练习题 (八)

题目：

Count Complete Tree Nodes

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.

解答1，（错误）

/**
* 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 == NULL)
return 0;

// int leftHeight = 0;
// int rightHeight = 0;

// TreeNode *pLeft = root;
// while(pLeft) {
//     ++leftHeight;
//     pLeft = pLeft->left;
// }

// TreeNode *pRight = root;
// while(pRight) {
//     ++rightHeight;
//     pRight = pRight->right;
// }

// if(leftHeight == rightHeight)
//     return pow(2, leftHeight)-1;

return countNodes(root->left) + countNodes(root->right) + 1;

}
};

解答，正确：

把上面的中间代码的反注释掉，运行通过。

心得：

这个题目，需要利用到满二叉树的节点数为2的N次方减1，并且我们做题目的时候，通常做出来的是前面一种解答的形式。

这个题目，混搭了满二叉树的求节点数，和完全二叉树的性质。当然，我也只做到了前面一种解答，测试代码报告效率不高，时间已经超过了最大时间。后面再补上了中间的代码。