Count pairs from two arrays whose modulo operation yields K

Given an integer k and two arrays arr1 and arr2, the task is to count the total pairs (formed after choosing an element from arr1 and another from arr2) from these arrays whose modulo operation yields k.
Note: If in a pair (a, b), a > b then the modulo must be performed as a % b. Also, pairs occurring more than once will be counted only once.

Examples:

Input: arr1[] = {1, 3, 7}, arr2[] = {5, 3, 1}, K = 2
Output: 2
(3, 5) and (7, 5) are the only possible pairs.
Since, 5 % 3 = 2 and 7 % 5 = 2

Input: arr1[] = {2, 5, 99}, arr2[] = {2, 8, 1, 4}, K = 0
Output: 6
All possible pairs are (2, 2), (2, 8), (2, 4), (2, 1), (5, 1) and (99, 1).

Approach:

  • Take one element from arr1 at a time and perform it’s modulo operation with all the other elements of arr2 one by one.
  • If the result from the previous step is equal to k then store the pair (a, b) in a set in order to avoid duplicates where a is the smaller element and b is the larger one.
  • Total required pairs will be the size of the set in the end.

Below is the implementation of the above approach:

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// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the total pairs
// of elements whose modulo yield K
int totalPairs(int arr1[], int arr2[], int K, int n, int m)
{
  
    // set is used to avoid duplicate pairs
    set<pair<int, int> > s;
  
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
  
            // check which element is greater and
            // proceed according to it
            if (arr1[i] > arr2[j]) {
  
                // check if modulo is equal to K
                if (arr1[i] % arr2[j] == K)
                    s.insert(make_pair(arr1[i], arr2[j]));
            }
            else {
                if (arr2[j] % arr1[i] == K)
                    s.insert(make_pair(arr2[j], arr1[i]));
            }
        }
    }
  
    // return size of the set
    return s.size();
}
  
// Driver code
int main()
{
    int arr1[] = { 8, 3, 7, 50 };
    int arr2[] = { 5, 1, 10, 4 };
    int K = 3;
    int n = sizeof(arr1) / sizeof(arr1[0]);
    int m = sizeof(arr2) / sizeof(arr2[0]);
  
    cout << totalPairs(arr1, arr2, K, n, m);
    return 0;
}

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Output:

3

Note: To print all the pairs just print the elements of set.



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