leetcode: Balanced Binary Tree

问题描述：

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 of every node never differ by more than 1.

原问题链接：https://leetcode.com/problems/balanced-binary-tree/

问题分析

　　这个问题的关键在于要能够推导出判断平衡二叉树的递归关系。从它本身的定义来看，一棵树是否为平衡的，要看它当前的左右子树的高度差是否超过１。同时也要递归的去看它的两个子树也是否满足这个关系。所以这个问题又给归结到了求一棵树的高度上来了。而求树的高度的递归关系也很简单，就是递归的找它两个子树中最大的那个并加一。

　　所以，我们可以得到如下的实现代码：

/**
 * 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;
        if(Math.abs(height(root.left) - height(root.right)) > 1) return false;
        return isBalanced(root.left) && isBalanced(root.right);
    }
    
    public int height(TreeNode root) {
        if(root == null) return 0;
        return Math.max(height(root.left), height(root.right)) + 1;
    }
}