Question

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<sup>h</sup> nodes inclusive at the last level h.

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

Example 1:

Input: root = [1,2,3,4,5,6]
Output: 6

Example 2:

Input: root = []
Output: 0

Example 3:

Input: root = [1]
Output: 1

Constraints:

• The number of nodes in the tree is in the range [0, 5 * 10<sup>4</sup>].

• 0 <= Node.val <= 5 * 10<sup>4</sup>

• The tree is guaranteed to be complete.

Solution

# 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 __init__(self):
        self.count = 0
    def countNodes(self, root: Optional[TreeNode]) -> int:
        self.count_nodes(root)
        return self.count

    def count_nodes(self,root):
        if root:
            self.count+=1
            if root.left:
                self.count_nodes(root.left)
            if root.right:
                self.count_nodes(root.right)
        return

Time Complexity: O(n)