108. Convert Sorted Array to Binary Search Tree

Description

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:

tree

Solution

DFS, time O(n), space O(h)

/**
 * 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) {
        if (nums == null) {
            return null;
        }
        
        return dfs(nums, 0, nums.length);
    }
    
    public TreeNode dfs(int[] nums, int s, int e) {
        if (s >= e) {
            return null;
        }
        
        int m = s + (e - s) / 2;
        TreeNode root = new TreeNode(nums[m]);
        root.left = dfs(nums, s, m);
        root.right = dfs(nums, m + 1, e);
        
        return root;
    }
}