974. Subarray Sums Divisible by K

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974. Subarray Sums Divisible by K

Description

Difficulty: Medium

Related Topics: Array, Hash Table, Prefix Sum

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:

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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:

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

Constraints:

  • 1 <= nums.length <= 3 * 104
  • -104 <= nums[i] <= 104
  • 2 <= k <= 104

Hints/Notes

  • preSum and mod

Solution

Language: C++

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class Solution {
public:
    int subarraysDivByK(vector<int>& nums, int k) {
        vector<int> preSumMod(k, 0);
        int res = 0, preSum = 0;
        preSumMod[0] = 1;
        for (int num : nums) {
            preSum = (num % k + k + preSum) % k;
            res += preSumMod[preSum];
            preSumMod[preSum]++;
        }
        return res;
    }
};