222 Count Complete Tree Nodes

🔀 Pick One

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:

     1
   /   \
  2     3
 / \   /
4   5 6

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.
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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:
        # count the depth of left-most and right-most nodes
        l, r = root, root
        lh, rh = 0, 0
        while l:
            l = l.left
            lh += 1
        while r:
            r = r.right
            rh += 1

        # if left-most and right-most have the same depth
        # the current tree is a full binary tree
        if lh == rh:
            return 2 ** lh - 1
        return 1 + self.countNodes(root.left) + self.countNodes(root.right)