATA[<h3 id="ABSTRACT"><a href="#ABSTRACT" class="headerlink" title="ABSTRACT"></a>ABSTRACT</h3><p>We extend current models to deal with two key challenges present in this task: corpora and vocabulary sizes, and complex, long term structure of language. We perform an exhaustive study on techniques such as character Convolutional Neural Networks or Long-Short Term Memory, on the One Billion Word Benchmark.</p><h3 id="Introduction"><a href="#Introduction" class="headerlink" title="Introduction"></a>Introduction</h3><p>Models which can accurately place distributions over sentences not only encode complexities of language such as grammatical structure, but also distill a fair amount of information about the knowledge that a corpora may contain.(提取大量关于语料库可能包含的知识的信息).</p><p>Language Modeling can apply in speech recoginition, machine translation, text summarization etc. (such as word error rate for speech recognition, or BLEU score for translation). </p><p>When trained on vast amounts of data, language models compactly extract knowledge encoded in the training data. For example, when trained on movie subtitles, language models are able to generate basic answers to questions about object colors, facts about people, etc.</p><a id="more"></a><p>language model such as N-grams, only use a short history of previous words to predict the next word, , they are still a key component to high quality, low perplexity Language Modeling. RNNs based language model are great in combination with N-grams.</p><p>The contributions:</p><blockquote><p>Unify some of the current research on larger scale LM</p><p>Designed a Softmax loss which is based on character level CNNs instead of a full softmax</p><p>Reduce the number of parameters </p></blockquote><h3 id="Related-Work"><a href="#Related-Work" class="headerlink" title="Related Work"></a>Related Work</h3><h4 id="Language-Models"><a href="#Language-Models" class="headerlink" title="Language Models"></a>Language Models</h4><p>Much work has been done on both parametric (e.g., log-linear models) and non-parametric approaches (e.g., count-based LMs).</p><p>Count-based approaches(based on statistics of N-grams). For example: unigram, bigram, trigram, 5-gram models. Log-linear approaches(based on recurrent neural network). For example: RNN-based, LSTM, GRU.</p><p><img src="../img/char_RNN.png" alt="char_RNN"></p><h4 id="Convolution-Embedding-Models"><a href="#Convolution-Embedding-Models" class="headerlink" title="Convolution Embedding Models"></a>Convolution Embedding Models</h4><p>There is an increased interest in incorporating character-level inputs to build word embeddings for various NLP problems, including part-of-speech tagging, parsing and language modeling.</p><p>Several approach building word embedding: </p><blockquote><p><strong>Bidirectional LSTMs </strong>over the characters.<br><strong>The recurrent networks</strong> process sequences of characters from both sides and their final state vectors are concatenated.<br>The words characters are processed by a <strong>1-d CNN</strong> with max-pooling across the sequence for each convolutional feature. <strong>The resulting features are fed to a 2-layer highway network, which allows the embedding to learn semantic representations.</strong></p></blockquote><h4 id="Softmax-Over-Large-Vocabularies"><a href="#Softmax-Over-Large-Vocabularies" class="headerlink" title="Softmax Over Large Vocabularies"></a>Softmax Over Large Vocabularies</h4><p>Assigning probability distributions over large vocabularies is computationally challenging. For modeling language, maximizing log-likelihood of a given word sequence leads to optimizing cross entropy between the target probability distribution, and our model predictions $p$. Generaly, predictions come from a linear layer follows by a Sofemax non-linearity: $p(w)={\exp(z_w) \over \sum_{w’ \in V} exp(z_{w’})}$,where $z_w$ is the logit corresponding to a word $w$. The logit is generally computed as an inner product $z_w = h^Te_w$ where $h$ is a context vector and $e_w$ is a “word embedding” for $w$.</p><p>The main challenge when $|V|$ is very large is the fact that computing all inner products between h and all embeddings becomes prohibitively slow during training. Several approaches have been proposed to cope with the scaling issue: <strong>importance sampling , Noise Contrastive Estimation (NCE), self normalizing partition functions, Hierarchical Softmax</strong>.</p><h3 id="Language-Modeling-Improvements"><a href="#Language-Modeling-Improvements" class="headerlink" title="Language Modeling Improvements"></a>Language Modeling Improvements</h3><p>Recurrent Neural Networks based LMs employ the chain rule to model joint probabilities over word sequences:</p><script type="math/tex; mode=display">p(w_1,...,w_N)=\prod_{i=1}^{N}p(w_i|w_{i-1},...,x_1)</script><p>where the context of all previous words is encoded with an LSTM, and the probability over words uses a Softmax.</p><h4 id="Relationship-between-Noise-Contrastive-Estimation-and-Importance-Sampling"><a href="#Relationship-between-Noise-Contrastive-Estimation-and-Importance-Sampling" class="headerlink" title="Relationship between Noise Contrastive Estimation and Importance Sampling"></a>Relationship between Noise Contrastive Estimation and Importance Sampling</h4><p>A large scale Softmax is necessary for training good LMs because of the vocabulary size. A <strong>Hierarchical Softmax</strong> employs a tree in which the probability distribution over words is decomposed into a product of two probabilities for each word, greatly reducing training and inference time as only the path specified by the hierarchy needs to be computed and updated. Choosing a good hierarchy is important for obtaining good results and we did not explore this approach further for this paper as sampling methods worked well for our setup.</p><p><strong>Sampling approaches</strong> are only useful during training, as they propose an approximation to the loss which is cheap to compute (also in a distributed setting) – however, at inference time one still has to compute the normalization term over all words. Noise Contrastive Estimation (NCE) pro-<br>poses to consider a surrogate binary classification task in which a classifier is trained to discriminate between true data, or samples coming from some arbitrary distribution. If both the noise and data distributions were known, the optimal classifier would be:</p><script type="math/tex; mode=display">p(Y = true|w) = {p_d(w) \over p_d(w)+kp_n(w) }</script><p>where $Y$ is the binary random variable indicating whether w comes from the true data distribution, $k$ is the number of negative samples per positive word, and $p_d$ and $p_n$ are the data and noise distribution respectively (we dropped any dependency on previous words for notational simplicity). It is easy to show that if we train a logistic classifier $p_{\theta}(Y=true|w) = \sigma(s_{\theta}(w,h)-logkp_n(w))$, then, $p’(w)=softmax(s_{\theta}(w,h))$ is good approximation of $p_d(w)$($s_{\theta}$ is a logit which e.g. an LSTM LM computes).</p><p>The other technique, which is based on <strong>importance sampling (IS)</strong>, proposes to directly approximate the partition function (which comprises a sum over all words) with an estimate of it through importance sampling. Though the methods look superficially similar, we will derive a similar surrogate classification task akin to NCE which arrives at IS, showing a strong connection between the two.</p><p>Suppose that, instead of having a binary task to decide if a word comes from the data or from the noise distribution, we want to identify the words coming from the true data distribution in a set</p><p>$W={w_1,…,W_{k+1}}$, comprised of $k$ noise samples and one data distribution sample. we can train a multiclass loss over a multinomial random variable $Y$ which maximizes $logp(Y=1|W)$, assuming w.l.o.g. that $w_1 \in W$ is always the word coming from true data. By Bayes rule, and ignoring terms that are constant with respect to $Y$, we can write:</p><script type="math/tex; mode=display">p(Y=k|W) \propto_{Y}{p_d(w_k) \over p_n(w_k)}</script><p>and, following a similar argument than for NCE, if we define :$p(Y=k|W) = softmax(s_{\theta}(w_k)-logp_n(w_k))$ then $p’(w)=softmax(s_{\theta}(w,h))$. Note that the only difference between NCE and IS is that, in NCE, we define a binary classification task<br>between true or noise words with a logistic loss, whereas in IS we define a multiclass classification problem with a Softmax and cross entropy loss. We hope that our derivation helps clarify the similarities and differences between the two. In particular, we observe that IS, as it optimizes<br>a multiclass classification task (in contrast to solving a binary task), may be a better choice. Indeed, the updates to the logits with IS are tied whereas in NCE they are independent.</p><h4 id="CNN-softmax"><a href="#CNN-softmax" class="headerlink" title="CNN softmax"></a>CNN softmax</h4><p>The character-level features allow for a smoother and compact parametrization of the word embeddings. Recall that the Softmax computers a logit as $z_w=h^Te_w$ where $h$ is a context vector and $e_w$ is a “word embedding” for $w$. Instead of building a matrix of$|V| \times |h|$(whose rows correspond to $e_w$), we produce $e_w$w with a CNN over the characters of $w$ as$e_w=CNN(chars_w)$– we call this a CNN Softmax. We used the same network architecture to dynamically generate the Softmax word embeddings without sharing the parameters with the input word-embedding sub-network. For inference, the vectors $e_w$ can be precomputed, so there is no computational complexity increase w.r.t. the regular Softmax.