Number of Different Subsequences GCDs — LeetCode 1819 Python Solution

The problem

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.

Example

Input

nums = [6,10,3]

Output

5

Explanation

The figure shows all the non-empty subsequences and their GCDs.

Python solution

class Solution:
    def countDifferentSubsequenceGCDs(self, nums: List[int]) -> int:
        mx = max(nums)
        vis = set(nums)
        ans = 0
        for x in range(1, mx + 1):
            g = 0
            for y in range(x, mx + 1, x):
                if y in vis:
                    g = gcd(g, y)
                    if g == x:
                        ans += 1
                        break
        return ans

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 1819. Number of Different Subsequences GCDs is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math and Number Theory.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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