# Count all sub-arrays having sum divisible by k

In this tutorial, we will be discussing a program to find the number of sub-arrays having sum divisible by k.

For this we will be provided with an array and a value k. Our task is to find the number of sub arrays that are having their sum as equal to the given value k.

## Example

Live Demo

#include <bits/stdc++.h>
using namespace std;
//counting subarrays with k sum
int count_subarray(int arr[], int n, int k){
int mod[k];
memset(mod, 0, sizeof(mod));
int cumSum = 0;
for (int i = 0; i < n; i++) {
cumSum += arr[i];
//taking modulus to get positive sum
mod[((cumSum % k) + k) % k]++;
}
int result = 0;
for (int i = 0; i < k; i++)
if (mod[i] > 1)
result += (mod[i] * (mod[i] - 1)) / 2;
result += mod;
return result;
}
int main(){
int arr[] = { 4, 5, 0, -2, -3, 1 };
int k = 5;
int n = sizeof(arr) / sizeof(arr);
cout << count_subarray(arr, n, k) << endl;
int arr1[] = { 4, 5, 0, -12, -23, 1 };
nt k1 = 5;
int n1 = sizeof(arr1) / sizeof(arr1);
cout << count_subarray(arr1, n1, k1) << endl;
return 0;
}

## Output

7
7