Find minimum GCD of all pairs in an array

Last Updated : 18 Apr, 2023

Given an array arr of positive integers, the task is to find the minimum GCD possible for any pair of the given array.
Examples:

Input: arr[] = {1, 2, 3, 4, 5}
Output: 1
Explanation:
GCD(1, 2) = 1.

Input: arr[] = {2, 4, 6, 8, 3}
Output: 1

Naive approach: Generate all the pairs of elements and take GCD of them, finally minimizing the output with the result.

Initialize the result with the maximum possible gcd
Iterate over the array
Generate every pair
Find the gcd of pair of elements
Minimize the result with output.
Return result

Below is the implementation of the above approach:

C++

#include <bits/stdc++.h>
using namespace std;
 
int find_min_GCD_Pair(int arr[], int N)
{
 
    // Initialise the result with maximum possible gcd
    int result = INT_MAX;
 
    // Iterate over the array
    for (int i = 0; i < N; i++) {
 
        // Generate every pair
        for (int j = i + 1; j < N; j++) {
 
            // Find the gcd of pair of elements
            int gcd = __gcd(arr[i], arr[j]);
 
            // Minimise the result with output.
            result = min(result, gcd);
        }
    }
 
    // return result
    return result;
}
 
int main()
{
 
    int arr[] = { 6, 10, 15 };
    int N = 3;
    cout << find_min_GCD_Pair(arr, N);
 
    return 0;
}

Python3

# Python Equivalent
import math
 
 
def find_min_GCD_Pair(arr, N):
    # Initialise the result with maximum possible gcd
    result = float('inf')
 
    # Iterate over the array
    for i in range(N):
        # Generate every pair
        for j in range(i+1, N):
            # Find the gcd of pair of elements
            gcd = math.gcd(arr[i], arr[j])
 
            # Minimise the result with output.
            result = min(result, gcd)
 
    # return result
    return result
 
 
if __name__ == "__main__":
 
    arr = [6, 10, 15]
    N = 3
    print(find_min_GCD_Pair(arr, N))

Java

// Java program for the above approach
import java.util.*;
 
public class Main {
 
    public static int findMinGCDPair(int[] arr, int n)
    {
 
        // Initialize the result with maximum possible gcd
        int result = Integer.MAX_VALUE;
 
        // Iterate over the array
        for (int i = 0; i < n; i++) {
 
            // Generate every pair
            for (int j = i + 1; j < n; j++) {
 
                // Find the gcd of pair of elements
                int gcd = gcd(arr[i], arr[j]);
 
                // Minimise the result with output.
                result = Math.min(result, gcd);
            }
        }
 
        // return result
        return result;
    }
 
    public static int gcd(int a, int b)
    {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }
 
    public static void main(String[] args)
    {
 
        int[] arr = { 6, 10, 15 };
        int n = 3;
        System.out.println(findMinGCDPair(arr, n));
    }
}
 
// Contributed by adityasharmadev01

Javascript

// JS Equivalent
const findMinGCDPair = (arr, N) => {
    // Initialise the result with maximum possible gcd
    let result = Infinity;
 
    // Iterate over the array
    for (let i = 0; i < N; i++) {
        // Generate every pair
        for (let j = i + 1; j < N; j++) {
            // Find the gcd of pair of elements
            let gcd = gcdFunc(arr[i], arr[j]);
 
            // Minimise the result with output.
            result = Math.min(result, gcd);
        }
    }
 
    // return result
    return result;
}
 
const gcdFunc = (a, b) => {
    if (b === 0) {
        return a;
    }
    return gcdFunc(b, a % b);
};
 
const arr = [6, 10, 15];
const N = 3;
console.log(findMinGCDPair(arr, N));

C#

// C# code addition
using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
 
class Program {
    public static int _gcd(int a, int b)
    {
        if (a == 0)
            return b;
        return _gcd(b % a, a);
    }
    // The function finds the minimum gcd pair
    public static int find_min_GCD_Pair(int[] arr, int N)
    {
        // Initialise the result with maximum possible gcd
        int result = int.MaxValue;
 
        // Iterate over the array
        for (int i = 0; i < N; i++) {
            // Generate every pair
            for (int j = i + 1; j < N; j++) {
                // Find the gcd of pair of elements
                int gcd = _gcd(arr[i], arr[j]);
 
                // Minimise the result with output.
                result = Math.Min(result, gcd);
            }
        }
 
        // return result
        return result;
    }
 
    // Driver code.
    static void Main()
    {
        int[] arr = { 6, 10, 15 };
        int N = 3;
        Console.WriteLine(find_min_GCD_Pair(arr, N));
    }
}
 
// The code is contributed by Arushi Goel.

Output

Time Complexity: O(N²), where N is the length of the given input array.
Auxiliary Space: O(1)

Minimum gcd operations to make all array elements one

harshit23

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Find minimum GCD of all pairs in an array

C++

Python3

Java

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C#

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