Data Structures, Algorithms, & Applications in C++ Chapter 1, Exercise 5

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 function 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 and in the files rsubset.*. The code assumes that n and x are global variables.

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void Subsets(int i)

{// Output all subsets of x[1:n].

 // Only x[i:n] to be changed.

   if (i == n) {// x[n] can be 0 or 1

                // output subset without element n

                x[n] = 0;

                for (int j = 1; j <= n; j++)

                   cout << x[j] << " ";

                cout << endl;

                

                // output subset with element n

                x[n] = 1;

                for (int j = 1; j <= n; j++)

                   cout << x[j] << " ";

                cout << endl;

                return;

                }

                

    // leave element i out

    x[i] = 0;

    // generate all subsets with i out

    Subsets(i+1);

                

    // put element i into subset

    x[i] = 1;

    // generate all subsets with i included

    Subsets(i+1);