LeetCode Top Interview 150
222. Count Complete Tree Nodes
Medium
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
from typing import Optional
class TreeNode:
def __init__(self, val: int = 0, left: Optional["TreeNode"] = None, right: Optional["TreeNode"] = None):
self.val = val
self.left = left
self.right = right
class Solution:
def countNodes(self, root: Optional[TreeNode]) -> int:
if root is None:
return 0
left_height = self._left_height(root)
right_height = self._right_height(root)
if left_height == right_height:
return (1 << left_height) - 1
return 1 + self.countNodes(root.left) + self.countNodes(root.right)
def _left_height(self, node: Optional[TreeNode]) -> int:
if node is None:
return 0
return 1 + self._left_height(node.left)
def _right_height(self, node: Optional[TreeNode]) -> int:
if node is None:
return 0
return 1 + self._right_height(node.right)