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<h1 id="本科算法经验"><a href="#本科算法经验" class="headerlink" title="本科算法经验"></a>本科算法经验</h1><ul>
<li>本科期间学习过数据结构，算法设计与分析相关课程</li>
<li>有一些代码量，做过一些网站，小程序，系统</li>
<li>大三寒假曾备战过一个月的算法，来应对某个比较水的算法比赛
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<p>本章内容有点极端，字符串hash难度一般，理解起来问题不大，即利用素数和大数做hash散列避免冲突，之前八数码问题也使用过康拓展开式标识唯一的字符串；KMP学过三遍了，理解起来还是废了番功夫，重点仍然是next[]数组的含义和求解，除此之外增加了统计子串出现的次数，优化next[]数组，有限状态机解释KMP算法（对理解很有帮助）</p>
<h1 id="专题要点："><a href="#专题要点：" class="headerlink" title="专题要点："></a>专题要点：</h1><ul>
<li><p><strong>字符串hash</strong>：hash[i] = (hash[i - 1] * p + index(str[i])) % mod</p>
<ul>
<li><p>从进制转换的角度理解，<strong>hash是p进制转换为十进制的数字</strong>，<strong>把hash[i - 1]当做p进制，并将其转换为十进制</strong>，加上str[i]的int类型，对mod取余</p>
</li>
<li><p><strong>hash[]的理解</strong>：hash[i]表示从str[0~i]子串的hash值，hash[length - 1]（length是字符串的长度）表示整个字符串的hash值</p>
</li>
<li><p><strong>几个数据结构</strong>：</p>
<ul>
<li><p>powP[]:存放p^i^%mod的计算结果，便于求子串hash值直接访问，其中powP[0] = 1</p>
</li>
<li><p>hash[]:表示从str[0~i]子串的hash值</p>
</li>
<li><p>vector<pair<int, int> >sub:存放所有<子串hash值，子串长度></p>
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<p>这已经是本人第三遍学习动态规划了，其实现在脑子里还是乱糟糟的，容我想想怎么总结能有所收获，有所提升。<br>第一遍单纯地比葫芦画瓢，留下的印象只是要具体问题具体分析，状态转移方程各不相同；<br>第二遍对DP有了较为系统地认识，认识到了贪心只能达到局部最优，DP可以得到全局最优解；认识到了自底向上分析问题；认识到了状态转移的过程和分析；认识到了逆向求解决策选择情况。<br>第三遍感觉比前两次有所提升，却还是有点讲不明白到底具体学到了什么，也不想在这里写长篇大论或者都会提及的概念。<br>通过这篇博客捋一下思路，写一下新的收获和对DP的认识</p>
<p>本章题目使用递归和递推两种方式编写代码，随后会将代码放在github上<br><a href="https://github.com/LLeLeX/PAT-Algorithm/tree/master/%E5%85%B6%E4%BB%96/%E7%AE%97%E6%B3%95%E7%AC%94%E8%AE%B0%E8%AE%B2%E4%B9%89/11%20%E5%8A%A8%E6%80%81%E8%A7%84%E5%88%92" target="_blank" rel="noopener">传送站</a>
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<h1 id="专题要点："><a href="#专题要点：" class="headerlink" title="专题要点："></a>专题要点：</h1><p>在这一节中暴露出来了诸多问题！本节的四道模拟题目<strong>均未能AC</strong>，除此之外<strong>均未能一次注意到题目中的所有细节</strong>，<strong>均未能自己找出代码问题并AC（到最后都是不知道个人思路代码错在哪里）</strong>，这就是心态逐步崩盘的过程</p>
<h1 id="暴露出的问题"><a href="#暴露出的问题" class="headerlink" title="暴露出的问题"></a>暴露出的问题</h1><ul>
<li><p>个人对题目理解不够到位，要么是英文题目的细节描述没有读懂，要么是忽略了细节问题</p>
</li>
<li><p>并不能很快想到简化工作，比如排队问题的将时间统一转换为秒（最小单位，方便计算和比较大小）</p>
</li>
<li><p>数据结构的使用和其含义不够准确到位，比如排队问题的结构体数组是记录客户还是用来记录窗口，使用不到位会造成代码冗余复杂</p>
</li>
<li><p>模拟逻辑不清晰，无法将题意准确转换为代码思维，比如怕对问题的模拟时间还是模拟客户，如何将题目对vip球员的特权描述转换为4种情况的代码思维</p>
</li>
<li><p>初始化的妙用，将下标初始化为-1来进行扫描查找，可替代bool变量标记是否找到；或是类似最大值最小值的初始化；或是初始化一个不在范围内的时间</p>
</li>
<li><p>题目中还有一些比较神奇的亮眼步骤，比如螺旋矩阵中的回退到最内层</p>
