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;
}
};