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

Definition of a complete binary tree from :

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.

解题思路：如何巧妙的利用完全二叉树的性质来减少复杂度是这题的核心。一棵完全二叉树的左右两部分必有一部分是满二叉树。本题就是基于此产生了logn*logn的时间复杂度算法。

/** * Definition for a binary tree node. * struct TreeNode { *     int val; *     TreeNode *left; *     TreeNode *right; *     TreeNode(int x) : val(x), left(NULL), right(NULL) {} * }; */class Solution {public:    int countNodes(TreeNode* root) {       if(!root)return 0;       TreeNode *l=root,*r=root;       int hl=0,hr=0;       while(l){hl++;l=l->left;}       while(r){hr++;r=r->right;}       if(hl==hr)return (1<
     
      left)+countNodes(root->right);    }};