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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 "bool_mat.h"
/*
* Cycle detection, following
* https://en.wikipedia.org/wiki/Topological_sorting#Depth-first_search
*/
typedef struct
{
int *u; /* 'temporary mark' */
int *v; /* 'permanent mark' */
slong size;
} _cycle_detection_s;
static void
_cycle_detection_init(_cycle_detection_s *s, slong size)
{
s->size = size;
s->u = flint_calloc(size, sizeof(int));
s->v = flint_calloc(size, sizeof(int));
}
static void
_cycle_detection_clear(_cycle_detection_s *s)
{
flint_free(s->u);
flint_free(s->v);
}
static int
_cycle_detection_visit(_cycle_detection_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 (_cycle_detection_visit(s, A, m))
return 1;
s->v[n] = 1;
s->u[n] = 0;
}
return 0;
}
int
bool_mat_is_nilpotent(const bool_mat_t A)
{
slong n;
if (!bool_mat_is_square(A))
{
flint_printf("bool_mat_is_nilpotent: 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);
}
else
{
_cycle_detection_s s;
slong i;
int has_cycle;
_cycle_detection_init(&s, n);
for (has_cycle = 0, i = 0; !has_cycle && i < n; i++)
if (!s.v[i])
has_cycle = _cycle_detection_visit(&s, A, i);
_cycle_detection_clear(&s);
return !has_cycle;
}
}
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