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Array with GCD of any of its subset belongs to the given array

Given a set of N elements such that Nin [1, 1000], task is to generate an array such that the GCD of any subset of the generated array lies in the given set of elements. The generated array should not be more than thrice the length of the set of the GCD.

Prerequisite : GCD of an Array | Subset of Array

Examples :

Input : 3
        1 2 7
Output :  1 1 2 1 7

Input : 4
        2 4 6 12
Output : 2 2 4 2 6 2 12


Input : 5
        2 5 6 7 11
Output : No array can be build



Explanation :
Calculate the GCD of an array or in this case a set. Now, first sort the given set of GCD. If the GCD of this set is equal to the minimum number of the given set, then just by putting this GCD between each number. But, if this GCD is not the minimum element of the given set, then unfortunately “no array can be build”.

C++

// C++ implementation to generate the 
// required array
#include <bits/stdc++.h>
using namespace std;
  
// Function to return gcd of a and b
int gcd(int a, int b)
{
    if (a == 0)
       return b;       
    return gcd(b % a, a);
}
  
// Function to find gcd of
// array of numbers
int findGCD(vector<int> arr, int n)
{
    int result = arr[0];    
    for (int i = 1; i < n; i++)
        result = gcd(arr[i], result);
    return result;
}
  
// Function to generate the array
// with required constraints.
void compute(vector<int> arr, int n)
{
    vector<int> answer;
      
    // computing GCD of the given set
    int GCD_of_array = findGCD(arr, n);
  
    // Solution exists if GCD of array is equal
    // to the minimum element of the array
    if(GCD_of_array == arr[0])
    {
        answer.push_back(arr[0]);
        for(int i = 1; i < n; i++)
        {
            answer.push_back(arr[0]);
            answer.push_back(arr[i]);
        }
      
        // Printing the built array
        for (int i = 0; i < answer.size(); i++)
            cout << answer[i] << " ";
    }
    else
        cout << "No array can be build";
}
  
// Driver function
int main()
{
  
    // Taking in the input and initializing
    // the set STL set in cpp has a property
    // that it maintains the elements in
    // sorted order, thus we do not need 
    // to sort them externally
    int n = 3;
    int input[]= {2, 5, 6, 7, 11};
    set<int> GCD(input, input + n);
    vector<int> arr;
    set<int>::iterator it;
      
    for(it = GCD.begin(); it!= GCD.end(); ++it)
        arr.push_back(*it);
  
    // Calling the computing function.
    compute(arr,n);
      
    return 0;
}

Java

// Java implementation 
// to generate the 
// required array
import java.io.*;
import java.util.*;
  
class GFG
{
// Function to return
// gcd of a and b
static int gcd(int a,
               int b)
{
    if (a == 0)
    return b;     
    return gcd(b % a, a);
}
  
// Function to find gcd 
// of array of numbers
public static int findGCD(ArrayList<Integer> 
                                 arr, int n)
{
    int result = arr.get(0); 
    for (int i = 1; i < n; i++)
        result = gcd(arr.get(i), 
                    result);
    return result;
}
  
// Function to generate 
// the array with required 
// constraints.
public static void compute(ArrayList<Integer>
                                  arr, int n)
{
    ArrayList<Integer> answer = 
                    new ArrayList<Integer>();
      
    // computing GCD of
    // the given set
    int GCD_of_array = findGCD(arr, n);
  
    // Solution exists if GCD
    // of array is equal to the 
    // minimum element of the array
    if(GCD_of_array == arr.get(0))
    {
        answer.add(arr.get(0));
        for(int i = 1; i < n; i++)
        {
            answer.add(arr.get(0));
            answer.add(arr.get(i));
        }
      
        // Printing the 
        // built array
        for (int i = 0
                 i < answer.size(); i++)
            System.out.print(answer.get(i) + " ");
    }
    else
        System.out.print("No array " +
                      "can be build");
}
  
