222.Count Complete Tree Nodes

Description

Given the root of a complete binary tree, return the number of the nodes in the tree.

According to Wikipedia, every level, except possibly the last, is completely filled in a complete binary tree, and all nodes in the last level are as far left as possible. It can have between 1 and $2^h$ nodes inclusive at the last level h.

Design an algorithm that runs in less than O(n) time complexity.

Constraints:

  • The number of nodes in the tree is in the range $[0, 5 * 10^4]$.
  • $0$<= Node.val <= $5 * 10^4$
  • The tree is guaranteed to be complete.

Solution

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# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def countNodes(self, root: Optional[TreeNode]) -> int:
        if not root: return 0
        return self.countNodes(root.left)+1+self.countNodes(root.right)

Summary

I think this problem more like easy. and the complete binary tree node count is $2^h-1$.

  • The common solution is :Recursive
  • The inital boundary is none nodes need to be zero.