LeetCode #222 - Count Complete Tree Nodes

题目描述：

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

Note:

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.

Example:

Input: 
    1
   / \
  2   3
 / \  /
4  5 6

Output: 6

完全树的非叶子节点都有两个子节点，而最后一层的叶子节点都是尽量靠左排列，求一棵完全树的节点数。显然是利用完全树的性质递归，分别计算完全树的最左边和最右边叶节点的高度，如果相等说明是完美二叉树，可以直接计算节点数，否则继续递归。

class Solution {
public:
    int countNodes(TreeNode* root) {
        if(root==NULL) return 0;
        int l=left_height(root);
        int r=right_height(root);
        if(r==l) return pow(2,r)-1;
        else return countNodes(root->left)+countNodes(root->right)+1;
    }
    
    int left_height(TreeNode* root)
    {
        if(root==NULL) return 0;
        int height=1;
        while(root->left!=NULL)
        {
            root=root->left;
            height++;
        }
        return height;
    }
    
    int right_height(TreeNode* root)
    {
        if(root==NULL) return 0;
        int height=1;
        while(root->right!=NULL)
        {
            root=root->right;
            height++;
        }
        return height;
    }
};