Subarray Sums Divisible by K

Given an integer array nums and an integer k, return the number of non-empty subarrays that have a sum divisible by k.

A subarray is a contiguous part of an array.

 

Example 1:

Input: nums = [4,5,0,-2,-3,1], k = 5
Output: 7
Explanation: There are 7 subarrays with a sum divisible by k = 5:
[4, 5, 0, -2, -3, 1], [5], [5, 0], [5, 0, -2, -3], [0], [0, -2, -3], [-2, -3]

Example 2:

Input: nums = [5], k = 9
Output: 0

 

Constraints:

  • 1 <= nums.length <= 3 * 104
  • -104 <= nums[i] <= 104
  • 2 <= k <= 104
SOLUTION:
from collections import defaultdict

class Solution:
    def subarraysDivByK(self, nums: List[int], k: int) -> int:
        total = 0
        ctr = defaultdict(int)
        ctr[0] += 1
        for num in nums:
            total = (total + num) % k
            ctr[total] += 1
        return sum(n * (n - 1) // 2 for n in ctr.values())

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