974. Subarray Sums Divisible by K

Problem

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 * 10^4

• -10^4 <= nums[i] <= 10^4

• 2 <= k <= 10^4

Solution (Java)

class Solution {
    public int subarraysDivByK(int[] nums, int k) {
        int[] map = new int[k];
        int ans = 0;
        int sum = 0;
        map[0] = 1;
        for (int num : nums) {
            sum += num;
            int temp = sum % k;
            if (temp < 0) {
                temp += k;
            }
            ans += map[temp]++;
        }
        return ans;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).