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.

Example 1:

Given the following tree [3,9,20,null,null,15,7]:

    3
   /   9  20
    /     15   7

Return true.

Example 2:

Given the following tree [1,2,2,3,3,null,null,4,4]:

       1
      /      2   2
    /    3   3
  /  4   4

Return false.

給定一個二叉樹，判斷是否高度平衡。高度平衡二叉樹的定義：二叉樹的任意節點的兩個子樹的深度差不超過1。

Python:

class TreeNode:
    def __init__(self, x):
        self.val = x
        self.left = None
        self.right = None

class Solution:
    # @param root, a tree node
    # @return a boolean
    def isBalanced(self, root):
        return (self.getHeight(root) >= 0)
    
    def getHeight(self, root):
        if root is None:
            return 0
        left_height, right_height = self.getHeight(root.left), self.getHeight(root.right)
        if left_height < 0 or right_height < 0 or abs(left_height - right_height) > 1:
            return -1
        return max(left_height, right_height) + 1　

C++:

class Solution {
public:
    bool isBalanced(TreeNode *root) {
        if (!root) return true;
        if (abs(getDepth(root->left) - getDepth(root->right)) > 1) return false;
        return isBalanced(root->left) && isBalanced(root->right);    
    }
    int getDepth(TreeNode *root) {
        if (!root) return 0;
        return 1 + max(getDepth(root->left), getDepth(root->right));
    }
};

C++:

class Solution {
public:    
    bool isBalanced(TreeNode *root) {
        if (checkDepth(root) == -1) return false;
        else return true;
    }
    int checkDepth(TreeNode *root) {
        if (!root) return 0;
        int left = checkDepth(root->left);
        if (left == -1) return -1;
        int right = checkDepth(root->right);
        if (right == -1) return -1;
        int diff = abs(left - right);
        if (diff > 1) return -1;
        else return 1 + max(left, right);
    }
};

[LeetCode] 110. Balanced Binary Tree 平衡二叉樹