</p><p>When using an importance sampling loss only a few logits have non-zero gradient (those corresponding to the true and sampled words). With a Softmax where $e_w$ are independently<br>learned word embeddings, this is not a problem. But we observed that, when using a CNN, all the logits become tied as the function mapping from $w$ to $e_w$ w is quite smooth. As a result, a much smaller learning rate had to be used. Even with this, the model lacks capacity to differentiate<br>between words that have very different meanings but that are spelled similarly. Thus, a reasonable compromise was to add a small correction factor which is learned per word,<br>such that:</p><script type="math/tex; mode=display">z_w=h^TCNN(chars_w)+h^TM_{corr_w}</script><p>where M is a matrix projecting a low-dimensional embedding vector $corr_w$ back up to the dimensionality of the projected LSTM hidden state of h. This amounts to adding a bottleneck linear layer, and brings the CNN Softmax much closer to our best result, where adding a 128-dim correction halves the gap between regular and the CNN Softmax.</p><p>Aside from a big reduction in the number of parameters and incorporating morphological knowledge from words, the other benefit of this approach is that out-of-vocabulary (OOV) words can easily be scored. This may be useful for other problems such as Machine Translation where handling out-of-vocabulary words is very important . This approach also allows parallel training<br>over various data sets since the model is no longer explicitly parametrized by the vocabulary size – or the language. </p><h4 id="Char-LSTM-Predictions"><a href="#Char-LSTM-Predictions" class="headerlink" title="Char LSTM Predictions"></a>Char LSTM Predictions</h4><p>The CNN Softmax layer can handle arbitrary words and is much more efficient in terms of number of parameters than the full Softmax matrix. It is, though, still considerably slow, as to evaluate perplexities we need to compute the partition function. A class of models that solve this prob-<br>lem more efficiently are character-level LSTMs. They make predictions one character at a time, thus allowing to compute probabilities over a much smaller vocabulary. On the other hand,<br>these models are more difficult to train and seem to perform worse even in small tasks like PTB Most likely this is due to the sequences becoming much longer on average as the LSTM reads the input character by character instead of word by word. </p><p>Thus, we combine the word and character-level models by feeding a word-level LSTM hidden state h into a small LSTM that predicts the target word one character at a time. In order to make the whole process reasonably efficient, we train the standard LSTM model until convergence, freeze its weights, and replace the standard word-level Softmax layer with the aforementioned character-level LSTM.</p>]]></content>
<summary type="html">
<h3 id="ABSTRACT"><a href="#ABSTRACT" class="headerlink" title="ABSTRACT"></a>ABSTRACT</h3><p>We extend current models to deal with two key challenges present in this task: corpora and vocabulary sizes, and complex, long term structure of language. We perform an exhaustive study on techniques such as character Convolutional Neural Networks or Long-Short Term Memory, on the One Billion Word Benchmark.</p>
<h3 id="Introduction"><a href="#Introduction" class="headerlink" title="Introduction"></a>Introduction</h3><p>Models which can accurately place distributions over sentences not only encode complexities of language such as grammatical structure, but also distill a fair amount of information about the knowledge that a corpora may contain.(提取大量关于语料库可能包含的知识的信息).</p>
<p>Language Modeling can apply in speech recoginition, machine translation, text summarization etc. (such as word error rate for speech recognition, or BLEU score for translation). </p>
<p>When trained on vast amounts of data, language models compactly extract knowledge encoded in the training data. For example, when trained on movie subtitles, language models are able to generate basic answers to questions about object colors, facts about people, etc.</p>
</summary>
<category term="论文" scheme="http://yoursite.com/categories/%E8%AE%BA%E6%96%87/"/>
<category term="论文，语言模型待解决问题" scheme="http://yoursite.com/tags/%E8%AE%BA%E6%96%87%EF%BC%8C%E8%AF%AD%E8%A8%80%E6%A8%A1%E5%9E%8B%E5%BE%85%E8%A7%A3%E5%86%B3%E9%97%AE%E9%A2%98/"/>
</entry>
<entry>
<title>语言模型数据处理</title>
<link href="http://yoursite.com/2018/01/04/language-model-data/"/>
<id>http://yoursite.com/2018/01/04/language-model-data/</id>
<published>2018-01-04T07:25:32.000Z</published>
<updated>2018-01-04T08:25:57.020Z</updated>
<content type="html"><![CDATA[<figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div></pre></td><td class="code"><pre><div class="line">data = [(<span class="string">"me gusta comer en la cafeteria"</span>.split(), <span class="string">"SPANISH"</span>),</div><div class="line"> (<span class="string">"Give it to me"</span>.split(), <span class="string">"ENGLISH"</span>),</div><div class="line"> (<span class="string">"No creo que sea una buena idea"</span>.split(), <span class="string">"SPANISH"</span>),</div><div class="line"> (<span class="string">"No it is not a good idea to get lost at sea"</span>.split(), <span class="string">"ENGLISH"</span>)]</div></pre></td></tr></table></figure><blockquote><p>out[]</p><p>[([‘me’, ‘gusta’, ‘comer’, ‘en’, ‘la’, ‘cafeteria’], ‘SPANISH’),<br> ([‘Give’, ‘it’, ‘to’, ‘me’], ‘ENGLISH’),<br> ([‘No’, ‘creo’, ‘que’, ‘sea’, ‘una’, ‘buena’, ‘idea’], ‘SPANISH’),<br> ([‘No’, ‘it’, ‘is’, ‘not’, ‘a’, ‘good’, ‘idea’, ‘to’, ‘get’, ‘lost’, ‘at’, ‘sea’], ‘ENGLISH’)]</p></blockquote><a id="more"></a><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div></pre></td><td class="code"><pre><div class="line">word_to_ix = {}</div><div class="line"><span class="keyword">for</span> sent, _ <span class="keyword">in</span> data + test_data:</div><div class="line"> <span class="keyword">for</span> word <span class="keyword">in</span> sent:</div><div class="line"> <span class="keyword">if</span> word <span class="keyword">not</span> <span class="keyword">in</span> word_to_ix:</div><div class="line"> word_to_ix[word] = len(word_to_ix)</div><div class="line">print(word_to_ix)</div><div class="line"><span class="keyword">print</span> (word)</div></pre></td></tr></table></figure><blockquote><p>out[] sent</p><p>[‘me’, ‘gusta’, ‘comer’, ‘en’, ‘la’, ‘cafeteria’]<br>[‘Give’, ‘it’, ‘to’, ‘me’]<br>[‘No’, ‘creo’, ‘que’, ‘sea’, ‘una’, ‘buena’, ‘idea’]<br>[‘No’, ‘it’, ‘is’, ‘not’, ‘a’, ‘good’, ‘idea’, ‘to’, ‘get’, ‘lost’, ‘at’, ‘sea’]</p><p>out[] word </p><p>me<br>gusta<br>comer<br>en<br>la<br>cafeteria<br>Give</p><p>……</p><p> out[] word_to_ix</p><p>{‘en’: 3, ‘No’: 9, ‘buena’: 14, ‘it’: 7, ‘at’: 22, ‘sea’: 12, ‘cafeteria’: 5, ‘la’: 4, ‘to’: 8, ‘creo’: 10, ‘is’: 16, ‘a’: 18, ‘good’: 19, ‘get’: 20, ‘idea’: 15, ‘que’: 11, ‘not’: 17, ‘me’: 0, ‘gusta’: 1, ‘lost’: 21, ‘Give’: 6, ‘una’: 13, ‘comer’: 2}</p></blockquote><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div><div class="line">42</div><div class="line">43</div><div class="line">44</div><div class="line">45</div><div class="line">46</div><div class="line">47</div><div class="line">48</div><div class="line">49</div><div class="line">50</div><div class="line">51</div><div class="line">52</div><div class="line">53</div><div class="line">54</div><div class="line">55</div><div class="line">56</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">import</span> os</div><div class="line"><span class="keyword">import</span> torch</div><div class="line"></div><div class="line"><span class="keyword">from</span> collections <span class="keyword">import</span> Counter</div><div class="line"></div><div class="line"></div><div class="line"><span class="class"><span class="keyword">class</span> <span class="title">Dictionary</span><span class="params">(object)</span>:</span></div><div class="line"> <span class="function"><span class="keyword">def</span> <span class="title">__init__</span><span class="params">(self)</span>:</span></div><div class="line"> self.word2idx = {}</div><div class="line"> self.idx2word = []</div><div class="line"> self.counter = Counter()</div><div class="line"> self.total = <span class="number">0</span></div><div class="line"></div><div class="line"> <span class="function"><span class="keyword">def</span> <span class="title">add_word</span><span class="params">(self, word)</span>:</span></div><div class="line"> <span class="keyword">if</span> word <span class="keyword">not</span> <span class="keyword">in</span> self.word2idx:</div><div class="line"> self.idx2word.append(word)</div><div class="line"> self.word2idx[word] = len(self.idx2word) - <span class="number">1</span></div><div class="line"> token_id = self.word2idx[word]</div><div class="line"> self.counter[token_id] += <span class="number">1</span></div><div class="line"> self.total += <span class="number">1</span></div><div class="line"> <span class="keyword">return</span> self.word2idx[word]</div><div class="line"></div><div class="line"> <span class="function"><span class="keyword">def</span> <span class="title">__len__</span><span class="params">(self)</span>:</span></div><div class="line"> <span class="keyword">return</span> len(self.idx2word)</div><div class="line"></div><div class="line"></div><div class="line"><span class="class"><span class="keyword">class</span> <span class="title">Corpus</span><span class="params">(object)</span>:</span></div><div class="line"> <span class="function"><span class="keyword">def</span> <span class="title">__init__</span><span class="params">(self, path)</span>:</span></div><div class="line"> self.dictionary = Dictionary()</div><div class="line"> self.train = self.tokenize(os.path.join(path, <span class="string">'train.txt'</span>))</div><div class="line"> self.valid = self.tokenize(os.path.join(path, <span class="string">'valid.txt'</span>))</div><div class="line"> self.test = self.tokenize(os.path.join(path, <span class="string">'test.txt'</span>))</div><div class="line"></div><div class="line"> <span class="function"><span class="keyword">def</span> <span class="title">tokenize</span><span class="params">(self, path)</span>:</span></div><div class="line"> <span class="string">"""Tokenizes a text file."""</span></div><div class="line"> <span class="keyword">assert</span> os.path.exists(path)</div><div class="line"> <span class="comment"># Add words to the dictionary</span></div><div class="line"> <span class="keyword">with</span> open(path, <span class="string">'r'</span>) <span class="keyword">as</span> f:</div><div class="line"> tokens = <span class="number">0</span></div><div class="line"> <span class="keyword">for</span> line <span class="keyword">in</span> f:</div><div class="line"> words = line.split() + [<span class="string">'<eos>'</span>]</div><div class="line"> tokens += len(words)</div><div class="line"> <span class="keyword">for</span> word <span class="keyword">in</span> words:</div><div class="line"> self.dictionary.add_word(word)</div><div class="line"></div><div class="line"> <span class="comment"># Tokenize file content</span></div><div class="line"> <span class="keyword">with</span> open(path, <span class="string">'r'</span>) <span class="keyword">as</span> f:</div><div class="line"> ids = torch.LongTensor(tokens)</div><div class="line"> token = <span class="number">0</span></div><div class="line"> <span class="keyword">for</span> line <span class="keyword">in</span> f:</div><div class="line"> words = line.split() + [<span class="string">'<eos>'</span>]</div><div class="line"> <span class="keyword">for</span> word <span class="keyword">in</span> words:</div><div class="line"> ids[token] = self.dictionary.word2idx[word]</div><div class="line"> token += <span class="number">1</span></div><div class="line"></div><div class="line"> <span class="keyword">return</span> ids</div></pre></td></tr></table></figure>]]></content>
