Check if all array elements are pairwise co-prime or not

Given an array A[] consisting of N positive integers, the task is to check if all the array elements are pairwise co-prime, i.e. for all pairs (Ai , Aj), such that 1<=i<j<=N, GCD(Ai, Aj) = 1.

Examples: 

Input : A[] = {2, 3, 5}
Output : Yes
Explanation : All the pairs, (2, 3), (3, 5), (2, 5) are pairwise co-prime.

Input : A[] = {5, 10}
Output : No
Explanation : GCD(5, 10)=5 so they are not co-prime.

Naive Approach: The simplest approach to solve the problem is to generate all possible pairs from a given array and for each pair, check if it is coprime or not. If any pair is found to be non-coprime, print “No“. Otherwise, print “Yes“.
Time Complexity: O(N2)
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized based on the following observation: 



If any two numbers have a common prime factor, then their GCD can never be 1.  

This can also be interpreted as: 

The LCM of the array must be equal to the product of the elements in the array.

Therefore, the solution boils down to calculating the LCM of the given array and check if it is equal to the product of all the array elements or not.

Below is the implementation of the above approach :

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ Program for the above approach
#include <bits/stdc++.h>
using namespace std;
#define ll long long int
 
// Function to calculate GCD
ll GCD(ll a, ll b)
{
    if (a == 0)
        return b;
    return GCD(b % a, a);
}
 
// Function to calculate LCM
ll LCM(ll a, ll b)
{
    return (a * b)
        / GCD(a, b);
}
 
// Function to check if all elements
// in the array are pairwise coprime
void checkPairwiseCoPrime(int A[], int n)
{
    // Initialze variables
    ll prod = 1;
    ll lcm = 1;
 
    // Itertae over the array
    for (int i = 0; i < n; i++) {
 
        // Calculate product of
        // array elements
        prod *= A[i];
 
        // Calculate LCM of
        // array elements
        lcm = LCM(A[i], lcm);
    }
 
    // If the product of array elements
    // is equal to LCM of the array
    if (prod == lcm)
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
}
// Driver Code
int main()
{
    int A[] = { 2, 3, 5 };
    int n = sizeof(A) / sizeof(A[0]);
 
    // Function call
    checkPairwiseCoPrime(A, n);
}
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program for the above approach
import java.util.*;
import java.lang.*;
 
class GFG{
 
// Function to calculate GCD
static long GCD(long a, long b)
{
    if (a == 0)
        return b;
         
    return GCD(b % a, a);
}
 
// Function to calculate LCM
static long LCM(long a, long b)
{
    return (a * b) / GCD(a, b);
}
 
// Function to check if all elements
// in the array are pairwise coprime
static void checkPairwiseCoPrime(int A[], int n)
{
     
    // Initialze variables
    long prod = 1;
    long lcm = 1;
 
    // Itertae over the array
    for(int i = 0; i < n; i++)
    {
         
        // Calculate product of
        // array elements
        prod *= A[i];
 
        // Calculate LCM of
        // array elements
        lcm = LCM(A[i], lcm);
    }
     
    // If the product of array elements
    // is equal to LCM of the array
    if (prod == lcm)
        System.out.println("Yes");
    else
        System.out.println("No");
}
 
// Driver Code
public static void main (String[] args)
{
    int A[] = { 2, 3, 5 };
    int n = A.length;
     
    // Function call
    checkPairwiseCoPrime(A, n);
}
}
 
// This code is contributed by offbeat
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 program for the above approach
 
# Function to calculate GCD
def GCD(a, b):
     
    if (a == 0):
        return b
         
    return GCD(b % a, a)
 
# Function to calculate LCM
def LCM(a, b):
     
    return (a * b) // GCD(a, b)
 
# Function to check if aelements
# in the array are pairwise coprime
def checkPairwiseCoPrime(A, n):
     
    # Initialze variables
    prod = 1
    lcm = 1
 
    # Itertae over the array
    for i in range(n):
 
        # Calculate product of
        # array elements
        prod *= A[i]
 
        # Calculate LCM of
        # array elements
        lcm = LCM(A[i], lcm)
 
    # If the product of array elements
    # is equal to LCM of the array
    if (prod == lcm):
        print("Yes")
    else:
        print("No")
 
# Driver Code
if __name__ == '__main__':
     
    A = [ 2, 3, 5 ]
    n = len(A)
 
    # Function call
    checkPairwiseCoPrime(A, n)
 
# This code is contributed by mohit kumar 29
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program for
// the above approach
using System;
using System.Collections.Generic;
class GFG{
 
// Function to calculate GCD
static long GCD(long a,
                long b)
{
  if (a == 0)
    return b;
  return GCD(b % a, a);
}
 
// Function to calculate LCM
static long LCM(long a,
                long b)
{
  return (a * b) / GCD(a, b);
}
 
// Function to check if all elements
// in the array are pairwise coprime
static void checkPairwiseCoPrime(int []A,
                                 int n)
{    
  // Initialze variables
  long prod = 1;
  long lcm = 1;
 
  // Itertae over the array
  for(int i = 0; i < n; i++)
  {
    // Calculate product of
    // array elements
    prod *= A[i];
 
    // Calculate LCM of
    // array elements
    lcm = LCM(A[i], lcm);
  }
 
  // If the product of array elements
  // is equal to LCM of the array
  if (prod == lcm)
    Console.WriteLine("Yes");
  else
    Console.WriteLine("No");
}
 
// Driver Code
public static void Main(String[] args)
{
  int []A = {2, 3, 5};
  int n = A.Length;
 
  // Function call
  checkPairwiseCoPrime(A, n);
}
}
 
// This code is contributed by Rajput-Ji
chevron_right

Output: 
Yes



Time Complexity: O(N log (min(A[i])))
Auxiliary Space: O(1)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.





Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : mohit kumar 29, offbeat, Rajput-Ji

Article Tags :