110. Balanced Binary Tree

Given a binary tree, determine if it is height-balanced.

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

Analysis:

We can create a method to find the maxHeight of root.

usually such method, just do like" return Math.max(maxHeight(root.left), maxHeight(root.right)) +1"

but this one, we can make it, so that, if |leftHeight - rightHeight| > 1, return -1. and whenever -1 is returned, we return directly -1 without further traverse. This way, it is bubbling up whenever there is "un-balanced" subtree is detected.

Complexity:

Time: O(N) - bottom up approach, whenever un-balance is detected, we stop further traverse.

Space: O(logn)

Code:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public boolean isBalanced(TreeNode root) {
        if(root == null)
        {
            return true;
        }

        return maxHeight(root) != -1;
    }

    private int maxHeight(TreeNode root)
    {
        if(root == null)
        {
            return 0;
        }
        int left = maxHeight(root.left);
        if(left == -1)
        {
            return -1;
        }
        int right = maxHeight(root.right);
        if(right == -1)
        {
            return -1;
        }
        if(Math.abs(left - right) > 1)
        {
            return -1;
        }

        return Math.max(left, right) + 1;
    }
}