Maximum number which can divide all array element after one replacement

Last Updated : 06 Oct, 2021

Given an array arr, replace any one element in array with any other integer. The task is to return the maximum number which divides all elements in this array completely.

Examples:

Input: arr = [15, 9, 3]
Output: 3
Explanation: Here replace 15 with 3 so array becomes arr = [3, 9, 3] and now all elements in array are divisible by 3, so 3 is our answer

Input: arr = [16, 5, 10, 25]
Output: 5

Approach: To solve the above problem:

Iterate the array over integer i from zero to less than its length
Each time, remove ith element from the array and find the greatest common divisor and store in variable the gcd
Update maxGcd if current gcd is greater than maxGcd

Below is the implementation of the above approach:

C++14

// C++ Implementation for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to return gcd of two numbers
int gcdOfTwoNos(int num1, int num2)
{
 
    // If one of numbers is 0
    // then gcd is other number
    if (num1 == 0)
        return num2;
    if (num2 == 0)
        return num1;
 
    // If both are equal
    // then that value is gcd
    if (num1 == num2)
        return num1;
 
    // One is greater
    if (num1 > num2)
        return gcdOfTwoNos(num1 - num2, num2);
    return gcdOfTwoNos(num1, num2 - num1);
}
 
// Function to return minimum sum
int Min_sum(int arr[], int N)
{
    // Initialize min_sum with large value
    int min_sum = 1000000, maxGcd = 1;
    for (int i = 0; i < N; i++) {
 
        // Initialize variable gcd
        int gcd;
        if (i == 0)
            gcd = arr[1];
        else {
            gcd = arr[i - 1];
        }
        for (int j = 0; j < N; j++) {
            if (j != i)
                gcd = gcdOfTwoNos(gcd, arr[j]);
        }
 
        // Storing value of arr[i] in c
        int c = arr[i];
 
        // Update maxGcd if gcd is greater
        // than maxGcd
        if (gcd > maxGcd)
            maxGcd = gcd;
    }
 
    // returning the maximum divisor
    // of all elements
    return maxGcd;
}
// Driver code
int main()
{
    int arr[] = { 16, 5, 10, 25 };
    int N = sizeof(arr) / sizeof(int);
    cout << Min_sum(arr, N);
    return 0;
}

Java

// Java program for the above approach 
import java.io.*;
 
class GFG 
{
   
  // Function to return gcd of two numbers
static int gcdOfTwoNos(int num1, int num2)
{
 
    // If one of numbers is 0
    // then gcd is other number
    if (num1 == 0)
        return num2;
    if (num2 == 0)
        return num1;
 
    // If both are equal
    // then that value is gcd
    if (num1 == num2)
        return num1;
 
    // One is greater
    if (num1 > num2)
        return gcdOfTwoNos(num1 - num2, num2);
    return gcdOfTwoNos(num1, num2 - num1);
}
 
// Function to return minimum sum
static int Min_sum(int arr[], int N)
{
    // Initialize min_sum with large value
    int min_sum = 1000000, maxGcd = 1;
    for (int i = 0; i < N; i++) {
 
        // Initialize variable gcd
        int gcd;
        if (i == 0)
            gcd = arr[1];
        else {
            gcd = arr[i - 1];
        }
        for (int j = 0; j < N; j++) {
            if (j != i)
                gcd = gcdOfTwoNos(gcd, arr[j]);
        }
 
        // Storing value of arr[i] in c
        int c = arr[i];
 
        // Update maxGcd if gcd is greater
        // than maxGcd
        if (gcd > maxGcd)
            maxGcd = gcd;
    }
 
    // returning the maximum divisor
    // of all elements
    return maxGcd;
}
   
// Driver code
    public static void main (String[] args) {
      int arr[] = { 16, 5, 10, 25 };
      int N = arr.length;
   
        System.out.println( Min_sum(arr, N));
    }
}
 
// This code is contributed by Potta Lokesh

Python3

# Python 3 Implementation for the above approach
 
# Function to return gcd1 of two numbers
def gcd1OfTwoNos(num1, num2):
    # If one of numbers is 0
    # then gcd1 is other number
    if (num1 == 0):
        return num2
    if (num2 == 0):
        return num1
 
    # If both are equal
    # then that value is gcd1
    if (num1 == num2):
        return num1
 
    # One is greater
    if (num1 > num2):
        return gcd1OfTwoNos(num1 - num2, num2)
    return gcd1OfTwoNos(num1, num2 - num1)
 
