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：递归

从root开始，一直向左的深度 == 一直向右的深度，则说明root是一个满二叉树，节点个数为2^height - 1

若不是，则节点个数为 countNodes(root->left) + countNodes(root->right) + 1;

/**
 * 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 left_height = get_height(root, true); //从root开始
        int right_height = get_height(root, false);
        if (left_height == right_height) {
            return pow(2, left_height) - 1;
        }
        return countNodes(root->left) + countNodes(root->right) + 1;
    }
private:
    int get_height(TreeNode *root, bool toLeft) {
        if (root == NULL) {
            return 0;
        }
        if (toLeft) {
            return get_height(root->left, true) + 1;
        }
        return get_height(root->right, false) + 1;
        
    }
};