Data Structures, Algorithms, & Applications in C++
Chapter 1, Exercise 29

We may represent a subset of n elements by the one-dimensional array x[1:n], where x[j] is one if element j is included in the subset and x[j] is zero if element j is not included in the subset.

To output the subsets recursively, we define a method subsets(int i) which outputs all x[1:n] with preset values for x[1:i-1] and x[i:n] taking on all possible 0 and 1 values. The invocation subsets(1) will output all subsets.

The code is given below. 
/** generate all subsets of n elements */

package applications;

public class AllSubsets
{
   // class data member
   static int [] x;  // subset vector
   
   /** define array x and invoke private method subsets */
   public static void allSubsets(int n)
   {
      x = new int [n + 1];
      // output all subsets of x[1:n]
      subsets(1);
   }

   /** output x[1:i-1] followed by all subsets of x[i:x.length-1] */
   private static void subsets(int i)
   {
      if (i == x.length - 1)
      {// x[x.length - 1] can be 0 or 1
         // output subset without last element
         x[x.length - 1] = 0;
         for (int j = 1; j <= x.length - 1; j++)
            System.out.print(x[j] + " ");
         System.out.println();
         
         // output subset with last element
         x[x.length - 1] = 1;
         for (int j = 1; j <= x.length - 1; j++)
            System.out.print(x[j] + " ");
         System.out.println();
         return;
      }
                   
      // leave element i out
      x[i] = 0;
      // generate all subsets with i excluded
      subsets(i + 1);
                   
       // put element i into subset
       x[i] = 1;
       // generate all subsets with i included
       subsets(i + 1);
   }
    
   /** test program */
   public static void main(String [] args)
   {
      allSubsets(4);
   }
}


The above code may be modified if we are to output element identifiers for the selected elements rather than 0/1 vectors.