<summary type="html">
<figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div></pre></td><td class="code"><pre><div class="line">data = [(<span class="string">"me gusta comer en la cafeteria"</span>.split(), <span class="string">"SPANISH"</span>),</div><div class="line"> (<span class="string">"Give it to me"</span>.split(), <span class="string">"ENGLISH"</span>),</div><div class="line"> (<span class="string">"No creo que sea una buena idea"</span>.split(), <span class="string">"SPANISH"</span>),</div><div class="line"> (<span class="string">"No it is not a good idea to get lost at sea"</span>.split(), <span class="string">"ENGLISH"</span>)]</div></pre></td></tr></table></figure>
<blockquote>
<p>out[]</p>
<p>[([‘me’, ‘gusta’, ‘comer’, ‘en’, ‘la’, ‘cafeteria’], ‘SPANISH’),<br> ([‘Give’, ‘it’, ‘to’, ‘me’], ‘ENGLISH’),<br> ([‘No’, ‘creo’, ‘que’, ‘sea’, ‘una’, ‘buena’, ‘idea’], ‘SPANISH’),<br> ([‘No’, ‘it’, ‘is’, ‘not’, ‘a’, ‘good’, ‘idea’, ‘to’, ‘get’, ‘lost’, ‘at’, ‘sea’], ‘ENGLISH’)]</p>
</blockquote>
</summary>
<category term="工具资源" scheme="http://yoursite.com/categories/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90/"/>
<category term="工具资源，语言模型" scheme="http://yoursite.com/tags/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90%EF%BC%8C%E8%AF%AD%E8%A8%80%E6%A8%A1%E5%9E%8B/"/>
</entry>
<entry>
<title>前向神经网络</title>
<link href="http://yoursite.com/2018/01/03/Forward%20Neural%20Network/"/>
<id>http://yoursite.com/2018/01/03/Forward Neural Network/</id>
<published>2018-01-03T14:22:21.599Z</published>
<updated>2018-01-03T14:22:21.599Z</updated>
<content type="html"><![CDATA[<h2 id="深度学习应用于自然语言处理-前向神经网络"><a href="#深度学习应用于自然语言处理-前向神经网络" class="headerlink" title="深度学习应用于自然语言处理-前向神经网络"></a>深度学习应用于自然语言处理-前向神经网络</h2><h2 id="引言"><a href="#引言" class="headerlink" title="引言"></a>引言</h2><p>深度学习的浪潮袭来，现已在各个领域中应用。深度学习的表现令人叹为观止，不得不说我们迎来了依靠深度学习的人工智能学习时代。</p><blockquote><p> 人工智能，让世界更美好。</p></blockquote><p>这一章主要是通过学习 <a href="http://cs224d.stanford.edu/" target="_blank" rel="external">Stanford cs224d</a> 课程已经阅读一些有些的博客所作出的总结。</p><a id="more"></a><h2 id="本章介绍"><a href="#本章介绍" class="headerlink" title="本章介绍"></a>本章介绍</h2><p>从数学的角度对前向神经网络数学模型进行介绍、推导和证明。</p><h2 id="前提知识"><a href="#前提知识" class="headerlink" title="前提知识"></a>前提知识</h2><p><a href="http://cs229.stanford.edu/section/cs229-linalg.pdf" target="_blank" rel="external">线性代数(Linear Algebra)</a><br><a href="http://cs229.stanford.edu/section/cs229-prob.pdf" target="_blank" rel="external">概率论(Probability Theory)</a><br><a href="http://cs229.stanford.edu/section/cs229-cvxopt.pdf" target="_blank" rel="external">凸优化(Convex Optimization)</a></p><h2 id="前向神经网络"><a href="#前向神经网络" class="headerlink" title="前向神经网络"></a>前向神经网络</h2><p>所谓神经网络就是将许多个单一“神经元”联结在一起，这样，一个“神经元”的输出就可以是另一个“神经元”的输入。以下是一个简单的<strong>三层前向全连接神经网络：</strong></p><p><img src="http://oddpnmpll.bkt.clouddn.com/2016-10-18-14%3A47%3A20.jpg" alt="neural networks"></p><p>图中<strong>x</strong>为输入层，<strong>h</strong>为隐藏层，$\hat{y}$为输出层。在全连接网络中，上一层和下一层的每个神经元都相连。隐藏层在接收到输入x后会进行一个非线性变化，再将输出信号传递给下一层。非线性变换由激活函数(activation function)实现。在数学上，我们可以用矩阵乘法（Matrix multiplication）来解释:</p><script type="math/tex; mode=display">\begin{align*}\boldsymbol{h} &= \text{sigmoid}(\boldsymbol{xW}_1+\boldsymbol{b}_1)\\\boldsymbol{\hat{y}} &= \text{softmax}(\boldsymbol{hW}_2+\boldsymbol{b}_2)\\\end{align*}</script><p>式中<strong>sigmoid</strong>和<strong>softmax</strong>都是一个激活函数,<strong>W</strong>是指两层之间的权重，<strong>b</strong>是偏置量。我们可以看到<strong>x</strong>进行了线性变换后，再做非线性变换，<strong>x</strong>输出的信号将作为<strong>b</strong>的输入。</p><h3 id="激活函数-Activation-fuction"><a href="#激活函数-Activation-fuction" class="headerlink" title="激活函数(Activation fuction)"></a>激活函数(Activation fuction)</h3><p>激活函数的作用是能够给神经网络加入一些非线性因素，使得神经网络可以更好地解决较为复杂的问题。激活函数的缺点是如果模型比较复杂，面对样本数不大的情况时容易出现<a href="http://blog.csdn.net/artprog/article/details/51278643" target="_blank" rel="external"><strong>过拟合</strong></a>。常用的激活函数还有<strong>tanh函数</strong>，<strong>RelU函数</strong>等等。</p><p><strong>sigmoid</strong>函数的数学形式：</p><script type="math/tex; mode=display">\sigma(x) = \dfrac{1}{1+e^{-x}}</script><p><strong>sigmoid</strong>函数求导：</p><script type="math/tex; mode=display">\sigma '(x)= \dfrac{e^{-x}}{(1+e^{-x})^2}=(1-\sigma)\sigma</script><p><strong>sigmoid</strong>函数和导数python实现：</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">import</span> numpy <span class="keyword">as</span> np</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">def</span> <span class="title">sigmoid</span><span class="params">(x)</span>:</span></div><div class="line"> x = <span class="number">1.</span>/(<span class="number">1</span>+np.exp(-x))</div><div class="line"> <span class="keyword">return</span> x</div><div class="line"><span class="comment"># grad</span></div><div class="line"><span class="function"><span class="keyword">def</span> <span class="title">sigmoid_grad</span><span class="params">(f)</span>:</span></div><div class="line"> f = f*(<span class="number">1</span>-f)</div><div class="line"> <span class="keyword">return</span> f</div></pre></td></tr></table></figure><p><strong>softmax</strong>函数的数学形式：</p><script type="math/tex; mode=display">\text{softmax}(z_i) = \dfrac{e^{z_i}}{\sum_{j=1}^{c} e^{z_j}} \quad 假设a_i=\text{softmax}(z_i)</script><p><strong>softmax</strong>函数求导：</p><script type="math/tex; mode=display">\begin{align*}\dfrac{\partial a_i}{\partial z_i}&=-\dfrac{e^{z_i}(\sum_{j} e^{z_j})-e^{z_i}e^{z_i}}{(\sum_{j} e^{z_j})^2}\\&=-\dfrac{e^{z_i}}{\sum_{j} e^{z_j}}+(\dfrac{e^{z_i}}{\sum_{j} e^{z_j}})^2\\&= a_i(1-a_i)\end{align*}</script><p><strong>softmax函数</strong>的实现：</p><figure class="highlight python"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">import</span> numpy</div><div class="line"><span class="comment"># 输出softmax函数值，输入向量或矩阵x</span></div><div class="line"><span class="function"><span class="keyword">def</span> <span class="title">softmax</span><span class="params">(x)</span>:</span></div><div class="line"> <span class="keyword">if</span> len(x.shape)><span class="number">1</span>:</div><div class="line"> max = np.max(x,axis=<span class="number">1</span>)[:,np.newaxis]</div><div class="line"> x -= max</div><div class="line"> x = np.exp(x)</div><div class="line"> softmax_deno = np.sum(x, axis=<span class="number">1</span>)[:,np.newaxis]</div><div class="line"> x = x/softmax_deno</div><div class="line"> <span class="keyword">else</span>:</div><div class="line"> max = np.max(x)</div><div class="line"> x -= max</div><div class="line"> x = np.exp(x)</div><div class="line"> softmax_deno = np.sum(x)</div><div class="line"> x = x/softmax_deno</div><div class="line"> <span class="keyword">return</span> x</div></pre></td></tr></table></figure><h3 id="目标函数-Objective-fuction"><a href="#目标函数-Objective-fuction" class="headerlink" title=" 目标函数(Objective fuction)"></a> 目标函数(Objective fuction)</h3><p>目标函数，有时候又称<strong>损失函数（loss function），代价函数（cost function ）</strong>，是网络中的性能参数，也是编译一个模型必须的两个参数之一。在训练模型时，我们的最终目标就是最大化或者最小化目标函数，用$J$表示目标函数。</p><script type="math/tex; mode=display">\arg\min_{\theta}\ J</script><h4 id="交叉熵-Cross-entropy"><a href="#交叉熵-Cross-entropy" class="headerlink" title="交叉熵(Cross entropy)"></a>交叉熵(Cross entropy)</h4><p>一种常见的目标函数形式：</p><script type="math/tex; mode=display">J = -\sum_{i}y_i\log{\hat{y}_i}</script><p>其中$i$代表响应的类别，$y_i$是训练样本中的标签，而$\hat{y}_i$模型预测结果。</p><p>一般情况下，我们对$y_i$使用<strong>one-hot</strong>编码，而$\hat{y}$代表了对应类别的概率$p(y_i|w,x)$，因此，$\sum_i\hat{y_i}=1$,在这里我们称$y_i$为预测函数。</p><p>*对$\hat{y}$求导： </p><script type="math/tex; mode=display">\dfrac{\partial{J}}{\partial{\hat{y}_i}}=-\dfrac{y_i}{\hat{y}_i}</script><p>对向量$\hat{\boldsymbol{y}}=(\hat{y}_1,\ \dots\ ,\hat{y}_c)$求导：</p><script type="math/tex; mode=display">\dfrac{\partial{J}}{\partial\hat{\boldsymbol{y}}}=(-\dfrac{y_1}{\hat{y}_1},\ \dots\ ,-\dfrac{y_c}{\hat{y}_c})</script><h3 id="预测函数-Predict-function"><a href="#预测函数-Predict-function" class="headerlink" title=" 预测函数(Predict function)"></a> 预测函数(Predict function)</h3><p>对于预测函数$\hat{y}_i$,我们取$\hat{y}_i$最大的$i$作为模型最终预测的类别。使用softmax函数对输出层的输入进行归一化操作，数学表示为：</p><script type="math/tex; mode=display">\hat{y_i}=p(y_i|w,x)=\dfrac{e^{z_i}}{\sum_{j=1}^{c} e^{z_j}}</script><p>其中$c$表示类别个数，在这里即是输出层的神经元个数。$z_i$为输出层的输入。