Finding ‘k’ such that its modulus with each array element is same in C++

In this tutorial, we are going to write a program that finds a number such that its modulus with each array element is same. Let's see an example.

Input − arr = {10, 4, 2}

Output − 1 2

If there are two numbers x, y and x > y, assume that x - y = d.

Then the x = y + d.

Let's say we have a number k such that x%k = y%k. Apply modulo k for the above equation and find the value d.

x%k = (y+d)%k
y%k = y%k +d%k
d%k = 0

From the above calculation, if the number k is the divisor of the difference between the x and y. Then it will be a divisor of the numbers x and y.

Let's apply the same concept to the array of elements. And find the k value. See the steps to solve the problem.

Initialize the array with numbers
Here, the d will be the difference between the max and min values of the array elements.
Sort the values of the array using sort method.
Find the difference between the last and first numbers.
If the difference is zero, then all the numbers are same. Then the result of module with any number gives the same result.
Else find the divisors of the number d. And store them.
Iterate over all the divisors and find number whose modulo with all the array elements are same.

Example

Let's see the code.

Live Demo

#include <bits/stdc++.h>
using namespace std;
void findNumbers(int arr[], int n) {
   sort(arr, arr + n);
   int d = arr[n - 1] - arr[0];
   // check whether all elements are same or not
   if (d == 0) {
      cout << "Infinite number of k's";
      return;
   }
   // finding the divisors of d
   vector <int> v;
   for (int i = 1; i * i <= d; i++) {
      if (d % i == 0) {
         v.push_back(i);
         if (i != d / i) {
            v.push_back(d / i);
         }
      }
   }
   // findind the k's
   for (int i = 0; i < v.size(); i++) {
      int temp = arr[0] % v[i];
      int j;
      for (j = 1; j < n; j++) {
         if (arr[j] % v[i] != temp) {
            break;
         }
      }
      if (j == n)
         cout << v[i] << " ";
      }
      cout << endl;
   }
   int main() {
      int arr[] = {10, 4, 2};
      findNumbers(arr, 3);
   return 0;
}