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/* 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;
}
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