C++ Program to Generate All Pairs of Subsets Whose Union Make the Set

This is a C++ program to generate all pairs of subsets, whose union make the Set.

Algorithms

Begin
   function UnionSet():
   Arguments:
      a[] = an array.
      n = number of elements.
      Body of the function:
      1) Generate binary code from 0 to 2^(n-1)-1 for all 2^(n-1) pairs.
      2) Print the array element which has 0 or 1 in corresponding indexes in code string for each code.
      3) Print them in a different set, which on the union of both sets gives the super set.
End

Example

#include<iostream>
#include<math.h>
#include<iomanip>
using namespace std;
void display(char code[], int a[], int n) //display the pairs
{
   int i;
   cout<<"\t{ ";
      for(i = 0; i < n; i++) {
         if(code[i] == '1')
            cout<<a[i]<<" ";
      }
   cout<<"}";
   cout<<" { ";
      for(i = 0; i < n; i++) {
         if(code[i] == '0')
            cout<<a[i]<<" ";
      }
   cout<<"}\n";
}
void UnionSet(int a[], int n) {
   int i, r, l;
   char binary[n];
   r = pow(2, n-1);
   for(i = 0; i < n; i++)
      binary[i] = '0';
   for(i = 0; i < r; i++) {
      display(binary, a, n);
      l=n-1;
      h:
      if(binary[l] == '0')
         binary[l] = '1';
      else {
         binary[l] = '0';
         l--;
         goto h;
      }
   }
}
int main() {
   int i, n;
   cout<<"\nEnter the number of elements: ";
   cin>>n;
   int a[n];
   cout<<"\n";
   for(i = 0; i < n; i++) {
      cout<<"Enter "<<i+1<<" element: ";
      cin>>a[i];
   }
   cout<<"\nThe possible subset pairs which on union generates the superset, are: \n";
   UnionSet(a, n);
   return 0;
}

Output

Enter the number of elements: 4
Enter 1 element: 4
Enter 2 element: 3
Enter 3 element: 2
Enter 4 element: 1
The possible subset pairs which on union generates the superset, are:
{ } { 4 3 2 1 }
{ 1 } { 4 3 2 }
{ 2 } { 4 3 1 }
{ 2 1 } { 4 3 }
{ 3 } { 4 2 1 }
{ 3 1 } { 4 2 }
{ 3 2 } { 4 1 }
{ 3 2 1 } { 4 }