Create 108. Convert Sorted Array to Binary Search Tree.md

競技プロ就活部PR用/108. Convert Sorted Array to Binary Search Tree.md

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+### DFS(再帰)
+
+時間計算量: O(N)<br>
+空間計算量: O(N)<br>
+
+---
+### 1回目 (20m15s)
+二分探索のアイデアでいけば書けることはパッと思いついたが、コードにうまくできず時間がかかった。
+以前といた時よりはかなりアイデアそのものは簡単に感じた。
+root.left, root.rightを作って、下から木を構築していく問題がやや苦手だが、今回の問題でかなり克服できたと考える。
+(結果を伝播させていく問題はわかってきた。)
+
+
+```py
+class Solution:
+    def sortedArrayToBST(self, nums: List[int]) -> Optional[TreeNode]:
+        if not nums:
+            return []
+
+        def sorted_array_to_bst_helper(left, right):
+            if left > right:
+                return
+
+            mid_index = (left + right) // 2
+            root = TreeNode(nums[mid_index])
+
+            root.left = sorted_array_to_bst_helper(left, mid_index - 1)
+            root.right = sorted_array_to_bst_helper(mid_index + 1, right)   
+
+            return root         
+
+        return sorted_array_to_bst_helper(0, len(nums) - 1)
+```
+
+
+### 2回目
+left, mid, rightは、それぞれ_indexをつけるかつけないか統一した方が良いと考えた。
+```python
+class Solution:
+    def sortedArrayToBST(self, nums: List[int]) -> Optional[TreeNode]:
+
+        def sorted_array_to_bst_helper(left, right):
+            if left > right:
+                return
+            mid = (left + right) // 2
+            root = TreeNode(nums[mid])
+            root.left = sorted_array_to_bst_helper(left, mid - 1)
+            root.right = sorted_array_to_bst_helper(mid + 1, right)
+            return root
+
+        return sorted_array_to_bst_helper(0, len(nums) - 1)
+```
+
+### 3回目 (半開区間に変更)
+```python
+class Solution:
+    def sortedArrayToBST(self, nums: List[int]) -> Optional[TreeNode]:
+        def sorted_array_to_bst_helper(left, right):
+            if left == right:
+                return 
+            mid = (left + right) // 2
+            root = TreeNode(nums[mid])
+            root.left = sorted_array_to_bst_helper(left, mid)
+            root.right = sorted_array_to_bst_helper(mid + 1, right)
+            return root
+
+        return sorted_array_to_bst_helper(0, len(nums))
+```
+
+
+### helper関数なし
+---
+```python
+class Solution:
+    def sortedArrayToBST(self, nums: List[int]) -> Optional[TreeNode]:
+        if not nums:
+            return None
+        mid = len(nums) // 2
+        root = TreeNode(nums[mid])
+        root.left = self.sortedArrayToBST(nums[:mid])
+        root.right = self.sortedArrayToBST(nums[mid + 1:])
+
+        return root
+```
+
+### DFS (スタック)
+
+時間計算量: O(N)<br>
+空間計算量: O(N)<br>
+
+再帰をベースに考えて15分ほどで書いた。
+---
+```python
+class Solution:
+    def sortedArrayToBST(self, nums: List[int]) -> Optional[TreeNode]: 
+        if not nums:
+            return [] 
+
+        mid = (len(nums) - 1) // 2
+        root = TreeNode(nums[mid])
+        node_and_divided_array = [(root, nums[:mid], nums[mid+1:])]
+        while node_and_divided_array:
+            node, nums_left, nums_right = node_and_divided_array.pop()
+
+            if nums_right:
+                mid_right = (len(nums_right) - 1) // 2
+                node.right = TreeNode(nums_right[mid_right])
+                node_and_divided_array.append((node.right, nums_right[:mid_right], nums_right[mid_right+1:]))
+
+            if nums_left:
+                mid_left = (len(nums_left) - 1) // 2
+                node.left = TreeNode(nums_left[mid_left])
+                node_and_divided_array.append((node.left, nums_left[:mid_left], nums_left[mid_left+1:]))
+
+        return root
+```
+
+
+### BFS
+
+時間計算量: O(N)<br>
+空間計算量: O(N)<br>
+
+---
+```python
+class Solution:
+    def sortedArrayToBST(self, nums: List[int]) -> Optional[TreeNode]: 
+        if not nums:
+            return [] 
+
+        mid = (len(nums) - 1) // 2
+        root = TreeNode(nums[mid])
+        node_and_divided_array = deque([(root, nums[:mid], nums[mid+1:])])
+        while node_and_divided_array:
+            node, nums_left, nums_right = node_and_divided_array.popleft()
+
+            if nums_left:
+                mid_left = (len(nums_left) - 1) // 2
+                node.left = TreeNode(nums_left[mid_left])
+                node_and_divided_array.append((node.left, nums_left[:mid_left], nums_left[mid_left+1:]))
+
+            if nums_right:
+                mid_right = (len(nums_right) - 1) // 2
+                node.right = TreeNode(nums_right[mid_right])
+                node_and_divided_array.append((node.right, nums_right[:mid_right], nums_right[mid_right+1:]))
+
+        return root
+```
+