</p><p>根据softmax函数的求导可知，预测函数$\hat{y}_i$对$z_i$求导：</p><script type="math/tex; mode=display">\begin{align*}\dfrac{\partial \hat{y_i}}{\partial z_i} &= -\hat{y_i}(1-\hat{y_i})\\\dfrac{\partial \hat{y_k}}{\partial z_i} &= -\hat{y_k}\hat{y_i}\end{align*}</script><p>根据链式法则，目标函数$J$对$z_i$求导：</p><script type="math/tex; mode=display">\begin{align*}\dfrac{\partial J}{\partial z_i} &=\dfrac{\partial J}{\partial \hat{y_1}} \dfrac{\partial \hat{y_1}}{\partial z_i}+\dots+ \dfrac{\partial J}{\partial \hat{y_c}} \dfrac{\partial \hat{y_c}}{\partial z_i}\\&= y_1\hat{y_i}+\dots+y_i(\hat{y_i}-1)+\dots+y_c\hat{y_i}\\&=\hat{y}_i\sum_{j=1}^cy_c-y_i\\&=\hat{y}_i-y_i\end{align*}</script><p>目标函数$J$对向量$z$求导：</p><script type="math/tex; mode=display">\begin{align*}\dfrac{\partial J}{\partial \boldsymbol{z}} = {\boldsymbol{y}}-{\hat{\boldsymbol{y}}}\end{align*}</script><h3 id="前向传播-Forward-propagation"><a href="#前向传播-Forward-propagation" class="headerlink" title="前向传播(Forward propagation)"></a>前向传播(Forward propagation)</h3><p><strong>前向传播是求目标函数值的过程</strong>，从输入层开始，样本的特征向量$x$遍历模型，到达输出层$\hat{y}$，再将$\hat{y}$和 $y$进行比较，得到目标函数值$J$： </p><script type="math/tex; mode=display">\begin{align*}\boldsymbol{h} &= sigmoid(\boldsymbol{xW}_1+\boldsymbol{b}_1)\\\boldsymbol{\hat{y}} &= sigmoid(\boldsymbol{hW}_2+\boldsymbol{b}_2)\\J &= -\sum_{i}y_i\log{\hat{y}_i}\end{align*}</script><p>训练模型的过程就是优化目标函数的过程，我们需要最小化$J=J(\boldsymbol{W}_1,\boldsymbol{b}_1,\boldsymbol{W}_2,\boldsymbol{b_2})$,这歌优化过程我们可以使用<a href="http://www.cnblogs.com/pinard/p/5970503.html" target="_blank" rel="external">梯度下降法</a>,但是由于$J$是一个非凸函数，因此不能使用梯度下降法求得全局最优，也就是不能获得的$J$最小值。</p><h3 id="随机梯度下降-Stochastic-gradient-descent"><a href="#随机梯度下降-Stochastic-gradient-descent" class="headerlink" title="随机梯度下降(Stochastic gradient descent)"></a>随机梯度下降(Stochastic gradient descent)</h3><p>我们可以求目标函数的梯度，它代表目标函数变化增加最快的地方。相反，沿着梯度相反的方向，梯度减少最快，所以我们可以使用迭代的方法更新参数，使得目标函数往着最优的方向进行优化，找到目标函数的最小值：</p><script type="math/tex; mode=display">\boldsymbol{g}^{(t)} = \dfrac{\partial{J}}{\partial{\boldsymbol{W}^{(t)}}}\\\boldsymbol{W}^{(t+1)} =\boldsymbol{W}^{(t)}+ \alpha\boldsymbol{g}^{(t)}</script><p>$t$表示第$t$次进行迭代更新，$\alpha$表示学习率，代表着每一次迭代要走的步长，$Ｗ$表示我们需要更新的参数，在本例子中，我们需要对$W_1$,$b_2$,$W_2$,$b_2$进行参数更新，每次迭代都需要进行梯度的计算，每次迭代都要计算目标函数的值。</p><p>假设训练样本数量为$N$，如果每次迭代都使用所有的训练样本。这时的目标函数是：</p><script type="math/tex; mode=display">\mathbb{J}=\mathbb{E}(J)=\dfrac{1}{N}\sum_nJ_n</script><p>当$N$很大的时候，每次迭代都十分耗时，因此收敛的速度会较慢。我们可以使用一种逼近方法，称为<strong>mini-batch</strong>。</p><ul><li><strong>mini-batch</strong>很简单，就是每次迭代更新只使用$k$个训练样本，$k$可以是100这种相对较小的数。</li><li>而<strong>随机梯度下降(SGD)</strong>是每次更新迭代只使用$1$个训练样本，即$k=1$。<strong>SGD</strong>是<strong>mini-batch</strong>的特殊情况，但是我们一般说<strong>SGD</strong>就是指<strong>mini-batch</strong>。</li></ul><h3 id="后向传播-Backward-propagation"><a href="#后向传播-Backward-propagation" class="headerlink" title="后向传播(Backward propagation)"></a>后向传播(Backward propagation)</h3><p><strong>后向传播就是一个求梯度的过程</strong>从输出层开始往输入层传入误差。</p><p>我们将三层全连接神经网络模型的前向传播表示为：</p><script type="math/tex; mode=display">\begin{align*}&\boldsymbol{z}_1 = \boldsymbol{xW_1}+\boldsymbol{b}_1\\&\boldsymbol{h} = {\text sigmoid}(\boldsymbol{z}_1)\\&\boldsymbol{z}_2 = \boldsymbol{xW_2}+\boldsymbol{b}_2\\&\hat{\boldsymbol{y}} = softmax(\boldsymbol{z}_2)\\&J = -\sum_{i}y_i\log{\hat{y}_i}\end{align*}</script><p>计算后向传播：</p><script type="math/tex; mode=display">\begin{align*}&\boldsymbol{\delta}_1 = \dfrac{\partial J}{\partial \boldsymbol{z}_2} = \hat{\boldsymbol{y}}-\boldsymbol{y}\\&\boldsymbol{\delta}_2 = \dfrac{\partial J}{\partial \boldsymbol{h}} = \boldsymbol{\delta}_1\dfrac{\partial \boldsymbol{z}_2}{\partial \boldsymbol{h}} =\boldsymbol{\delta}_1\boldsymbol{W}^T_2 \\&\boldsymbol{\delta}_3 = \dfrac{\partial J}{\partial \boldsymbol{z}_1} = \boldsymbol{\delta}_2\dfrac{\partial \boldsymbol{h}}{\partial \boldsymbol{z}_1} =\boldsymbol{\delta}_2*\sigma'(\boldsymbol{z}_1) \\&\boldsymbol{\delta}_4 = \dfrac{\partial J}{\partial \boldsymbol{x}} = \boldsymbol{\delta}_3\dfrac{\partial \boldsymbol{z}_1}{\partial \boldsymbol{x}} =\boldsymbol{\delta}_3\boldsymbol{W}^T_1 \\\end{align*}</script><p>$\boldsymbol{\delta}_1$就是预测误差，得到上面传播的误差，我们对每一层的参数求梯度：</p><script type="math/tex; mode=display">\begin{align*}\dfrac{\partial J}{\partial \boldsymbol{W}_2}&= \boldsymbol{\delta}_1 \dfrac{\partial\boldsymbol{z}_2 }{\partial \boldsymbol{W}_2} = \boldsymbol{h}^T\boldsymbol{\delta}_1\\\dfrac{\partial J}{\partial \boldsymbol{b}_2} &= \boldsymbol{\delta}_1 \dfrac{\partial\boldsymbol{z}_2 }{\partial \boldsymbol{b}_2} = \boldsymbol{\delta}_1\\\dfrac{\partial J}{\partial \boldsymbol{W}_1} &= \boldsymbol{\delta}_3 \dfrac{\partial\boldsymbol{z}_1 }{\partial \boldsymbol{W}_1} = \boldsymbol{x}^T\boldsymbol{\delta}_3\\\dfrac{\partial J}{\partial \boldsymbol{b}_1} &= \boldsymbol{\delta}_3 \dfrac{\partial\boldsymbol{z}_1 }{\partial \boldsymbol{b}_1} = \boldsymbol{\delta}_3\\\end{align*}</script>]]></content>
<summary type="html">
<h2 id="深度学习应用于自然语言处理-前向神经网络"><a href="#深度学习应用于自然语言处理-前向神经网络" class="headerlink" title="深度学习应用于自然语言处理-前向神经网络"></a>深度学习应用于自然语言处理-前向神经网络</h2><h2 id="引言"><a href="#引言" class="headerlink" title="引言"></a>引言</h2><p>深度学习的浪潮袭来，现已在各个领域中应用。深度学习的表现令人叹为观止，不得不说我们迎来了依靠深度学习的人工智能学习时代。</p>
<blockquote>
<p> 人工智能，让世界更美好。</p>
</blockquote>
<p>这一章主要是通过学习 <a href="http://cs224d.stanford.edu/" target="_blank" rel="external">Stanford cs224d</a> 课程已经阅读一些有些的博客所作出的总结。</p>
</summary>
<category term="工具资源" scheme="http://yoursite.com/categories/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90/"/>
<category term="工具资源" scheme="http://yoursite.com/tags/%E5%B7%A5%E5%85%B7%E8%B5%84%E6%BA%90/"/>
<category term="NLP" scheme="http://yoursite.com/tags/NLP/"/>
</entry>
<entry>
<title>栈和队列</title>
<link href="http://yoursite.com/2018/01/03/stack/"/>
<id>http://yoursite.com/2018/01/03/stack/</id>
<published>2018-01-03T13:30:09.000Z</published>
<updated>2018-01-03T14:15:58.074Z</updated>
<content type="html"><![CDATA[<h2 id="栈和队列"><a href="#栈和队列" class="headerlink" title="栈和队列"></a>栈和队列</h2><h3 id="栈"><a href="#栈" class="headerlink" title="栈"></a>栈</h3><p>栈(stack) 限定仅在表尾进行插入或删除操作的线性表。</p><p>表尾端称为<strong>栈顶(top)</strong>，表头端称为<strong>栈底(bottom)</strong>。</p><p><img src="../img/stackfeature.png" alt="stackfeature"></p><p><strong>后进先出</strong>的线性表。栈的抽象数据类型定义：</p><a id="more"></a><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div></pre></td><td class="code"><pre><div class="line">ADT Stack{</div><div class="line"> 数据对象： D = {ai|ai belong to ElemSet,i=<span class="number">1</span>,<span class="number">2</span>,....,n, n>=<span class="number">0</span>}</div><div class="line"> 数据关系： R1 = {<ai<span class="number">-1</span>,ai>|ai<span class="number">-1</span>,ai belong to D,i=<span class="number">1</span>,<span class="number">2</span>,....,n}</div><div class="line"> InitStack(&S)</div><div class="line"> <span class="comment">// 构造一个空栈Ｓ。</span></div><div class="line"> DestoryStack(&S)</div><div class="line"> <span class="comment">// 销毁栈Ｓ。</span></div><div class="line"> ClearStack(&S)</div><div class="line"> <span class="comment">//将S清为空栈。</span></div><div class="line"> StackEmpty(S)</div><div class="line"> <span class="comment">// 若栈Ｓ为空栈，则返回true,否则False。</span></div><div class="line"> StackLength(S)</div><div class="line"> <span class="comment">//返回S的元素个数，即栈的长度。</span></div><div class="line"> GetTop(S,&e)</div><div class="line"> <span class="comment">//用e返回S的栈顶元素。</span></div><div class="line"> Push(&S,e)</div><div class="line"> <span class="comment">//插入元素e为新的栈顶元素。</span></div><div class="line"> Pop(&S,&e)</div><div class="line"> <span class="comment">//删除S的栈顶元素，并用e返回其值。</span></div><div class="line"> </div><div class="line">}ADT Stack</div></pre></td></tr></table></figure><p>顺序栈定义：</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">typedef</span> <span class="class"><span class="keyword">struct</span>{</span></div><div class="line"> SElemType *base;</div><div class="line"> SElemType *top;</div><div class="line"> <span class="keyword">int</span> stacksize;</div><div class="line">}SqStack</div></pre></td></tr></table></figure><p>设定两个常量：<strong>STACK_INIT_SIZE</strong>(存储空间初始分配量) 和<strong>STACKINCREMENT</strong>（存储空间分配增量)</p><p><strong>top</strong>:栈顶指针，初始值指向栈底，<strong>base</strong>:栈底指针，初始值指向栈底顶，<strong>stacksize</strong>:栈当前可用容量</p><p>顺序栈模块说明：</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div><div class="line">42</div><div class="line">43</div><div class="line">44</div><div class="line">45</div><div class="line">46</div><div class="line">47</div><div class="line">48</div><div class="line">49</div><div class="line">50</div><div class="line">51</div><div class="line">52</div><div class="line">53</div><div class="line">54</div><div class="line">55</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">define</span> STACK_INIT_SIZE 100;</span></div><div class="line"><span class="meta">#<span class="meta-keyword">define</span> STACKINCREMENT 10;</span></div><div class="line"><span class="keyword">typedef</span> <span class="class"><span class="keyword">struct</span>{</span></div><div class="line"> SElemType *base;</div><div class="line"> SElemType *top;</div><div class="line"> <span class="keyword">int</span> stacksize;</div><div class="line">}SqStack;</div><div class="line"><span class="comment">//－－－－－基本操作的函数原型说明－－－－－</span></div><div class="line"><span class="function">Status <span class="title">InitStack</span><span class="params">(SqStack &S)</span></span>;</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">DestoryStack</span><span class="params">(SqStack &S)</span></span>;</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">ClearStack</span><span class="params">(SqStack &S)</span></span>;</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">StackEmpty</span><span class="params">(SqStack S)</span></span>;</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">StackLength</span><span class="params">(SqStack S)</span></span>;</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">GetTop</span><span class="params">(SqStack S,SElemType &e)</span></span>;</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">Push</span><span class="params">(SqStack &S,SElemType e)</span></span>;</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">Pop</span><span class="params">(SqStack &S,SElemType &e)</span></span>;</div><div class="line"></div><div class="line"><span class="comment">//－－－－－基本操作的算法描述－－－－－</span></div><div class="line"><span class="function">Status <span class="title">InitStack</span><span class="params">(SqStack &S)</span></span>{</div><div class="line"> S.base = (SElemType *)<span class="built_in">malloc</span>(STACK_INIT_SIZE*<span class="keyword">sizeof</span>(SElemType))</div><div class="line"> <span class="keyword">if</span>(!S.base) <span class="built_in">exit</span> (OVERFLOW); <span class="comment">//存储分配失败</span></div><div class="line"> S.top = S.base;</div><div class="line"> S.stacksize = STACK_INIT_SIZE;</div><div class="line"> <span