Absolute Difference between the Product of Non-Prime numbers and Prime numbers of an Array?

Here we will see how we can find the absolute difference between the product of all prime numbers and all non-prime numbers of an array. To solve this problem, we have to check whether a number is prime or not. One possible way for primality testing is by checking a number is not divisible by any number between 2 to square root of that number. So this process will take ?(√?) amount of time. Then get the product and try to find the absolute difference.

Algorithm

diffPrimeNonPrimeProd(arr)

begin
   prod_p := product of all prime numbers in arr
   prod_np := product of all non-prime numbers in arr
   return |prod_p – prod_np|
end

Example

 Live Demo

#include <iostream>
#include <cmath>
using namespace std;
bool isPrime(int n){
   for(int i = 2; i<=sqrt(n); i++){
      if(n % i == 0){
         return false; //not prime
      }
   }
   return true; //prime
}
int diffPrimeNonPrimeProd(int arr[], int n) {
   int prod_p = 1, prod_np = 1;
   for(int i = 0; i<n; i++){
      if(isPrime(arr[i])){
         prod_p *= arr[i];
      } else {
         prod_np *= arr[i];
      }
   }
   return abs(prod_p - prod_np);
}
main() {
   int arr[] = { 4, 5, 3, 8, 13, 10};
   int n = sizeof(arr) / sizeof(arr[0]);
   cout << "Difference: " << diffPrimeNonPrimeProd(arr, n);
}

Output

Difference: 125