Next: , Previous: Permutations in cyclic form, Up: Permutations   [Index]

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.

Next: , Previous: Permutations in cyclic form, Up: Permutations   [Index]