[LeetCode] 108. Convert Sorted Array to Binary Search Tree

Given an integer array nums where the elements are sorted in ascending order, convert it to a height-balanced binary search tree.

A height-balanced binary tree is a binary tree in which the depth of the two subtrees of every node never differs by more than one.

Example 1:

Input: nums = [-10,-3,0,5,9]
Output: [0,-3,9,-10,null,5]
Explanation: [0,-10,5,null,-3,null,9] is also accepted:

Example 2:

Input: nums = [1,3]
Output: [3,1]
Explanation: [1,3] and [3,1] are both a height-balanced BSTs.

Constraints:

1 <= nums.length <= 104
-104 <= nums[i] <= 104
nums is sorted in a strictly increasing order.

将有序数组转化为二叉搜索树。

题目即是题意。只要输出一个有效的BST即可。此题可以跟109题一起做，要求很接近但是做法不太一样。

这个题可以用递归做。因为是BST的关系，而且input是有序数组，如果熟练，就会想到中序遍历BST的output就是一个有序数组。思路是找到数组的mid元素，即是找到了BST的根节点。小于根节点的节点是左孩子，反之是右孩子。但是注意中序遍历的结果并不能确定唯一的BST。代码如下

时间O(n)

空间O(n)

Java实现

 1 class Solution {
 2     public TreeNode sortedArrayToBST(int[] nums) {
 3         // corner case
 4         if (nums == null || nums.length == 0) {
 5             return null;
 6         }
 7         return helper(nums, 0, nums.length - 1);
 8     }
 9 
10     private TreeNode helper(int[] nums, int left, int right) {
11         if (left > right)
12             return null;
13         int mid = left + (right - left) / 2;
14         TreeNode root = new TreeNode(nums[mid]);
15         root.left = helper(nums, left, mid - 1);
16         root.right = helper(nums, mid + 1, right);
17         return root;
18     }
19 }

JavaScript实现

 1 /**
 2  * @param {number[]} nums
 3  * @return {TreeNode}
 4  */
 5 var sortedArrayToBST = function (nums) {
 6     if (nums == null || nums.length == 0) return null;
 7     return helper(nums, 0, nums.length - 1);
 8 }
 9 
10 var helper = function (nums, low, high) {
11     if (low > high) return null;
12     var mid = parseInt((high + low) / 2);
13     var root = new TreeNode(nums[mid]);
14     root.left = helper(nums, low, mid - 1);
15     root.right = helper(nums, mid + 1, high);
16     return root;
17 }