108. Convert Sorted Array to Binary Search Tree

tree-bst/108.md

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+- 問題: [108. Convert Sorted Array to Binary Search Tree](https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/description/)
+- 条件
+  - `1 <= nums.length <= 10^4`
+  - `-10^4 <= nums[i] <= 10^4`
+  - `nums is sorted in a strictly increasing order.`
+- 方針
+  - 再帰関数というか、2分探索
+    - int middle = nums.length / 2 を真ん中とする
+    - 0 ~ middle までを左に振り
+    - middle + 1 ~ nums.length までを右に振る
+    - 上記をひたすら繰り返す
+  - 時間計算量: `O(log n)` 
+  - 空間計算量: TreeNode を nums.length - 1 分作るので、`O(N)`, 再帰の深さは`O(log n)`
+  - 時間: 10分
+
+```java
+/**
+ * Definition for a binary tree node.
+ * public class TreeNode {
+ *     int val;
+ *     TreeNode left;
+ *     TreeNode right;
+ *     TreeNode() {}
+ *     TreeNode(int val) { this.val = val; }
+ *     TreeNode(int val, TreeNode left, TreeNode right) {
+ *         this.val = val;
+ *         this.left = left;
+ *         this.right = right;
+ *     }
+ * }
+ */
+class Solution {
+    public TreeNode sortedArrayToBST(int[] nums) {
+        if (nums.length == 0) {
+            return null;
+        }
+        return createTreeNode(nums, 0, nums.length);
+    }
+
+    private TreeNode createTreeNode(int[] nums, int left, int right) {
+        if (right <= 0 || left >= right) {
+            return null;
+        }
+
+        int middle = (left + right) / 2;
+        TreeNode root = new TreeNode(nums[middle]);
+        root.left = createTreeNode(nums, left, middle);
+        root.right = createTreeNode(nums, middle + 1, right);
+
+        return root;
+    }
+}
+```
+- 条件が冗長だったので書き直し
+```java
+/**
+ * Definition for a binary tree node.
+ * public class TreeNode {
+ *     int val;
+ *     TreeNode left;
+ *     TreeNode right;
+ *     TreeNode() {}
+ *     TreeNode(int val) { this.val = val; }
+ *     TreeNode(int val, TreeNode left, TreeNode right) {
+ *         this.val = val;
+ *         this.left = left;
+ *         this.right = right;
+ *     }
+ * }
+ */
+class Solution {
+    public TreeNode sortedArrayToBST(int[] nums) {
+        return createBST(nums, 0, nums.length);
+    }
+
+    private TreeNode createBST(int[] nums, int left, int right) {
+        if (left >= right) {
+            return null;
+        }
+        int middle = (left + right) / 2;
+        TreeNode newNode = new TreeNode(nums[middle]);
+        newNode.left = createBST(nums, left, middle);
+        newNode.right = createBST(nums, middle + 1, right);
+        return newNode;
+    }
+}
+```