2447. Number of Subarrays With GCD Equal to K

Problem Link

Description

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Given an integer array nums and an integer k, return the number of subarrays of nums where the greatest common divisor of the subarray's elements is k.

A subarray is a contiguous non-empty sequence of elements within an array.

The greatest common divisor of an array is the largest integer that evenly divides all the array elements.

 

Example 1:

Input: nums = [9,3,1,2,6,3], k = 3
Output: 4
Explanation: The subarrays of nums where 3 is the greatest common divisor of all the subarray's elements are:
- [9,3,1,2,6,3]
- [9,3,1,2,6,3]
- [9,3,1,2,6,3]
- [9,3,1,2,6,3]

Example 2:

Input: nums = [4], k = 7
Output: 0
Explanation: There are no subarrays of nums where 7 is the greatest common divisor of all the subarray's elements.

 

Constraints:

• 1 <= nums.length <= 1000
• 1 <= nums[i], k <= 109

Solution

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Python3

class Solution:
    def subarrayGCD(self, nums: List[int], k: int) -> int:
        N = len(nums)
        res = 0
        
        for i in range(N):
            g = 0
 
            for j in range(i, N):
                g = gcd(g, nums[j])
                
                if g == k:
                    res += 1
        
        return res