Leetcode: Count Complete Tree Nodes

## 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