Code:
import java.util.Random;
import java.util.Scanner;
public class Pair_Subset_Union_Set
{
public static int[] binary(int N)
{
int[] binary = new int[(int) Math.pow(2, N)];
for (int i = 0; i < Math.pow(2, N); i++)
{
int b = 1;
binary[i] = 0;
int num = i;
while (num > 0)
{
binary[i] += (num % 2) * b;
num /= 2;
b = b * 10;
}
}
return binary;
}
public static void main(String args[])
{
Random random = new Random();
Scanner sc = new Scanner(System.in);
System.out.println("Enter the number of elements in the set: ");
int N = sc.nextInt();
int[] sequence = new int[N];
for (int i = 0; i < N; i++)
sequence[i] = Math.abs(random.nextInt(100));
System.out.println("The elements in the set : ");
for (int i = 0; i < N; i++)
System.out.print(sequence[i] + " ");
int[] mask = new int[(int) Math.pow(2, N)];
mask = binary(N);
System.out
.println("\nThe pair of permutations whose union is original set are: ");
for (int i = 0; i < (Math.pow(2, N) / 2); i++)
{
System.out.print("{ ");
for (int j = 0; j < N; j++)
{
if (mask[i] % 10 == 1)
System.out.print(sequence[j] + " ");
mask[i] /= 10;
}
System.out.print("} and ");
System.out.print("{ ");
for (int j = 0; j < N; j++)
{
if (mask[(int) Math.pow(2, N) - 1 - i] % 10 == 1)
System.out.print(sequence[j] + " ");
mask[(int) Math.pow(2, N) - 1 - i] /= 10;
}
System.out.println("}");
}
sc.close();
}
}
Output:
Enter the number of elements in the set:
5
The elements in the set :
3 47 97 79 8
The pair of permutations whose union is original set are:
{ } and { 3 47 97 79 8 }
{ 3 } and { 47 97 79 8 }
{ 47 } and { 3 97 79 8 }
{ 3 47 } and { 97 79 8 }
{ 97 } and { 3 47 79 8 }
{ 3 97 } and { 47 79 8 }
{ 47 97 } and { 3 79 8 }
{ 3 47 97 } and { 79 8 }
{ 79 } and { 3 47 97 8 }
{ 3 79 } and { 47 97 8 }
{ 47 79 } and { 3 97 8 }
{ 3 47 79 } and { 97 8 }
{ 97 79 } and { 3 47 8 }
{ 3 97 79 } and { 47 8 }
{ 47 97 79 } and { 3 8 }
{ 3 47 97 79 } and { 8 }
Enter the number of elements in the set:
3
The elements in the set :
37 76 87
The pair of permutations whose union is original set are:
{ } and { 37 76 87 }
{ 37 } and { 76 87 }
{ 76 } and { 37 87 }
{ 37 76 } and { 87 }
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