Count Complete Tree Nodes

Description

Given the root of a complete binary tree, return the number of the nodes in the tree.

According to Wikipedia, every level, except possibly the last, is completely filled in a complete binary tree, 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.

Design an algorithm that runs in less than O(n) time complexity.

Example 1:

Input: root = [1,2,3,4,5,6] Output: 6

Example 2:

Input: root = [] Output: 0

Example 3:

Input: root = [1] Output: 1

Constraints:

• The number of nodes in the tree is in the range [0, 5 * 104].
• 0 <= Node.val <= 5 * 104
• The tree is guaranteed to be complete.

Code

Key: The subtree of a complete binary tree is also a complete binary tree.

compare the depth between left sub tree and right sub tree.

1. A, If it is equal, it means the left sub tree is a full binary tree
2. B, It it is not , it means the right sub tree is a full binary tree

為何是 pow(2, leftDepth)(or pow(2, rightDepth)) 是因為，得知左右子節點的樹高後，為 complete binary tree 的子節點，樹高為 h 時，會具有 $2^h-1$ 個節點，再加上自己，就會是 $2^h$，然後再遞迴加上另外一個子節點的回傳值即可。

Time Complexity: $O(\log n\cdot \log n)$, Space Complexity: $O(1)$

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    int countNodes(TreeNode* root) {
        if(!root) return 0;
        int leftDepth = getDepth(root->left);
        int rightDepth = getDepth(root->right);
        if(leftDepth == rightDepth) {
            return pow(2, leftDepth) + countNodes(root->right);
        } else {
            return pow(2, rightDepth)  + countNodes(root->left);
        }
 
    }
 
    int getDepth(TreeNode* root){
        if(!root) return 0;
        return 1 + getDepth(root->left);
    }
 
 
};

Source

• Count Complete Tree Nodes - LeetCode