// Driver Code
public static void main(String args[])
{
  
    // Taking in the input and 
    // initializing the set STL
    // set in cpp has a property
    // that it maintains the 
    // elements in sorted order, 
    // thus we do not need to 
    // sort them externally
    int n = 3;
    Integer input[]= {2, 5, 6, 7, 11};
    HashSet<Integer> GCD = new HashSet<Integer>
                        (Arrays.asList(input));
    ArrayList<Integer> arr = 
                new ArrayList<Integer>();
      
    for (int v : GCD)
        arr.add(v);
  
    // Calling the
    // computing function.
    compute(arr, n);
}
}
  
// This code is contributed by
// Manish Shaw(manishshaw1)

Python3

from math import gcd
# Python 3 implementation to generate the 
# required array
  
# Function to find gcd of
# array of numbers
def findGCD(arr, n):
    result = arr[0
    for i in range(1,n):
        result = gcd(arr[i], result)
    return result
  
# Function to generate the array
# with required constraints.
def compute(arr, n):
    answer = []
      
    # computing GCD of the given set
    GCD_of_array = findGCD(arr, n)
  
    # Solution exists if GCD of array is equal
    # to the minimum element of the array
    if(GCD_of_array == arr[0]):
        answer.append(arr[0])
        for i in range(1,n):
            answer.append(arr[0])
            answer.append(arr[i])
      
        # Printing the built array
        for i in range(len(answer)):
            print(answer[i],end = " ")
  
      
    else:
        print("No array can be build")
  
# Driver function
if __name__ == '__main__':
    # Taking in the input and initializing
    # the set STL set in cpp has a property
    # that it maintains the elements in
    # sorted order, thus we do not need 
    # to sort them externally
    n = 3
    input = [2, 5, 6, 7, 11]
    GCD = set()
    for i in range(len(input)):
        GCD.add(input[i])
  
    arr = []
  
    for i in GCD:
        arr.append(i)
  
    # Calling the computing function.
    compute(arr,n)
      
# This code is contributed by
# Surendra_Gangwar

C#

// C# implementation 
// to generate the 
// required array
using System;
using System.Collections.Generic;
  
class GFG
{
    // Function to return
    // gcd of a and b
    static int gcd(int a, int b)
    {
        if (a == 0)
        return b;     
        return gcd(b % a, a);
    }
      
    // Function to find gcd 
    // of array of numbers
    static int findGCD(List<int> arr, 
                               int n)
    {
        int result = arr[0]; 
        for (int i = 1; i < n; i++)
            result = gcd(arr[i], 
                         result);
        return result;
    }
      
    // Function to generate 
    // the array with required 
    // constraints.
    static void compute(List<int> arr, 
                                int n)
    {
        List<int> answer = new List<int>();
          
        // computing GCD of
        // the given set
        int GCD_of_array = findGCD(arr, n);
      
        // Solution exists if GCD
        // of array is equal to the 
        // minimum element of the array
        if(GCD_of_array == arr[0])
        {
            answer.Add(arr[0]);
            for(int i = 1; i < n; i++)
            {
                answer.Add(arr[0]);
                answer.Add(arr[i]);
            }
          
            // Printing the 
            // built array
            for (int i = 0; i < answer.Count; i++)
                Console.Write(answer[i] + " ");
        }
        else
            Console.Write("No array " +
                          "can be build");
    }
      
    // Driver Code
    static void Main()
    {
      
        // Taking in the input and 
        // initializing the set STL
        // set in cpp has a property
        // that it maintains the 
        // elements in sorted order, 
        // thus we do not need to 
        // sort them externally
        int n = 3;
        int []input= new int[]{2, 5, 6, 7, 11};
        HashSet<int> GCD = new HashSet<int>(input);
        List<int> arr = new List<int>();
          
        foreach (int b in GCD)
            arr.Add(b);
      
        // Calling the
        // computing function.
        compute(arr, n);
    }
}
  
// This code is contributed by
// Manish Shaw(manishshaw1)

Output:

No array can be build

Time Complexity : O(nlog(n)), where n is the size of array given.



This article is attributed to GeeksforGeeks.org

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