/* permutation/permutation.c

 * 

 * Copyright (C) 2001, 2002 Nicolas Darnis

 * 

 * This program is free software; you can redistribute it and/or modify

 * it under the terms of the GNU General Public License as published by

 * the Free Software Foundation; either version 3 of the License, or (at

 * your option) any later version.

 * 

 * This program is distributed in the hope that it will be useful, but

 * WITHOUT ANY WARRANTY; without even the implied warranty of

 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

 * General Public License for more details.

 * 

 * You should have received a copy of the GNU General Public License

 * along with this program; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

 */

/* Modified for GSL by Brian Gough.

 * Use in-place algorithms, no need for workspace

 * Use conventions for canonical form given in Knuth (opposite of Sedgewick)

 */

#include <config.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_permutation.h>

int

gsl_permutation_linear_to_canonical (gsl_permutation * q,

                                     const gsl_permutation * p)

{

  const size_t n = p->size;

  size_t i, k, s;

  size_t t = n;

  const size_t *const pp = p->data;

  size_t *const qq = q->data;

  if (q->size != p->size)

    {

      GSL_ERROR ("size of q does not match size of p", GSL_EINVAL);

    }

  for (i = 0; i < n; i++)

    {

      k = pp[i];

      s = 1;

      while (k > i)

        {

          k = pp[k];

          s++;

        }

      if (k < i)

        continue;

      /* Now have k == i, i.e the least in its cycle, and s == cycle length */

      t -= s;

      qq[t] = i;

      k = pp[i];

      s = 1;

      while (k > i)

        {

          qq[t + s] = k;

          k = pp[k];

          s++;

        }

      if (t == 0)

        break;

    }

  return GSL_SUCCESS;

}

int

gsl_permutation_canonical_to_linear (gsl_permutation * p,

                                     const gsl_permutation * q)

{

  size_t i, k, kk, first;

  const size_t n = p->size;

  size_t *const pp = p->data;

  const size_t *const qq = q->data;

  if (q->size != p->size)

    {

      GSL_ERROR ("size of q does not match size of p", GSL_EINVAL);

    }

  for (i = 0; i < n; i++)

    {

      pp[i] = i;

    }

  k = qq[0];

  first = pp[k];

  for (i = 1; i < n; i++)

    {

      kk = qq[i];

      if (kk > first)

        {

          pp[k] = pp[kk];

          k = kk;

        }

      else

        {

          pp[k] = first;

          k = kk;

          first = pp[kk];

        }

    }

  pp[k] = first;

  return GSL_SUCCESS;

}

size_t

gsl_permutation_inversions (const gsl_permutation * p)

{

  size_t count = 0;

  size_t i, j;

  const size_t size = p->size;

  for (i = 0; i < size - 1; i++)

    {

      for (j = i + 1; j < size; j++)

        {

          if (p->data[i] > p->data[j])

            {

              count++;

            }

        }

    }

  return count;

}

size_t

gsl_permutation_linear_cycles (const gsl_permutation * p)

{

  size_t i, k;

  size_t count = 0;

  const size_t size = p->size;

  for (i = 0; i < size; i++)

    {

      k = p->data[i];

      while (k > i)

        {

          k = p->data[k];

        }

      if (k < i)

        continue;

      count++;

    }

  return count;

}

size_t

gsl_permutation_canonical_cycles (const gsl_permutation * p)

{

  size_t i;

  size_t count = 1;

  size_t min = p->data[0];

  for (i = 0; i < p->size; i++)

    {

      if (p->data[i] < min)

        {

          min = p->data[i];

          count++;

        }

    }

  return count;

}