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/*
Copyright (C) 2016 Arb authors
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "flint/fmpz_mat.h"
#include "bool_mat.h"
/*
* Postorder traversal of a DAG follows
* https://en.wikipedia.org/wiki/Topological_sorting#Depth-first_search
*/
typedef struct
{
int *u; /* 'temporary mark' */
int *v; /* 'permanent mark' */
slong *post; /* postorder nodes */
slong npost; /* number of postorder nodes so far */
slong size;
} _toposort_s;
static void
_toposort_init(_toposort_s *s, slong size)
{
s->size = size;
s->u = flint_calloc(size, sizeof(int));
s->v = flint_calloc(size, sizeof(int));
s->post = flint_malloc(size * sizeof(slong));
s->npost = 0;
}
static void
_toposort_clear(_toposort_s *s)
{
flint_free(s->u);
flint_free(s->v);
flint_free(s->post);
}
static int
_toposort_visit(_toposort_s *s, const bool_mat_t A, slong n)
{
if (s->u[n])
return 1;
if (!s->v[n])
{
slong m;
s->u[n] = 1;
for (m = 0; m < s->size; m++)
if (bool_mat_get_entry(A, n, m))
if (_toposort_visit(s, A, m))
return 1;
s->v[n] = 1;
s->u[n] = 0;
s->post[s->npost++] = n;
}
return 0;
}
slong
bool_mat_nilpotency_degree(const bool_mat_t A)
{
slong n;
if (!bool_mat_is_square(A))
{
flint_printf("bool_mat_nilpotency_degree: a square matrix is required!\n");
flint_abort();
}
if (bool_mat_is_empty(A))
return 0;
n = bool_mat_nrows(A);
if (n == 1)
{
return bool_mat_get_entry(A, 0, 0) ? -1 : 1;
}
else
{
_toposort_s s;
slong i;
int has_cycle;
int result;
_toposort_init(&s, n);
for (has_cycle = 0, i = 0; !has_cycle && i < n; i++)
if (!s.v[i])
has_cycle = _toposort_visit(&s, A, i);
if (has_cycle)
{
result = -1;
}
else
{
/* Find the length of the longest path within the DAG */
/* http://stackoverflow.com/a/10737524/4072759 */
slong x, y, z;
slong max_overall;
fmpz_mat_t E;
fmpz_mat_init(E, n, n);
fmpz_mat_zero(E);
max_overall = 0;
for (i = n - 1; i >= 0; i--)
{
slong max_in = 0;
y = s.post[i];
for (x = 0; x < n; x++)
{
max_in = FLINT_MAX(max_in,
fmpz_get_si(fmpz_mat_entry(E, x, y)));
}
for (z = 0; z < n; z++)
{
if (bool_mat_get_entry(A, y, z))
{
fmpz_set_si(fmpz_mat_entry(E, y, z), max_in + 1);
max_overall = FLINT_MAX(max_overall, max_in + 1);
}
}
}
fmpz_mat_clear(E);
result = max_overall + 1;
}
_toposort_clear(&s);
return result;
}
}
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