leecode_222 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.

用暴力法, recursive求会超时 O(N).   如果从某节点一直向左的高度 = 一直向右的高度, 那么以该节点为root的子树一定是complete binary tree. 而 complete binary tree的节点数,可以用公式算出 2^h - 1. 如果高度不相等, 则递归调用 return countNode(left) + countNode(right)
+ 1.  复杂度为O(h^2)   

c++ 代码：

/**
* 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 l = getLeft(root) + 1;
int r = getRight(root) + 1;

if(l==r) {
return (2<<(l-1)) - 1;
} else {
return countNodes(root->left) + countNodes(root->right) + 1;
}
}

int getLeft(TreeNode* root) {
int count = 0;
while(root->left!=NULL) {
root = root->left;
++count;
}
return count;
}

int getRight(TreeNode* root) {
int count = 0;
while(root->right!=NULL) {
root = root->right;
++count;
}
return count;
}
};