122. Best Time To Sell and Buy Stock Ⅱ

122. Best Time To Sell and Buy Stock.md

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+### Step1
+
+- 頭の中でグラフを思い浮かべた。今より前の時点のやつを売買することができる(ズル)ので、今の値と比較してどうかで決めれる
+- is_havingのようなフラグ変数は管理しづらくなるだろうか。1個くらいならOK?
+
+```python
+python
+class Solution:
+    def maxProfit(self, prices: List[int]) -> int:
+        profit = 0
+        is_having = False
+        prev_price = None
+        for price in prices:
+            if prev_price is None:
+                pass
+            elif is_having and prev_price > price:
+                profit += prev_price
+                is_having = False
+            elif not is_having and prev_price < price:
+                profit -= prev_price
+                is_having = True
+            prev_price = price
+        if is_having:
+            profit += prev_price
+            is_having = False
+        return profit
+```
+
+- テストケースを考える(実は今まであんまりやってなかった😅)
+    - []
+    - [5]
+    - [-4] (株価がマイナスはなさそう)
+    - [0]
+    - [4, 5]
+    - [5, 4]
+    - [3, 3]
+    - [4, 5, 4]
+    - [5, 4, 5]
+    - [4, 5, 5]
+    - [4, 4, 5]
+    - [5, 4, 4]
+    - [5, 5, 4]
+    - [0, 0, 0, 0, 0, 0, 0, 0,,,,]
+    - [2, 2, 2, 2,,,,,,,,]
+    - [4, 5, 4, 5, 4, 5, 4, 5,,,,,,,]
+    - [5, 4, 5, 4, 5, 4, 5, 4,,,,]
+    - [4, 5, 6, 5, 4, 5, 6, 5, 4,,,,,]
+    - [6, 5, 4, 5, 6, 5, 4, 5, 6,,,,,]
+    - [1, 2, 3, 4, 5, 6,,,,]
+    - [100, 99, 98, 97, ,,,,,,]
+- くらいかな。うーん。
+
+
+
+https://discord.com/channels/1084280443945353267/1210494002277908491/1210793843260133477
+
+https://github.com/fhiyo/leetcode/pull/39/files
+
+[https://github.com/TORUS0818/leetcode/pull/40](https://github.com/TORUS0818/leetcode/pull/40#discussion_r1875358734)
+
+- 関数を定める方法、DPでやる方法などがある
+    - 関数を定める方法で書いてみる
+    - find_next_peakとfind_next_bottomはよく似て関数だが、ここを無理やり共通化しようとするのは流石にややこしい？
+
+```python
+class Solution:
+    def find_next_peak(self, start_index: int, nums: List[int])-> Tuple[int, int]:
+        assert start_index < len(nums)
+        i = start_index
+        while i + 1 < len(nums) and nums[i] <= nums[i + 1]:
+            i += 1
+        return i, nums[i]
+
+    def find_next_bottom(self, start_index: int, nums: List[int])-> Tuple[int, int]:
+        assert start_index < len(nums)
+        i = start_index
+        while i + 1 < len(nums) and nums[i] >= nums[i + 1]:
+            i += 1
+        return i, nums[i]
+
+    def maxProfit(self, prices: List[int]) -> int:
+        assert(len(prices) > 0)
+        profit = 0
+        i = 0
+        bought_price = prices[0]
+        while i < len(prices) - 1:
+            peak_index, peak_price = self.find_next_peak(i, prices)
+            profit += peak_price - bought_price
+            bottom_index, bottom_price = self.find_next_bottom(peak_index, prices)
+            i = bottom_index
+            bought_price = bottom_price
+        return profit
+```
+
+- 　https://github.com/hayashi-ay/leetcode/pull/56
+
+- find_next_bottom関数の返り値、indexだけの方がシンプルで良いだろうか、でも値もあった方が便利そうでむずい
+- https://github.com/Ryotaro25/leetcode_first60/pull/42
+    - price[i + 1] - prices[i] を変数に置いた方がいいのはなるほど
+- 持ってる時、持ってない時で出す
+
+```python
+
+class Solution:
+    def maxProfit(self, prices: List[int]) -> int:
+        assert(len(prices) > 0)
+        profit_having_stock_prev = -prices[0]
+        profit_not_having_stock_prev = 0
+        for i in range(1, len(prices)):
+            profit_having_stock = max(profit_having_stock_prev, profit_not_having_stock_prev - prices[i])
+            profit_not_having_stock = max(profit_not_having_stock_prev, profit_having_stock_prev + prices[i])
+            profit_having_stock_prev = profit_having_stock
+            profit_not_having_stock_prev = profit_not_having_stock
+        return max(profit_having_stock_prev, profit_not_having_stock_prev)
+ ```
+
+```
+
+- https://github.com/seal-azarashi/leetcode/pull/36
+    - 以下のコードでも通るっぽい。簡潔ではあるが、max(profit_not_having_stock, profit_having_stock + prices[i])　の時だけprofit_having_stockが実は同時点で、ただ前の行で更新されているならば-prices[i]と+prices[i]で打ち消しあって、前時点のprofit_not_having_stockに結果的になる、という推理が必要？
+
+```python
+
+class Solution:
+    def maxProfit(self, prices: List[int]) -> int:
+        assert(len(prices) > 0)
+        profit_having_stock= -prices[0]
+        profit_not_having_stock = 0
+        for i in range(1, len(prices)):
+            profit_having_stock = max(profit_having_stock, profit_not_having_stock - prices[i])
+            profit_not_having_stock = max(profit_not_having_stock, profit_having_stock + prices[i])
+        return max(profit_having_stock, profit_not_having_stock)
+```
+
+- https://github.com/goto-untrapped/Arai60/pull/59
+    - peakとbottomを交互にループするのは、最初にbottomをやった方が綺麗そう？気づかなかった。
+
+```python
+python
+class Solution:
+    def find_next_peak(self, start_index: int, nums: List[int])-> Tuple[int, int]:
+        assert start_index < len(nums)
+        i = start_index
+        while i + 1 < len(nums) and nums[i] <= nums[i + 1]:
+            i += 1
+        return i, nums[i]
+
+    def find_next_bottom(self, start_index: int, nums: List[int])-> Tuple[int, int]:
+        assert start_index < len(nums)
+        i = start_index
+        while i + 1 < len(nums) and nums[i] >= nums[i + 1]:
+            i += 1
+        return i, nums[i]
+
+    def maxProfit(self, prices: List[int]) -> int:
+        assert(len(prices) > 0)
+        profit = 0
+        i = 0
+        while i + 1 < len(prices):
+            bottom_i, bottom_price = self.find_next_bottom(i, prices)
+            peak_i, peak_price = self.find_next_peak(bottom_i, prices)
+            profit += peak_price - bottom_price
+            i = peak_i
+        return profit
+```
+
+- https://github.com/sakupan102/arai60-practice/pull/39
+
+https://github.com/shining-ai/leetcode/pull/38
+
+https://github.com/hroc135/leetcode/pull/36/files　　
+
+- profit_having_stockとprofit_not_having_stockを同時に更新するというてもあるか。ただ1行が長くなって見にくくなりそう。
+
+## Step3
+
+これが自然かな
+
+```python
+class Solution:
+    def maxProfit(self, prices: List[int]) -> int:
+        profit = 0
+        for i in range(len(prices) - 1):
+            diff = prices[i + 1] - prices[i]
+            if diff > 0:
+                profit += diff
+        return profit
+```