108. Convert Sorted Array to Bin

Given an array where elements are sorted in ascending order, convert it to a height balanced BST.

For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1.

Example:

Given the sorted array: [-10,-3,0,5,9],

One possible answer is: [0,-3,9,-10,null,5], which represents the following height balanced BST:

      0
     / \
   -3   9
   /   /
 -10  5

二叉搜索树(BST)

1. 若任意节点的左子树不空，则左子树上所有结点的值均小于它的根结点的值；
2. 若任意节点的右子树不空，则右子树上所有结点的值均大于它的根结点的值；
3. 它是一棵空树或它的左右两个子树的高度差的绝对值不超过1，并且左右两个子树都是一棵平衡二叉树

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public TreeNode sortedArrayToBST(int[] nums) {
        TreeNode root = treeHelper(nums, 0, nums.length-1);
        return root;
    }
    public TreeNode treeHelper(int[] nums, int left, int right){
        if (left > right){
            return null;
        }
        int mid = (left + right)/2;
        TreeNode root = new TreeNode(nums[mid]);
        root.left = treeHelper(nums, left, mid - 1);
        root.right = treeHelper(nums, mid + 1, right);
        return root;
    }
}