class="keyword">return</span> Ok;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">GetTop</span><span class="params">(SqStack S,SElemType &e)</span></span>{</div><div class="line"> <span class="keyword">if</span>(S.top == S.base) <span class="keyword">return</span> ERROR;</div><div class="line"> e = *(S.top<span class="number">-1</span>);</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">Push</span><span class="params">(SqStack &S,SElemType e)</span></span>{</div><div class="line"> <span class="keyword">if</span>(S.top-S.base>=S.stacksize){</div><div class="line"> S.base = (SElemType *)<span class="built_in">realloc</span> (S.base,(S.stacksize+STACKINCREMENT)*<span class="keyword">sizeof</span>(SElemType));</div><div class="line"> <span class="keyword">if</span>(!S.base) <span class="built_in">exit</span> (OVERFLOW);</div><div class="line"> S.top = S.base+S.stacksize;</div><div class="line"> S.stacksize+= STACKINCREMENT;</div><div class="line"> }</div><div class="line"> *S.top ++ = e;</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">Pop</span><span class="params">(SqStack &S,SElemType &e)</span></span>{</div><div class="line"> <span class="keyword">if</span>(S.top == S.base) <span class="keyword">return</span> ERROR;</div><div class="line"> e = *--S.top;</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">}</div></pre></td></tr></table></figure><h3 id="栈的应用举例"><a href="#栈的应用举例" class="headerlink" title="栈的应用举例"></a>栈的应用举例</h3><p>迷宫求解（从入口到出口的路径算法）</p><p><img src="../img/migong.png" alt="migong"></p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div></pre></td><td class="code"><pre><div class="line"><span class="keyword">typedef</span> <span class="class"><span class="keyword">struct</span>{</span></div><div class="line"> <span class="keyword">int</span> ord; <span class="comment">//通道块在路径上的“序号”</span></div><div class="line"> PosType seat; <span class="comment">//通道块在迷宫中的“坐标位置”</span></div><div class="line"> <span class="keyword">int</span> di; <span class="comment">//从此通道走向下一通道块的“方向”</span></div><div class="line">}SElemType;</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">MazePath</span><span class="params">(MazeType maze,PosType start,PosType end)</span></span>{</div><div class="line"> InitStack(S); curpos = start; <span class="comment">//设定“当前位置”为“入口位置”</span></div><div class="line"> curpos = <span class="number">1</span>; <span class="comment">//探索第一步</span></div><div class="line"> <span class="keyword">do</span>{</div><div class="line"> <span class="keyword">if</span>(Pass(curpos)){ <span class="comment">//当前位置可以通过，即是未曾走到过的通道块</span></div><div class="line"> FootPrint(curpos); <span class="comment">//留下足迹</span></div><div class="line"> e = (curstep,curpos,<span class="number">1</span>);</div><div class="line"> Push(S,e); <span class="comment">//加入路径</span></div><div class="line"> <span class="keyword">if</span>(corpos == end) <span class="keyword">return</span> (TRUE);</div><div class="line"> curpos = NextPos(curpos,<span class="number">1</span>);</div><div class="line"> curpos ++; <span class="comment">//探索下一步</span></div><div class="line"> }</div><div class="line"> <span class="keyword">else</span>{ <span class="comment">//当前位置不可以通过</span></div><div class="line"> <span class="keyword">if</span>(!StackEmpty(S)){</div><div class="line"> Pop(S,e);</div><div class="line"> <span class="keyword">while</span>(e.di == <span class="number">4</span> && !StackEmpty(S)){</div><div class="line"> MarkPrint(e.seat); Pop(S,e); <span class="comment">//留下不能通过的标记，并退回一步</span></div><div class="line"> }</div><div class="line"> <span class="keyword">if</span>(e.di<<span class="number">4</span>){</div><div class="line"> e.di++; Push(S,e); <span class="comment">//换下一个方向探索</span></div><div class="line"> curpos = NextPos(e.seat,e.di);</div><div class="line"> }</div><div class="line"> }</div><div class="line"> }</div><div class="line"> }<span class="keyword">while</span>(!StackEmpty(S));</div><div class="line"> <span class="keyword">return</span> (FALSE);</div><div class="line">}</div></pre></td></tr></table></figure><h3 id="栈与递归的实现"><a href="#栈与递归的实现" class="headerlink" title="栈与递归的实现"></a>栈与递归的实现</h3><h3 id="队列"><a href="#队列" class="headerlink" title="队列"></a>队列</h3><p><strong>队列</strong>(queue)是一种<strong>先进先出</strong>的线性表。只允许在表的<strong>一端进行插入，而在另一端删除元素</strong>。</p><p>队列的抽象数据类型定义：</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div></pre></td><td class="code"><pre><div class="line">ADT Queue{</div><div class="line"> 数据对象： D = {ai|ai belong to ElemSet,i=<span class="number">1</span>,<span class="number">2</span>,....,n, n>=<span class="number">0</span>}</div><div class="line"> 数据关系： R1 = {<ai<span class="number">-1</span>,ai>|ai<span class="number">-1</span>,ai belong to D,i=<span class="number">1</span>,<span class="number">2</span>,....,n}</div><div class="line"> InitQueue(&Q)</div><div class="line"> <span class="comment">// 构造一个空队列Q。</span></div><div class="line"> DestoryQueue(&Q)</div><div class="line"> <span class="comment">// 销毁栈Q。</span></div><div class="line"> ClearQueue(&Q)</div><div class="line"> <span class="comment">//将Q清为空队列。</span></div><div class="line"> QueueEmpty(Q)</div><div class="line"> <span class="comment">// 若栈Q为空队列，则返回true,否则False。</span></div><div class="line"> QueueLength(Q)</div><div class="line"> <span class="comment">//返回S的元素个数，即队列的长度。</span></div><div class="line"> GetHead(Q,&e)</div><div class="line"> <span class="comment">//用e返回Q的队头元素。</span></div><div class="line"> EnQueue(&Q,e)</div><div class="line"> <span class="comment">//插入元素e为Q的新的队尾元素。</span></div><div class="line"> DeQueue(&S,&e)</div><div class="line"> <span class="comment">//删除Q的队头元素，并用e返回其值。</span></div><div class="line"> </div><div class="line">}ADT Queue</div></pre></td></tr></table></figure><p>链队列</p><p><img src="../img/queue.png" alt="queue"></p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div><div class="line">42</div><div class="line">43</div><div class="line">44</div><div class="line">45</div><div class="line">46</div><div class="line">47</div><div class="line">48</div><div class="line">49</div><div class="line">50</div><div class="line">51</div><div class="line">52</div><div class="line">53</div><div class="line">54</div><div class="line">55</div><div class="line">56</div><div class="line">57</div><div class="line">58</div><div class="line">59</div><div class="line">60</div><div class="line">61</div><div class="line">62</div><div class="line">63</div><div class="line">64</div><div class="line">65</div></pre></td><td class="code"><pre><div class="line"><span class="comment">//－－－－－ADT Queue的表示与实现－－－－－</span></div><div class="line"></div><div class="line"><span class="comment">//－－－－－单链队列－－队列的链式存储结构－－－－－</span></div><div class="line"><span class="keyword">typedef</span> <span class="class"><span class="keyword">struct</span> <span class="title">QNode</span>{</span></div><div class="line"> QElemType data;</div><div class="line"> <span class="class"><span class="keyword">struct</span> <span class="title">QNOde</span> *<span class="title">next</span>;</span></div><div class="line">}QNOde, *QueuePtr;</div><div class="line"></div><div class="line"><span class="keyword">typedef</span> <span class="class"><span class="keyword">struct</span>{</span></div><div class="line"> QueuePtr front <span class="comment">//队头指针</span></div><div class="line"> QueuePtr rear <span class="comment">//队尾指针</span></div><div class="line">}LinkQueue;</div><div class="line"></div><div class="line"><span class="comment">//－－－－－基本操作的函数原型说明－－－－－</span></div><div class="line"><span class="function">Status <span class="title">InitQueue</span><span class="params">(LinkQueue &Q)</span></span></div><div class="line"><span class="function"> </span></div><div class="line"><span class="function">Status <span class="title">DestoryQueue</span><span class="params">(LinkQueue &Q)</span></span></div><div class="line"><span class="function"></span></div><div class="line"><span class="function">Status <span class="title">ClearQueue</span><span class="params">(LinkQueue &Q)</span></span></div><div class="line"><span class="function"> </span></div><div class="line"><span class="function">Status <span class="title">QueueEmpty</span><span class="params">(LinkQueue Q)</span></span></div><div class="line"><span class="function"></span></div><div class="line"><span class="function">Status <span class="title">QueueLength</span><span class="params">(LinkQueue Q)</span></span></div><div class="line"><span class="function"> </span></div><div class="line"><span class="function">Status <span class="title">GetHead</span><span class="params">(LinkQueue &Q, QElemType &e)</span></span></div><div class="line"><span class="function"> </span></div><div class="line"><span class="function">Status <span class="title">EnQueue</span><span class="params">(LinkQueue &Q, QElemType e)</span></span></div><div class="line"><span class="function"> </span></div><div class="line"><span class="function">Status <span class="title">DeQueue</span><span class="params">(LinkQueue &Q, QElemType &e)</span></span></div><div class="line"><span class="function"></span></div><div class="line"><span class="function"><span class="comment">//－－－－－基本操作的算法描述－－－－－</span></span></div><div class="line"><span class="function">Status <span class="title">InitQueue</span><span class="params">(LinkQueue &Q)</span></span>{</div><div class="line"> Q.front = Q.rear = (QueuePtr)<span class="built_in">malloc</span>(<span class="keyword">sizeof</span>(QNode));</div><div class="line"> <span class="keyword">if</span>(!Q.front)<span class="built_in">exit</span>(OVERFLOW);</div><div class="line"> Q.front->next = <span class="literal">NULL</span>;</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">DestoryQueue</span><span class="params">(LinkQueue &Q)</span></span>{</div><div class="line"> <span class="keyword">while</span>(Q.front){</div><div class="line"> Q.rear = Q.front->next;</div><div class="line"> <span class="built_in">free</span>(Q.front);</div><div class="line"> Q.front = Q.rear;</div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">EnQueue</span><span class="params">(LinkQueue &Q, QElemType e)</span></span>{</div><div