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

Given a set of N elements such that N , 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


## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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  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;          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)      {          answer.push_back(arr);          for(int i = 1; i < n; i++)          {              answer.push_back(arr);              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                                    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                                    arr, int n)  {      ArrayList answer =                       new ArrayList();             // 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 GCD = new HashSet                          (Arrays.asList(input));      ArrayList arr =                   new ArrayList();             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       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):          answer.append(arr)          for i in range(1,n):              answer.append(arr)              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;           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)          {              answer.Add(arr);              for(int i = 1; i < n; i++)              {                  answer.Add(arr);                  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. My Personal Notes arrow_drop_up Check out this Author's contributed articles.

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