Q110 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 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.

解题思路：

明白了平衡二叉树的定义，则对于每个结点，都需要判断其左右子树的高度，因此需要借助一个求高度的函数。

Python实现：

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None
class Solution:
    def isBalanced(self, root):
        """
        :type root: TreeNode
        :rtype: bool
        """
        if root == None:
            return True
        left = self.maxheight(root.left)  # 当前结点左子树最大深度
        right = self.maxheight(root.right) # 当前结点右子树最大深度
        if abs(left - right) <= 1:  # 如果当前结点满足平衡二叉树的条件
            return self.isBalanced(root.left) and self.isBalanced(root.right) # 当前结点的左右结点也必须满足平衡二叉树的条件
        else: 
            return False
        
    def maxheight(self, root): # 找到左右子树最大深度
        if root == None:
            return 0
        return max(self.maxheight(root.left), self.maxheight(root.right)) + 1