# Function to return minimum sum
def Min_sum(arr, N):
    # Initialize min_sum with large value
    min_sum = 1000000
    maxgcd1 = 1
    for i in range(N):
        # Initialize variable gcd1
        gcd1 = 1
        if (i == 0):
            gcd1 = arr[1]
        else:
            gcd1 = arr[i - 1]
        for j in range(N):
            if (j != i):
                gcd1 = gcd1OfTwoNos(gcd1, arr[j])
 
        # Storing value of arr[i] in c
        c = arr[i]
 
        # Update maxgcd1 if gcd1 is greater
        # than maxgcd1
        if (gcd1 > maxgcd1):
            maxgcd1 = gcd1
 
    # returning the maximum divisor
    # of all elements
    return maxgcd1
 
# Driver code
if __name__ == '__main__':
    arr = [16, 5, 10, 25]
    N = len(arr)
    print(Min_sum(arr, N))
     
    # This code is contributed by SURENDRA_GANGWAR.

C#

// C# program for the above approach 
 
using System;
 
public class GFG 
{
   
  // Function to return gcd of two numbers
static int gcdOfTwoNos(int num1, int num2)
{
 
    // If one of numbers is 0
    // then gcd is other number
    if (num1 == 0)
        return num2;
    if (num2 == 0)
        return num1;
 
    // If both are equal
    // then that value is gcd
    if (num1 == num2)
        return num1;
 
    // One is greater
    if (num1 > num2)
        return gcdOfTwoNos(num1 - num2, num2);
    return gcdOfTwoNos(num1, num2 - num1);
}
 
// Function to return minimum sum
static int Min_sum(int []arr, int N)
{
    // Initialize min_sum with large value
    int min_sum = 1000000, maxGcd = 1;
    for (int i = 0; i < N; i++) {
 
        // Initialize variable gcd
        int gcd;
        if (i == 0)
            gcd = arr[1];
        else {
            gcd = arr[i - 1];
        }
        for (int j = 0; j < N; j++) {
            if (j != i)
                gcd = gcdOfTwoNos(gcd, arr[j]);
        }
 
 
        // Update maxGcd if gcd is greater
        // than maxGcd
        if (gcd > maxGcd)
            maxGcd = gcd;
    }
 
    // returning the maximum divisor
    // of all elements
    return maxGcd;
}
   
// Driver code
    public static void Main (string[] args) {
      int []arr = { 16, 5, 10, 25 };
      int N = arr.Length;
   
        Console.WriteLine(Min_sum(arr, N));
    }
}
 
// This code is contributed by AnkThon

Javascript

  <script>
        // JavaScript Program to implement
        // the above approach
 
  // Function to return gcd of two numbers
function gcdOfTwoNos(num1, num2)
{
 
    // If one of numbers is 0
    // then gcd is other number
    if (num1 == 0)
        return num2;
    if (num2 == 0)
        return num1;
 
    // If both are equal
    // then that value is gcd
    if (num1 == num2)
        return num1;
 
    // One is greater
    if (num1 > num2)
        return gcdOfTwoNos(num1 - num2, num2);
    return gcdOfTwoNos(num1, num2 - num1);
}
 
// Function to return minimum sum
function Min_sum(arr, N)
{
    // Initialize min_sum with large value
    let min_sum = 1000000, maxGcd = 1;
    for (let i = 0; i < N; i++) {
 
        // Initialize variable gcd
        let gcd;
        if (i == 0)
            gcd = arr[1];
        else {
            gcd = arr[i - 1];
        }
        for (let j = 0; j < N; j++) {
            if (j != i)
                gcd = gcdOfTwoNos(gcd, arr[j]);
        }
 
        // Storing value of arr[i] in c
        let c = arr[i];
 
        // Update maxGcd if gcd is greater
        // than maxGcd
        if (gcd > maxGcd)
            maxGcd = gcd;
    }
 
    // returning the maximum divisor
    // of all elements
    return maxGcd;
}
         
 // Driver Code
         
      let arr = [ 16, 5, 10, 25 ];
      let N = arr.length;
   
      document.write( Min_sum(arr, N));
 
// This code is contributed by sanjoy_62.
    </script>

Output:

Time Complexity: O((N^2) * Log(M)), Where M is minimum value in array
Auxiliary Space: O(1)

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Share your thoughts in the comments

Maximum number which can divide all array element after one replacement

C++14

Java

Python3

C#

Javascript

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