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.

思路：

我居然在这道题上卡了一个小时。关键是对于平衡的定义，我开始理解错了，我以为是要所有叶节点的高度差不大于1.

但题目中的定义是如下这样的：

Below is a representation of the tree input: {1,2,2,3,3,3,3,4,4,4,4,4,4,#,#,5,5}:

        ____1____

       /         \

      2           2

     /  \        / \

    3    3      3   3

   /\    /\    /\

  4  4  4  4  4  4

 /\

5  5

Let's start with the root node (1). As you can see, left subtree's depth is 5, while right subtree's depth is 4. Therefore, the condition for a height-balanced binary tree holds for the root node. We continue the same comparison recursively for both left and right subtree, and we conclude that this is indeed a balanced binary tree.

我AC的代码：我觉得我的代码就挺好挺短的。

bool isBalanced3(TreeNode* root){

        int depth = ;

        return isBalancedDepth(root, depth);

    }

    bool isBalancedDepth(TreeNode* root, int &depth)

    {

        if(root == NULL) return true;

        int depthl = , depthr = ;

        bool ans = isBalancedDepth(root->left, depthl) && isBalancedDepth(root->right, depthr) && abs(depthl - depthr) < ;

        depth = ((depthl > depthr) ? depthl : depthr) + ;

        return ans;

    }

其他人的代码，对高度多遍历了一遍，会比较慢：

bool isBalanced(TreeNode *root) {

        if (!root) return true;

        if (abs(depth(root->left) - depth(root->right)) > ) return false;

        return isBalanced(root->left) && isBalanced(root->right);

    }

    int depth(TreeNode *node){

      if (!node) return ;

      return max(depth(node->left) + , depth(node->right) + );

    }