Balanced Binary Tree

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,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).

# 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: TreeNode) -> bool:
        def getHeight(node: TreeNode) -> int:
            if not node:
                return 0
            return max(getHeight(node.left), getHeight(node.right)) + 1
        
        if not root:
            return True
        left_val = getHeight(root.left)
        right_val = getHeight(root.right)
        if abs(left_val - right_val) > 1:
            return False
        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).

# 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: TreeNode) -> bool:
        def getHeight(node: TreeNode) -> int:
            if not node:
                return 0
            left = getHeight(node.left)
            right = getHeight(node.right)
            if left == -1 or right == -1:
                return -1
            if abs(left - right) > 1:
                return -1
            return max(left, right) + 1
        
        if not root:
            return True
        return getHeight(root) != -1