Balanced Binary Tree

发布时间：2020-12-14 05:09:36 所属栏目：大数据来源：网络整理

导读：Question 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: Giv

Question

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,15,7]:

    3
   /   9  20
    /     15   7

Return true.

Solution -- Recursion

Key point of solution is that we need a helper function to get max height of left child tree and right child tree.

In each level,get height is O(N) time complexity; and considering it‘s binary tree,level number is logN,so total time complexity is O(NlogN).

 1 # Definition for a binary tree node.
 2 # class TreeNode:
 3 #     def __init__(self,x):
 4 #         self.val = x
 5 #         self.left = None
 6 #         self.right = None
 7 
 8 class Solution:
 9     def isBalanced(self,root: TreeNode) -> bool:
10         def getHeight(node: TreeNode) -> int:
11             if not node:
12                 return 0
13             return max(getHeight(node.left),getHeight(node.right)) + 1
14         
15         if not root:
16             return True
17         left_val = getHeight(root.left)
18         right_val = getHeight(root.right)
19         if abs(left_val - right_val) > 1:
20             return False
21         return self.isBalanced(root.left) and self.isBalanced(root.right)

Improved Solution?

Evaluate child tree is balanced or not while calculation heights. Time complexity is O(N).

 1 # Definition for a binary tree node.
 2 # class TreeNode:
 3 #     def __init__(self,root: TreeNode) -> bool:
10         def getHeight(node: TreeNode) -> int:
11             if not node:
12                 return 0
13             left = getHeight(node.left)
14             right = getHeight(node.right)
15             if left == -1 or right == -1:
16                 return -1
17             if abs(left - right) > 1:
18                 return -1
19             return max(left,right) + 1
20         
21         if not root:
22             return True
23         return getHeight(root) != -1

（编辑：李大同）

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