class="line"> p = (QueuePtr)<span class="built_in">malloc</span>(<span class="keyword">sizeof</span>(QNode));</div><div class="line"> <span class="keyword">if</span>(!p) <span class="built_in">exit</span>(OVERFLOW);</div><div class="line"> p->data = e; p->next = <span class="literal">NULL</span>;</div><div class="line"> Q.rear->next = p;</div><div class="line"> Q.rear = p;</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">DeQueue</span><span class="params">(LinkQueue &Q, QElemType &e)</span></span>{</div><div class="line"> <span class="keyword">if</span>(Q.front == Q.rear) <span class="keyword">return</span> ERROR;</div><div class="line"> p = Q.front->next;</div><div class="line"> e = p->data;</div><div class="line"> Q.front->next = p->next;</div><div class="line"> <span class="keyword">if</span>(Q.rear == p) Q.rear = Q.front;</div><div class="line"> <span class="built_in">free</span>(p);</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">}</div></pre></td></tr></table></figure><p>循环队列</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div></pre></td><td class="code"><pre><div class="line"><span class="comment">//－－－－－循环队列－－队列的顺序存储结构－－－－－</span></div><div class="line"><span class="meta">#<span class="meta-keyword">define</span> MAXQSIZE 100 <span class="comment">//最大队列长度</span></span></div><div class="line"><span class="keyword">typedef</span> <span class="class"><span class="keyword">struct</span>{</span></div><div class="line"> QElemType *base; <span class="comment">//初始化的动态分配存储空间</span></div><div class="line"> <span class="keyword">int</span> front; <span class="comment">//头指针，若队列不为空，指向队列头元素</span></div><div class="line"> <span class="keyword">int</span> rear; <span class="comment">//尾指针，若队列不为空，指向队列尾元素的下一个位置</span></div><div class="line">}sqQueue;</div><div class="line"></div><div class="line"><span class="comment">//－－－－－循环队列的基本操作的算法描述－－－－－</span></div><div class="line"><span class="function">Status <span class="title">InitQueue</span><span class="params">(SqQueue &Q)</span></span>{</div><div class="line"> <span class="comment">//构造一个空队列</span></div><div class="line"> Q.base = (QElemType ×)<span class="built_in">malloc</span>(MAXQSIZE *<span class="keyword">sizeof</span>(QElemType));</div><div class="line"> <span class="keyword">if</span>(!Q.base) <span class="built_in">exit</span>(OVERFLOW);</div><div class="line"> Q.front = Q.rear = <span class="number">0</span>;</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">QueueLength</span><span class="params">(SqQueue Q)</span></span>{</div><div class="line"> <span class="comment">//返回Ｑ的元素个数，即队列的长度</span></div><div class="line"> <span class="keyword">return</span>(Q.rear-Q.front+MAXQSIZE) % MAXQSIZE;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">EnQueue</span><span class="params">(SqQueue &Q, QElemType e)</span></span>{</div><div class="line"> <span class="comment">//插入元素ｅ为Ｑ的新的队尾元素</span></div><div class="line"> <span class="keyword">if</span>((Q.rear+<span class="number">1</span>)%MAXQSIZE == Q.front) <span class="keyword">return</span> ERROR; <span class="comment">//队列满</span></div><div class="line"> Q.base[Q.rear]= e;</div><div class="line"> Q.rear = (Q.rear+<span class="number">1</span>) % MAXQSIZE;</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function">Status <span class="title">DEQueue</span><span class="params">(SqQueue &Q, QElemType e)</span></span>{</div><div class="line"> <span class="comment">//若对垒不为空，则删除Ｑ的队头元素，用ｅ返回其值，并返回ＯＫ；</span></div><div class="line"> <span class="comment">//否则返回ＥＲＲＯＲ</span></div><div class="line"> <span class="keyword">if</span>(Q.front == Q.rear) <span class="keyword">return</span> ERROR;</div><div class="line"> e = Q.base[Q.front];</div><div class="line"> Q.front = (Q.front+<span class="number">1</span>) % MAXQSIZE;</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">}</div></pre></td></tr></table></figure>]]></content>
<summary type="html">
<h2 id="栈和队列"><a href="#栈和队列" class="headerlink" title="栈和队列"></a>栈和队列</h2><h3 id="栈"><a href="#栈" class="headerlink" title="栈"></a>栈</h3><p>栈(stack) 限定仅在表尾进行插入或删除操作的线性表。</p>
<p>表尾端称为<strong>栈顶(top)</strong>，表头端称为<strong>栈底(bottom)</strong>。</p>
<p><img src="../img/stackfeature.png" alt="stackfeature"></p>
<p><strong>后进先出</strong>的线性表。栈的抽象数据类型定义：</p>
</summary>
<category term="阅读" scheme="http://yoursite.com/categories/%E9%98%85%E8%AF%BB/"/>
<category term="阅读，栈和队列" scheme="http://yoursite.com/tags/%E9%98%85%E8%AF%BB%EF%BC%8C%E6%A0%88%E5%92%8C%E9%98%9F%E5%88%97/"/>
</entry>
<entry>
<title>Array</title>
<link href="http://yoursite.com/2018/01/02/array/"/>
<id>http://yoursite.com/2018/01/02/array/</id>
<published>2018-01-02T12:24:44.000Z</published>
<updated>2018-01-03T13:32:44.268Z</updated>
<content type="html"><![CDATA[<h2 id="线性表"><a href="#线性表" class="headerlink" title="线性表"></a>线性表</h2><h3 id="类型定义"><a href="#类型定义" class="headerlink" title="类型定义"></a>类型定义</h3><p>简言之，一个线性表是n个数据元素的有限序列。</p><p>在复杂的线性表中，一个数据元素可由若干个数据项(item)组成。在这种情况下，常把数据元素称为记录(record)，含有大量记录的线性表又称为文件（file）。</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div></pre></td><td class="code"><pre><div class="line">ADT List{</div><div class="line"> <span class="comment">//数据对象</span></div><div class="line"> D = {a1|a2 belong to ElemSet, i=<span class="number">1</span>,<span class="number">2</span>,....,n, n><span class="number">0</span>}</div><div class="line"> <span class="comment">//数据关系</span></div><div class="line"> R1 = {<ai<span class="number">-1</span>,ai>|ai<span class="number">-1.</span>ai belong to D,i = <span class="number">1</span>,<span class="number">2.</span>..n}</div><div class="line"> <span class="comment">//基本操作</span></div><div class="line"> InitList(&L)</div><div class="line"> <span class="comment">//构造一个空的线性表Ｌ</span></div><div class="line"> DestoryList(&L)</div><div class="line"> <span class="comment">//销毁线性表Ｌ</span></div><div class="line"> ClearList(&L)</div><div class="line"> <span class="comment">//将Ｌ重置为空表</span></div><div class="line"> ListEmpty(L)</div><div class="line"> <span class="comment">//若L为空表，返回True,否则False</span></div><div class="line"> ListLength(L)</div><div class="line"> <span class="comment">//返回L中数据元素个数</span></div><div class="line"> GetElem(L,i,&e)</div><div class="line"> <span class="comment">//用e返回L中第i个数据元素的值</span></div><div class="line"> ListInsert(&L,i,e)</div><div class="line"> <span class="comment">//在Ｌ中第i个位置之前插入新的数据元素e，Ｌ的长度加1。</span></div><div class="line">}</div></pre></td></tr></table></figure><a id="more"></a><p>例2.1 LA和LB中的数据元素按值非递减有序排列，要求将LA和LB归并为新的线性表LC，且LC中的数据元素仍然按值非递减有序排列。</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div></pre></td><td class="code"><pre><div class="line"><span class="comment">// LA = (3,5,8,11) LB = (2,6,8,9,11,15,20)</span></div><div class="line"><span class="comment">// LC =(2,3,5,6,8,8,9,11,11,15,20)</span></div><div class="line"></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">MergeList</span><span class="params">(List La,List Lb,List &Lc)</span></span>{</div><div class="line"> InitList(Lc);</div><div class="line"> i = j = <span class="number">1</span>; k=<span class="number">0</span>;</div><div class="line"> La_len = ListLength(La); Lb_len = ListLength(Lb);</div><div class="line"> <span class="keyword">while</span>((i<=La_len)&&(j<=Lb_len)){</div><div class="line"> GetElem(La,i,ai); GetElem(Lb,j,bj);</div><div class="line"> <span class="keyword">if</span>(ai<=bj){ListInsert(Lc,++k,ai);++i;}</div><div class="line"> <span class="keyword">else</span>{ListInsert(Lc,++k,bj);++j;}</div><div class="line"> }</div><div class="line"> <span class="keyword">while</span>(i<=La_len){</div><div class="line"> GetElem(La,i,ai);ListInsert(Lc,++k,ai);</div><div class="line"> }</div><div class="line"> <span class="keyword">while</span>(j<=Lb_len){</div><div class="line"> GetElem(Lb,i,bj);ListInsert(Lc,++k,bj);</div><div class="line"> }</div><div class="line">}</div></pre></td></tr></table></figure><h3 id="线性表的顺序表示和实现"><a href="#线性表的顺序表示和实现" class="headerlink" title="线性表的顺序表示和实现"></a>线性表的顺序表示和实现</h3><p>线性表的顺序表示指的是用一组地址连续的存储单元以此存储线性表的数据元素。</p><p>一般来说，线性表的第$i$个数据元素$a_j$的存储位置为 $LOC(a_i) = LOC(a_1)+(i-1) \times l$</p><p>线性表的这种机内表示称作线性表的顺序存储结构或顺序映像(sequential mapping)。</p><p>Ｃ语言中可用动态分配的一维数组：</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div></pre></td><td class="code"><pre><div class="line"><span class="comment">// －－－－－线性表的动态分配顺序存储结构－－－－－</span></div><div class="line"><span class="meta">#<span class="meta-keyword">define</span> LIST_INIT_SIZE 100 <span class="comment">// 线性表存储空间的初始分配量</span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">define</span> LISTINCREMENT 10 <span class="comment">// 线性表存储空间的分配增量</span></span></div><div class="line"><span class="keyword">typedef</span> <span class="class"><span class="keyword">struct</span>{</span></div><div class="line"> ElemType *elem; <span class="comment">// 存储空间基址</span></div><div class="line"> <span class="keyword">int</span> length; <span class="comment">// 当前长度</span></div><div class="line"> <span class="keyword">int</span> listsize; <span class="comment">// 当前分配的存储容量</span></div><div class="line">}SqList;</div></pre></td></tr></table></figure><p>线性表插入和删除操作：</p><p><img src="../Pictures/datastructure/insert.png" alt="insert"></p><p>一般情况下，把第$i(1\le i\le n)$个元素之前插入一个元素时，需要将第$n$至第$i$（共$n-i+1$）个元素向后移动一个位置。