LeetCode 1819. Number of Different Subsequences GCDs

You are given an array nums that consists of positive integers.

The GCD of a sequence of numbers is defined as the greatest integer that divides all the numbers in the sequence evenly.

• For example, the GCD of the sequence [4,6,16] is 2.

A subsequence of an array is a sequence that can be formed by removing some elements (possibly none) of the array.

• For example, [2,5,10] is a subsequence of [1,2,1,2,4,1,5,10].

Return the number of different GCDs among all non-empty subsequences of nums.

Example 1:

Input: nums = [6,10,3]
Output: 5
Explanation: The figure shows all the non-empty subsequences and their GCDs.
The different GCDs are 6, 10, 3, 2, and 1.

Example 2:

Input: nums = [5,15,40,5,6]
Output: 7

Constraints:

• 1 <= nums.length <= 10^5

• 1 <= nums[i] <= 2 * 10^5

Solution

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class Solution {
public:
    int countDifferentSubsequenceGCDs(vector<int>& nums) {
        int max_num = *max_element(nums.begin(), nums.end());
        vector<bool> vec(max_num + 1, false);
        for (int num: nums) {
            vec[num] = true;
        }
        int ans = 0;
        for (int i = 1; i <= max_num; i++) {
            int gcd = 0;
            for (int j = i; j <= max_num; j += i) {
                if (vec[j] == true) {
                    gcd = __gcd(gcd, j);
                }
            }
            if (gcd == i) ans++;
        }
        
        return ans;
    }
};