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<a name="Permutation-Examples"></a>
<div class="header">
<p>
Next: <a href="Permutation-References-and-Further-Reading.html#Permutation-References-and-Further-Reading" accesskey="n" rel="next">Permutation References and Further Reading</a>, Previous: <a href="Permutations-in-cyclic-form.html#Permutations-in-cyclic-form" accesskey="p" rel="previous">Permutations in cyclic form</a>, Up: <a href="Permutations.html#Permutations" accesskey="u" rel="up">Permutations</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Examples-3"></a>
<h3 class="section">9.9 Examples</h3>
<p>The example program below creates a random permutation (by shuffling the
elements of the identity) and finds its inverse.
</p>
<div class="example">
<pre class="verbatim">#include &lt;stdio.h&gt;
#include &lt;gsl/gsl_rng.h&gt;
#include &lt;gsl/gsl_randist.h&gt;
#include &lt;gsl/gsl_permutation.h&gt;

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

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

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

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

  return 0;
}
</pre></div>

<p>Here is the output from the program,
</p>
<div class="example">
<pre class="example">$ ./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
</pre></div>

<p>The random permutation <code>p[i]</code> and its inverse <code>q[i]</code> are
related through the identity <code>p[q[i]] = i</code>, which can be verified
from the output.
</p>
<p>The next example program steps forwards through all possible third order
permutations, starting from the identity,
</p>
<div class="example">
<pre class="verbatim">#include &lt;stdio.h&gt;
#include &lt;gsl/gsl_permutation.h&gt;

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

  gsl_permutation_init (p);

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

  gsl_permutation_free (p);

  return 0;
}
</pre></div>

<p>Here is the output from the program,
</p>
<div class="example">
<pre class="example">$ ./a.out 
 0 1 2
 0 2 1
 1 0 2
 1 2 0
 2 0 1
 2 1 0
</pre></div>

<p>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 <code>gsl_permutation_next</code> with
<code>gsl_permutation_prev</code>.
</p>
<hr>
<div class="header">
<p>
Next: <a href="Permutation-References-and-Further-Reading.html#Permutation-References-and-Further-Reading" accesskey="n" rel="next">Permutation References and Further Reading</a>, Previous: <a href="Permutations-in-cyclic-form.html#Permutations-in-cyclic-form" accesskey="p" rel="previous">Permutations in cyclic form</a>, Up: <a href="Permutations.html#Permutations" accesskey="u" rel="up">Permutations</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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