Permutation Examples - GNU Scientific Library -- Reference Manual
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### 9.9 Examples

The example program below creates a random permutation (by shuffling the elements of the identity) and finds its inverse.

         #include <stdio.h>
         #include <gsl/gsl_rng.h>
         #include <gsl/gsl_randist.h>
         #include <gsl/gsl_permutation.h>

         int
         main (void)
         {
           const size_t N = 10;
           const gsl_rng_type * T;
           gsl_rng * r;

           gsl_permutation * p = gsl_permutation_alloc (N);
           gsl_permutation * q = gsl_permutation_alloc (N);

           gsl_rng_env_setup();
           T = gsl_rng_default;
           r = gsl_rng_alloc (T);

           printf ("initial permutation:");
           gsl_permutation_init (p);
           gsl_permutation_fprintf (stdout, p, " %u");
           printf ("\n");

           printf (" random permutation:");
           gsl_ran_shuffle (r, p->data, N, sizeof(size_t));
           gsl_permutation_fprintf (stdout, p, " %u");
           printf ("\n");

           printf ("inverse permutation:");
           gsl_permutation_inverse (q, p);
           gsl_permutation_fprintf (stdout, q, " %u");
           printf ("\n");

           gsl_permutation_free (p);
           gsl_permutation_free (q);
           gsl_rng_free (r);

           return 0;
         }

Here is the output from the program,

         $ ./a.out
         initial permutation: 0 1 2 3 4 5 6 7 8 9
          random permutation: 1 3 5 2 7 6 0 4 9 8
         inverse permutation: 6 0 3 1 7 2 5 4 9 8

The random permutation `p[i]` and its inverse `q[i]` are related through the identity `p[q[i]] = i`, which can be verified from the output.

The next example program steps forwards through all possible third order permutations, starting from the identity,

         #include <stdio.h>
         #include <gsl/gsl_permutation.h>

         int
         main (void)
         {
           gsl_permutation * p = gsl_permutation_alloc (3);

           gsl_permutation_init (p);

           do
            {
               gsl_permutation_fprintf (stdout, p, " %u");
               printf ("\n");
            }
           while (gsl_permutation_next(p) == GSL_SUCCESS);

           gsl_permutation_free (p);

           return 0;
         }

Here is the output from the program,

         $ ./a.out
          0 1 2
          0 2 1
          1 0 2
          1 2 0
          2 0 1
          2 1 0

The permutations are generated in lexicographic order. To reverse the sequence, begin with the final permutation (which is the reverse of the identity) and replace `gsl_permutation_next` with `gsl_permutation_prev`.

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