Subarray_Sums_Divisible_by_K.java

/*

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

*/

import java.util.*;
class Subarray_Sums_Divisible_by_K {
    public int subarraysDivByK(int[] nums, int k) {
        int n = nums.length ;
        int prefix = 0;
        int count =0 ;
        HashMap <Integer,Integer> map = new HashMap <>();
        map.put(0,1);
        for(int i = 0; i<n ; i++){
            prefix = prefix + nums[i];
            int need = prefix %k ;
            if(need <0){
                need = need + k ;
            }
            if(map.containsKey(need)){
                count = count + map.get(need);
            }
            map.put(need , map.getOrDefault(need,0)+1);
        }
        return count ;
    }
}