5.1.8 Balanced Binary Tree

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本文详细介绍了平衡二叉树的概念及其性质，即AVL树，强调了其左右子树高度差不超过1的特点，并通过深度优先搜索算法来判断一棵二叉树是否为平衡二叉树。

平衡二叉树（Balanced Binary Tree）又被称为AVL树（有别于AVL算法），且具有以下性质：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。

	Notes:
	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.

	Solution: DFS.
	*/

	/**
	* Definition for binary tree
	* struct TreeNode {
	* int val;
	* TreeNode *left;
	* TreeNode *right;
	* TreeNode(int x) : val(x), left(NULL), right(NULL) {}
	* };
	*/

class Solution {
public:
    bool isBalanced(TreeNode *root) {
        return solve(root) != -1;
    }
    int solve(TreeNode *root) {
        if (root == NULL) return 0;
        int left = solve(root->left);
        int right = solve(root->right);
        if (left == -1 || right == -1 || abs(left - right) > 1) return -1;
        return max(left,right) + 1;
    }
};