</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div></pre></td><td class="code"><pre><div class="line"><span class="function">Status <span class="title">ListInsert_Sq</span><span class="params">(SqList &L,<span class="keyword">int</span> i,ElemType e)</span></span>{</div><div class="line"> <span class="keyword">if</span>(i<<span class="number">1</span>||i>L.length+<span class="number">1</span>) <span class="keyword">return</span> ERROR;</div><div class="line"> <span class="keyword">if</span>(L.length>=L.listsize){ <span class="comment">//当前存储空间已满，增加分配</span></div><div class="line"> newbase = (ElemType *)<span class="built_in">realloc</span>(L.elem, (L.listsize+LISTINCREMENT)*<span class="keyword">sizeof</span>(ElemType));</div><div class="line"> <span class="keyword">if</span>(!newbase)<span class="built_in">exit</span>(OVERFLOW); <span class="comment">//存储分配失败</span></div><div class="line"> L.elem = newbase; <span class="comment">//新基址 </span></div><div class="line"> L.listsize+= LISTINCREMENT; <span class="comment">//增加爱存储容量</span></div><div class="line"> }</div><div class="line"> q = &(L.elem[i<span class="number">-1</span>]); <span class="comment">//q为插入位置</span></div><div class="line"> <span class="keyword">for</span>(p = &(L.elem[L.length<span class="number">-1</span>]);p>=<span class="number">1</span>;--p) *(p+<span class="number">1</span>) = *(p);</div><div class="line"> <span class="comment">//插入位置及之后的元素右移</span></div><div class="line"> *q = e; <span class="comment">//插入e</span></div><div class="line"> ++L.length; <span class="comment">//表长增１</span></div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">} <span class="comment">//时间复杂度Ｏ(n)</span></div></pre></td></tr></table></figure><p>线性表删除操作</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div></pre></td><td class="code"><pre><div class="line"><span class="function">Status <span class="title">ListDelete_Sq</span><span class="params">(SqList &L,<span class="keyword">int</span> i,ElemType e)</span></span>{</div><div class="line"> <span class="keyword">if</span>(i<<span class="number">1</span>||i>L.length+<span class="number">1</span>) <span class="keyword">return</span> ERROR;</div><div class="line"> p = &(L.elem[i<span class="number">-1</span>]); <span class="comment">//p被删除元素的位置</span></div><div class="line"> e = *p; <span class="comment">//被删除元素的值赋给e</span></div><div class="line"> q = L.elem + L.length<span class="number">-1</span>; <span class="comment">//表尾元素的位置</span></div><div class="line"> <span class="keyword">for</span>(++p;p<=q;++p) *(p<span class="number">-1</span>) = *p; <span class="comment">//被删除元素之后的元素左移 </span></div><div class="line"> --L.length; <span class="comment">//表长减1 </span></div><div class="line"> <span class="keyword">return</span> Ok;</div><div class="line">} <span class="comment">//时间复杂度Ｏ(n)</span></div></pre></td></tr></table></figure><p>案例</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div><div class="line">42</div><div class="line">43</div><div class="line">44</div><div class="line">45</div><div class="line">46</div><div class="line">47</div><div class="line">48</div><div class="line">49</div><div class="line">50</div><div class="line">51</div><div class="line">52</div><div class="line">53</div><div class="line">54</div><div class="line">55</div><div class="line">56</div><div class="line">57</div><div class="line">58</div><div class="line">59</div><div class="line">60</div><div class="line">61</div><div class="line">62</div><div class="line">63</div><div class="line">64</div><div class="line">65</div><div class="line">66</div><div class="line">67</div><div class="line">68</div><div class="line">69</div><div class="line">70</div><div class="line">71</div><div class="line">72</div><div class="line">73</div><div class="line">74</div><div class="line">75</div><div class="line">76</div><div class="line">77</div><div class="line">78</div><div class="line">79</div><div class="line">80</div><div class="line">81</div><div class="line">82</div><div class="line">83</div><div class="line">84</div><div class="line">85</div><div class="line">86</div><div class="line">87</div><div class="line">88</div><div class="line">89</div><div class="line">90</div><div class="line">91</div><div class="line">92</div><div class="line">93</div><div class="line">94</div><div class="line">95</div><div class="line">96</div><div class="line">97</div><div class="line">98</div><div class="line">99</div><div class="line">100</div><div class="line">101</div><div class="line">102</div><div class="line">103</div><div class="line">104</div><div class="line">105</div><div class="line">106</div><div class="line">107</div><div class="line">108</div><div class="line">109</div><div class="line">110</div><div class="line">111</div><div class="line">112</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">"stdio.h"</span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">define</span> MAXSIZE 100</span></div><div class="line"><span class="keyword">typedef</span> <span class="class"><span class="keyword">struct</span></span></div><div class="line"><span class="class">{</span></div><div class="line"> <span class="keyword">int</span> NO;</div><div class="line"> <span class="keyword">int</span> score;</div><div class="line">}ElemType;</div><div class="line"><span class="keyword">typedef</span> <span class="class"><span class="keyword">struct</span> </span></div><div class="line"><span class="class">{</span></div><div class="line"> ElemType elem[MAXSIZE];</div><div class="line"> <span class="keyword">int</span> length;</div><div class="line">}SqList;</div><div class="line"></div><div class="line"><span class="comment">//初始化</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">InitList</span><span class="params">(SqList *pL)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> pL->length =<span class="number">0</span>;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">//插入</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">InsertList</span><span class="params">(SqList *pL,ElemType e,<span class="keyword">int</span> i)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">if</span>(pL->length >MAXSIZE)</div><div class="line"> <span class="keyword">return</span>;</div><div class="line"> pL->elem [i]=e;</div><div class="line"> pL->length ++;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">//排序</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">SortScore</span><span class="params">(SqList *pL)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<pL->length ;i++)</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j=i+<span class="number">1</span>;j<pL->length ;j++)</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(pL->elem [i].score<pL->elem [j].score )</div><div class="line"> {</div><div class="line"> ElemType temp=pL->elem [i];</div><div class="line"> pL->elem [i]=pL->elem [j];</div><div class="line"> pL->elem [j]=temp;</div><div class="line"> }</div><div class="line"> }</div><div class="line">}</div><div class="line"></div><div class="line"></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Merge</span><span class="params">(SqList *pL,SqList *pS,SqList *T)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">int</span> i=<span class="number">0</span>,j=<span class="number">0</span>,k=<span class="number">0</span>;</div><div class="line"> <span class="keyword">while</span>(i<pL->length &&j<pS->length )</div><div class="line"> {</div><div class="line"> <span class="keyword">if</span>(pL->elem [i].score >pS->elem [j].score )</div><div class="line"> T->elem [k++]=pL->elem [i++];</div><div class="line"> </div><div class="line"> <span class="keyword">else</span></div><div class="line"> </div><div class="line"> T->elem [k++]=pS->elem [j++];</div><div class="line"> </div><div class="line"> }</div><div class="line"> <span class="keyword">while</span>(i<pL->length )</div><div class="line"> T->elem [k ++]=pL->elem [i++ ];</div><div class="line"> </div><div class="line"> <span class="keyword">while</span>(j<pS->length )</div><div class="line"> T->elem [k ++]=pS->elem [j ++]; </div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">//输出</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Printf</span><span class="params">(SqList *pL)</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>;i<pL->length ;i++)</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"(%2d,%2d)\n"</span>,pL->elem [i].NO ,pL->elem [i].score );</div><div class="line">}</div><div class="line"></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">main</span><span class="params">()</span></span></div><div class="line"><span class="function"></span>{</div><div class="line"> SqList L,S,T;</div><div class="line"> ElemType e;</div><div class="line"> InitList(&L);</div><div class="line"> e.NO =<span class="number">5</span>; e.score =<span class="number">60</span>;</div><div class="line"> InsertList(&L,e,<span class="number">0</span>);</div><div class="line"> e.NO =<span class="number">6</span>; e.score =<span class="number">80</span>;</div><div class="line"> InsertList(&L,e,<span class="number">1</span>);</div><div class="line"> e.NO =<span class="number">7</span>; e.score =<span class="number">76</span>;</div><div class="line"> InsertList(&L,e,<span class="number">2</span>);</div><div class="line"> e.NO =<span class="number">8</span>; e.score =<span class="number">50</span>;</div><div class="line"> InsertList(&L,e,<span class="number">3</span>);</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"顺序表L:\n"</span>);</div><div class="line"> Printf(&L);</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"\n按照成绩大小排序后的顺序表L：\n"</span>);</div><div class="line"> SortScore(&L);</div><div class="line"> Printf(&L);</div><div class="line"></div><div class="line"> InitList(&S);</div><div class="line"> e.NO =<span class="number">10</span>; e.score =<span class="number">70</span>;</div><div class="line"> InsertList(&S,e,<span class="number">0</span>);</div><div class="line"> e.NO =<span class="number">20</span>; e.score =<span class="number">85</span>;</div><div class="line"> InsertList(&S,e,<span class="number">1</span>);</div><div class="line"> e.NO =<span class="number">30</span>; e.score =<span class="number">75</span>;</div><div class="line"> InsertList(&S,e,<span class="number">2</span>);</div><div class="line"> e.NO =<span class="number">40</span>; e.score =<span class="number">90</span>;</div><div class="line"> InsertList(&S,e,<span class="number">3</span>);</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"\n顺序表S:\n"</span>);</div><div class="line"> Printf(&S);</div><div class="line"> <span class="built_in">printf</span>(<span class="string">"\n按照成绩大小排序后的顺序表S：\n"</span>);</div><div class="line"> SortScore(&S);</div><div class="line"> Printf(&S);</div><div class="line"></div><div class="line"> <span class="built_in">printf</span>(<span class="string">"\n\n"</span>);</div><div class="line"></div><div class="line"> InitList(&T);</div><div class="line"> T.length =L.length +S.length ;</div><div class="line"> Merge(&L,&S,&T);</div><div class="line"> Printf(&T);</div><div class="line">}</div></pre></td></tr></table></figure><p>线性表的顺序存储结构特点：逻辑关系上相邻的两个单元在物理位置上也相邻。