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 2hnodes inclusive at the last level h.

 

方法1：遞歸

從root開始，一直向左的深度 == 一直向右的深度，則說明root是一個滿二叉樹，節點個數爲2^height - 1

若不是，則節點個數爲 countNodes(root->left) + countNodes(root->right) + 1;

 1 /**
 2  * Definition for a binary tree node.
 3  * struct TreeNode {
 4  *     int val;
 5  *     TreeNode *left;
 6  *     TreeNode *right;
 7  *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 8  * };
 9  */
10 class Solution {
11 public:
12     int countNodes(TreeNode* root) {
13         if (root == NULL) {
14             return 0;
15         }
16         int left_height = get_height(root, true); //從root開始
17         int right_height = get_height(root, false);
18         if (left_height == right_height) {
19             return pow(2, left_height) - 1;
20         }
21         return countNodes(root->left) + countNodes(root->right) + 1;
22     }
23 private:
24     int get_height(TreeNode *root, bool toLeft) {
25         if (root == NULL) {
26             return 0;
27         }
28         if (toLeft) {
29             return get_height(root->left, true) + 1;
30         }
31         return get_height(root->right, false) + 1;
32         
33     }
34 };