Count Complete Tree Nodes

题目：

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.

分析：

http://www.programcreek.com/2014/06/leetcode-count-complete-tree-nodes-java/

Steps to solve this problem:
1) get the height of left-most part
2) get the height of right-most part
3) when they are equal, the # of nodes = 2^h -1
4) when they are not equal, recursively get # of nodes from left&right sub-trees

Time complexity is O(h^2).

参考代码如下：

/** * Definition for a binary tree node. * public class TreeNode { *     int val; *     TreeNode left; *     TreeNode right; *     TreeNode(int x) { val = x; } * } */public class Solution {    public int countNodes(TreeNode root) {        if(root==null)            return 0;             int left = getLeftHeight(root)+1;            int right = getRightHeight(root)+1;             if(left==right){            return (2<<(left-1))-1;        }else{            return countNodes(root.left)+countNodes(root.right)+1;        }    }         public int getLeftHeight(TreeNode n){        if(n==null) return 0;             int height=0;        while(n.left!=null){            height++;            n = n.left;        }        return height;    }         public int getRightHeight(TreeNode n){        if(n==null) return 0;             int height=0;        while(n.right!=null){            height++;            n = n.right;        }        return height;    }}