缺点：在作插入或删除操作时，需要移动大量元素。</p><h3 id="线性表的链式表现和实现"><a href="#线性表的链式表现和实现" class="headerlink" title="线性表的链式表现和实现"></a>线性表的链式表现和实现</h3><p>线性表链式存储结构特点：用一组任意的存储单元(连续或不连续)存储线性表的数据元素 。</p><p>如何表示数据元素$a_i$与其直接后继数据元素$a_{i+1}$之间关系:结点｛<strong>本身信息+直接后继的存储位置</strong>｝</p><p>结点包含两个域：数据域＋指针域 n个结点链结成一个链表。</p><p><img src="../../Pictures/datastructure/list_operate.png" alt="list_operate"></p><blockquote><p>线性单链表：(ZHAO, QIAN, SUN, LI, ZHOU, WU, ZHENG, WANG)</p></blockquote><p><img src="../Pictures/datastructure/linear_list.png" alt="linear_list"></p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div></pre></td><td class="code"><pre><div class="line"><span class="comment">//－－－－－线性表的单链存存储结构－－－－－－</span></div><div class="line"><span class="keyword">typedef</span> <span class="class"><span class="keyword">struct</span> <span class="title">LNode</span>{</span></div><div class="line"> ElemType data;</div><div class="line"> <span class="class"><span class="keyword">struct</span> <span class="title">LNode</span> *<span class="title">next</span>;</span></div><div class="line">}LNode, *LinkList;</div></pre></td></tr></table></figure><p>$p->data = a_i$, 则$p->next->data = a_{i+1}$。</p><p>GetElem在单链表中的实现</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div></pre></td><td class="code"><pre><div class="line"><span class="function">Status <span class="title">GetElem_L</span><span class="params">(LinkList L,<span class="keyword">int</span> i,ElemType &e)</span></span>{</div><div class="line"> <span class="comment">//L为带头结点的单链表的头指针。</span></div><div class="line"> <span class="comment">//当第i个元素存在时，其值赋给e并返回OK，否则返回error。</span></div><div class="line"> p = L->next; j = <span class="number">1</span>;</div><div class="line"> <span class="keyword">while</span>(p&&j<i){</div><div class="line"> p = p->next;++j;</div><div class="line"> }</div><div class="line"> <span class="keyword">if</span>(!p||j>i) <span class="keyword">return</span> ERROR;</div><div class="line"> e = p->data; <span class="comment">//取第i个元素</span></div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">}</div></pre></td></tr></table></figure><p>单链表插入操作</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div></pre></td><td class="code"><pre><div class="line"><span class="function">Status <span class="title">ListInsert_L</span><span class="params">(LinkList &L,<span class="keyword">int</span> i,ElemType e)</span></span>{</div><div class="line"> <span class="comment">//在带头结点的单链表Ｌ中第i个位置之前插入元素e</span></div><div class="line"> p = L; j = <span class="number">0</span>;</div><div class="line"> <span class="keyword">while</span>(p&&j<i<span class="number">-1</span>){p = p->next;++j;} <span class="comment">//寻找第i－１个结点</span></div><div class="line"> <span class="keyword">if</span>(!p||j>i) <span class="keyword">return</span> ERROR;</div><div class="line"> s = (LinkList)<span class="built_in">malloc</span>(<span class="keyword">sizeof</span> (LNode)); <span class="comment">//生成新结点</span></div><div class="line"> s->data = e; s->next = p->next; <span class="comment">//插入Ｌ中</span></div><div class="line"> p->next = s;</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">} <span class="comment">//O(n)</span></div></pre></td></tr></table></figure><p>单链表删除操作</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div></pre></td><td class="code"><pre><div class="line"><span class="function">Status <span class="title">ListDelete_L</span><span class="params">(LinkList &L,<span class="keyword">int</span> i,ElemType &e)</span></span>{</div><div class="line"> <span class="comment">//在带头结点的单链表Ｌ中删除第i个元素，并由e返回其值</span></div><div class="line"> p = L;j=<span class="number">0</span>;</div><div class="line"> <span class="keyword">while</span>(p->next&&j<i<span class="number">-1</span>){ <span class="comment">//寻找第i个结点，并令p指向其前趋</span></div><div class="line"> p = p->next;++j;</div><div class="line"> }</div><div class="line"> <span class="keyword">if</span>(!(p->next)||j>i) <span class="keyword">return</span> ERROR;</div><div class="line"> q = p->next; p->next = q->next; <span class="comment">//删除并释放结点</span></div><div class="line"> e = q->data; <span class="built_in">free</span>(q);</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">} <span class="comment">//O(n)</span></div></pre></td></tr></table></figure><p>两个有序链表合并为一个有序链表</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">MergeList_L</span><span class="params">(LinkList &La,LinkList &Lb,LinkList &Lc)</span></span>{</div><div class="line"> pa = La->next; pb = Lb->next;</div><div class="line"> Lc = pc = La; <span class="comment">//用La的头结点作为Lc的头结点</span></div><div class="line"> <span class="keyword">while</span>(pa&&pb){</div><div class="line"> <span class="keyword">if</span>(pa->data <= pb->data){</div><div class="line"> pc->next = pa; pc = pa; pa= pa->next;</div><div class="line"> } </div><div class="line"> <span class="keyword">else</span>{pa-next = pb; pc=pb; pb = pb->next;}</div><div class="line"> }</div><div class="line"> pc->next = pa?pa:pb; <span class="comment">//插入剩余段</span></div><div class="line"> <span class="built_in">free</span>(Lb);</div><div class="line">}</div></pre></td></tr></table></figure><p><strong>双向链表</strong>：结点有两个指针域，其一指向直接后继，另一指向直接前趋</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div></pre></td><td class="code"><pre><div class="line"><span class="comment">//－－－－－线性表的双向链表存储结构－－－－－</span></div><div class="line"><span class="keyword">typedef</span> <span class="class"><span class="keyword">struct</span> <span class="title">DuLNode</span>{</span></div><div class="line"> ElemType data;</div><div class="line"> <span class="class"><span class="keyword">struct</span> <span class="title">DuLNode</span> *<span class="title">prior</span>;</span></div><div class="line"> <span class="class"><span class="keyword">struct</span> <span class="title">DuLNode</span> *<span class="title">next</span>;</span></div><div class="line">}</div></pre></td></tr></table></figure><p><img src="../Pictures/datastructure/dulnode.png" alt="dulnode"></p><p>结构特性：$d->next->prior = d->prior->next = d$></p><p>双向链表插入操作</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div></pre></td><td class="code"><pre><div class="line"><span class="function">Status <span class="title">ListInsert_DuL</span><span class="params">(DuLinkList &L,<span class="keyword">int</span> i,ElemType e)</span></span>{</div><div class="line"> <span class="comment">//在带头结点的双链循环表Ｌ中第i个位置之前插入元素e</span></div><div class="line"> <span class="keyword">if</span>(!(p = GetElemP_Dul(L,i))) <span class="comment">//在Ｌ中确定插入位置</span></div><div class="line"> <span class="keyword">return</span> ERROR;</div><div class="line"> <span class="keyword">if</span>(!(s = (DuLinkList)<span class="built_in">malloc</span>(<span class="keyword">sizeof</span>(DuLNode))))</div><div class="line"> <span class="keyword">return</span> ERROR</div><div class="line"> s->data = e;</div><div class="line"> s->prior = p->prior; p->prior->next = s;</div><div class="line"> s->next = p; p->prior = s;</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">}</div></pre></td></tr></table></figure><p>双向链表删除操作</p><figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div></pre></td><td class="code"><pre><div class="line"><span class="function">Status <span class="title">ListDElete_DuL</span><span class="params">(DuLinkList &L,<span class="keyword">int</span> i,ElemType e)</span></span>{</div><div class="line"> <span class="comment">//删除带头结点的双链循环表Ｌ第i个元素</span></div><div class="line"> <span class="keyword">if</span>(!(p = GetElemP_Dul(L,i))) <span class="comment">//在Ｌ中确定插入位置</span></div><div class="line"> <span class="keyword">return</span> ERROR;</div><div class="line"> e = p->data;</div><div class="line"> p->prior->next = p->next;</div><div class="line"> p->next->prior = p->prior;</div><div class="line"> <span class="built_in">free</span>(p);</div><div class="line"> <span class="keyword">return</span> OK;</div><div class="line">}</div></pre></td></tr></table></figure>]]></content>
<summary type="html">
<h2 id="线性表"><a href="#线性表" class="headerlink" title="线性表"></a>线性表</h2><h3 id="类型定义"><a href="#类型定义" class="headerlink" title="类型定义"></a>类型定义</h3><p>简言之，一个线性表是n个数据元素的有限序列。</p>
<p>在复杂的线性表中，一个数据元素可由若干个数据项(item)组成。在这种情况下，常把数据元素称为记录(record)，含有大量记录的线性表又称为文件（file）。</p>
<figure class="highlight c"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div></pre></td><td class="code"><pre><div class="line">ADT List&#123;</div><div class="line"> <span class="comment">//数据对象</span></div><div class="line"> D = &#123;a1|a2 belong to ElemSet, i=<span class="number">1</span>,<span class="number">2</span>,....,n, n&gt;<span class="number">0</span>&#125;</div><div class="line"> <span class="comment">//数据关系</span></div><div class="line"> R1 = &#123;&lt;ai<span class="number">-1</span>,ai&gt;|ai<span class="number">-1.</span>ai belong to D,i = <span class="number">1</span>,<span class="number">2.</span>..n&#125;</div><div class="line"> <span class="comment">//基本操作</span></div><div class="line"> InitList(&amp;L)</div><div class="line"> <span class="comment">//构造一个空的线性表Ｌ</span></div><div class="line"> DestoryList(&amp;L)</div><div class="line"> <span class="comment">//销毁线性表Ｌ</span></div><div class="line"> ClearList(&amp;L)</div><div class="line"> <span class="comment">//将Ｌ重置为空表</span></div><div class="line"> ListEmpty(L)</div><div class="line"> <span class="comment">//若L为空表，返回True,否则False</span></div><div class="line"> ListLength(L)</div><div class="line"> <span class="comment">//返回L中数据元素个数</span></div><div class="line"> GetElem(L,i,&amp;e)</div><div class="line"> <span class="comment">//用e返回L中第i个数据元素的值</span></div><div class="line"> ListInsert(&amp;L,i,e)</div><div class="line"> <span class="comment">//在Ｌ中第i个位置之前插入新的数据元素e，Ｌ的长度加1。</span></div><div class="line">&#125;</div></pre></td></tr></table></figure>
</summary>
<category term="阅读" scheme="http://yoursite.com/categories/%E9%98%85%E8%AF%BB/"/>
<category term="阅读，线性表" scheme="http://yoursite.com/tags/%E9%98%85%E8%AF%BB%EF%BC%8C%E7%BA%BF%E6%80%A7%E8%A1%A8/"/>
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