Count Complete Tree Nodes

Similar Problems:

Given a complete binary tree, count the number of nodes.

Definition of a complete binary tree from Wikipedia:

In a complete binary tree every level, except possibly the last, is completely filled, 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.

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

## https://code.dennyzhang.com/count-complete-tree-nodes ## Basic Ideas: Cut the examine dataset into half ## Check height of sub-tree and right-tree ## For each divide-conquer, one half will be solved without recursive ## ## Sample Data: ## 1 ## / \ ## 2 3 ## / ## 4 ## ## Complexity: Time O(h*log(n)) = O(log(n)*log(n)). Space O(1). If include system stack, Space O(log(n)) # Definition for a binary tree node. # class TreeNode(object): # def __init__(self, x): # self.val = x # self.left = None # self.right = None class Solution(object): def countNodes(self, root): """ :type root: TreeNode :rtype: int """ if root is None: return 0 # root node is with height 0 lh, rh = 0, 0 lnode, rnode = root, root while lnode: lnode = lnode.left lh += 1 while rnode: rnode = rnode.right rh += 1 if lh == rh: return pow(2, lh) - 1 else: return self.countNodes(root.left) + self.countNodes(root.right) + 1