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222. Count Complete Tree Nodes

Difficulty Topics

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 2h 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 * 104].
  • 0 <= Node.val <= 5 * 104
  • The tree is guaranteed to be complete.

Solution

count-complete-tree-nodes.py
# 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:

        def countDepth(node, countLeft = True):
            depth = 0

            while node:
                depth += 1
                if countLeft:
                    node = node.left
                else:
                    node = node.right

            return depth

        left, right = countDepth(root), countDepth(root, False)

        if left == right:
            return (1 << left) - 1
        else:
            return 1 + self.countNodes(root.left) + self.countNodes(root.right)