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<h1 id="专题要点："><a href="#专题要点：" class="headerlink" title="专题要点："></a>专题要点：</h1><p>树状数组结构仍是普通数组，但在数组中的查询和更新过程类似于树状</p>
<ul>
<li><strong>核心函数运算</strong> <strong>lowbit(i) ((i) & (-i))的三种解释</strong>： 求i元素的二进制形式中最右侧“1”的位置；等价于求元素i的因数，且该因数是最大2的幂次；或者说是能被i整除的最大的2的幂次</li>
<li><strong>数据结构</strong>：int c[]：表示存放i号位之前lowbit(i)个元素和</li>
<li><strong>功能</strong>：<ul>
<li>getSum(int x)：求x之前所有整数和，<strong>向前遍历</strong></li>
<li>update(int x, int v)：将第x个元素加上v，会影响到c[x]后的树状数组值，因此要<strong>向后遍历</strong>更新</li>
</ul>
</li>
<li><strong>离散化思想</strong>：当数据的值的范围超过连续可表示的范围（即数组大小），可将数据在输入个数范围内离散化排序（即排名次）存入数组中，即将数值范围转化为数据个数范围</li>
</ul>
<h1 id="可解问题："><a href="#可解问题：" class="headerlink" title="可解问题："></a>可解问题：</h1><ul>
<li>求序列中元素左侧小于该元素的元素个数</li>
<li>求第K大元素<h1 id="几个问题："><a href="#几个问题：" class="headerlink" title="几个问题："></a>几个问题：</h1></li>
<li><strong>为什么会呈现树状</strong>：c[i]中表示i前2^k^个元素和，根据二进制，logN个c[i]便可覆盖1~i所有元素</li>
<li><strong>如何统计个数</strong>：当元素输入后，每次加一统计个数，update(x, 1)</li>
<li><strong>为什么使用getSum(x)能得到左侧小于x的元素个数</strong>：因为c[]是递增的，getSum()访问的是x左侧元素（x左侧元素均小于x），求和统计次数即为小于x的元素个数</li>
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<h1 id="专题要点："><a href="#专题要点：" class="headerlink" title="专题要点："></a>专题要点：</h1><ul>
<li><strong>数据结构</strong>：<ul>
<li>blockNum：块数</li>
<li>eleNum：块中的元素范围</li>
<li>table[]：统计第i个整数的个数</li>
<li>block[]：统计每个块中元素个数</li>
</ul>
</li>
<li><strong>算法思想</strong>：通过累加块中元素个数block[i]，快速定位第K大元素所在块号，在定位的块中遍历table[]，快速找到第K大元素</li>
<li><strong>注意</strong>：一个block块负责一个范围，在这个范围内遍历累加table[]并与K作比较</li>
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<a class="article-title" href="/2020/03/17/%E5%85%A5%E9%97%A8%E7%AF%87-%E6%95%B0%E5%AD%A6%E9%97%AE%E9%A2%98-%E3%80%8A%E7%AE%97%E6%B3%95%E7%AC%94%E8%AE%B0%E3%80%8B%E5%90%8C%E6%AD%A5%E7%AC%94%E8%AE%B0%E6%80%BB%E7%BB%93%E4%B8%8E%E8%A1%A5%E5%85%85/">入门篇-数学问题-《算法笔记》同步笔记总结与补充</a>
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<time datetime="2020-03-17T03:30:16.000Z" itemprop="datePublished"><i class="icon-calendar icon"></i>2020-03-17</time>
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<h1 id="专题要点："><a href="#专题要点：" class="headerlink" title="专题要点："></a>专题要点：</h1><ul>
<li><strong>编程实现数学算法</strong>：如欧几里得算法（最大公约数gcd）</li>
<li><strong>模拟运算法则</strong>：如有理数（分数Fraction）四则运算，大整数（高精度）运算，更要注意细节的处理</li>
<li><strong>取模，除法的思想</strong>：取模用于取某一数位的数值，除法用于分解原数（在进制转换和分解质因数运用）</li>
<li><strong>判断素数的方法</strong><ul>
<li>根号枚举法—— 能否整除2~sqrt(n)</li>
<li>用素数打表得到的bool isPrime[]数组判断
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<article id="post-提高篇-图论-《算法笔记》同步笔记总结与补充" class="article article-type-post article-index" itemscope itemprop="blogPost">
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<a class="article-title" href="/2020/03/12/%E6%8F%90%E9%AB%98%E7%AF%87-%E5%9B%BE%E8%AE%BA-%E3%80%8A%E7%AE%97%E6%B3%95%E7%AC%94%E8%AE%B0%E3%80%8B%E5%90%8C%E6%AD%A5%E7%AC%94%E8%AE%B0%E6%80%BB%E7%BB%93%E4%B8%8E%E8%A1%A5%E5%85%85/">提高篇-图论-《算法笔记》同步笔记总结与补充</a>
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<time datetime="2020-03-12T03:22:57.000Z" itemprop="datePublished"><i class="icon-calendar icon"></i>2020-03-12</time>
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<h1 id="专题要点："><a href="#专题要点：" class="headerlink" title="专题要点："></a>专题要点：</h1><ul>
<li><strong>点权和边权</strong>：顶点和边均可具有权值，根据题意判断。<strong>邻接矩阵</strong>：边的权值可以存入矩阵中，点的权值需要另存储在一位数组中；<strong>邻接表</strong>：点权边权都可以用结构体存储</li>
<li><strong>图的遍历dfs，bfs</strong>：<ul>
<li>遍历时，要对所有顶点进行搜索，防止出现图不连通的情况。</li>
<li>搜索的次数即为图中<strong>连通块的个数</strong></li>
</ul>
</li>
<li><strong>最短路径问题</strong>：求源点到其他顶点的最短距离
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<h1 id="专题要点："><a href="#专题要点：" class="headerlink" title="专题要点："></a>专题要点：</h1><ul>
<li><strong>无负环的单源最短路径</strong><ul>
<li>Dijkstra（配合dfs，优先队列优化）</li>
</ul>
</li>
<li><strong>一般单源最短路径</strong><ul>
<li>Dijkstra</li>
<li>Bellman-Ford</li>
<li>SPFA
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<article id="post-提高篇-树结构-《算法笔记》同步笔记总结与补充" class="article article-type-post article-index" itemscope itemprop="blogPost">
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<time datetime="2020-03-05T07:57:07.000Z" itemprop="datePublished"><i class="icon-calendar icon"></i>2020-03-05</time>
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<h1 id="可解问题"><a href="#可解问题" class="headerlink" title="可解问题"></a>可解问题</h1><p>题目中正儿八经构造一颗树的题目不多，但关于运用树的思想却很多，一定要熟练掌握！尤其是树结构在<strong>并查集，堆</strong>，这些数据结构实用且高效。</p>
<ul>
<li><strong>树的遍历</strong>：<br><a href="https://blog.csdn.net/weixin_44343282/article/details/104553696" target="_blank" rel="noopener">树的前中后层序遍历（已知两种遍历求其他遍历结果）</a><br><a href="https://blog.csdn.net/weixin_44343282/article/details/104575889" target="_blank" rel="noopener">树的深搜广搜</a><br><a href="https://blog.csdn.net/weixin_44343282/article/details/104563156" target="_blank" rel="noopener">二叉树的建立</a></li>
<li><strong>二叉搜索树</strong>：<br><a href="https://blog.csdn.net/weixin_44343282/article/details/104594224" target="_blank" rel="noopener">二叉搜索树的遍历</a><br><a href="https://blog.csdn.net/weixin_44343282/article/details/104598692" target="_blank" rel="noopener">二叉搜索树中序遍历的性质</a>
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