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/* weak.c (find all weakly connected components of graph) */
/***********************************************************************
* This code is part of GLPK (GNU Linear Programming Kit).
*
* Copyright (C) 2009-2016 Andrew Makhorin, Department for Applied
* Informatics, Moscow Aviation Institute, Moscow, Russia. All rights
* reserved. E-mail: <mao@gnu.org>.
*
* GLPK 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.
*
* GLPK 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 GLPK. If not, see <http://www.gnu.org/licenses/>.
***********************************************************************/
#include "env.h"
#include "glpk.h"
/***********************************************************************
* NAME
*
* glp_weak_comp - find all weakly connected components of graph
*
* SYNOPSIS
*
* int glp_weak_comp(glp_graph *G, int v_num);
*
* DESCRIPTION
*
* The routine glp_weak_comp finds all weakly connected components of
* the specified graph.
*
* The parameter v_num specifies an offset of the field of type int
* in the vertex data block, to which the routine stores the number of
* a (weakly) connected component containing that vertex. If v_num < 0,
* no component numbers are stored.
*
* The components are numbered in arbitrary order from 1 to nc, where
* nc is the total number of components found, 0 <= nc <= |V|.
*
* RETURNS
*
* The routine returns nc, the total number of components found. */
int glp_weak_comp(glp_graph *G, int v_num)
{ glp_vertex *v;
glp_arc *a;
int f, i, j, nc, nv, pos1, pos2, *prev, *next, *list;
if (v_num >= 0 && v_num > G->v_size - (int)sizeof(int))
xerror("glp_weak_comp: v_num = %d; invalid offset\n", v_num);
nv = G->nv;
if (nv == 0)
{ nc = 0;
goto done;
}
/* allocate working arrays */
prev = xcalloc(1+nv, sizeof(int));
next = xcalloc(1+nv, sizeof(int));
list = xcalloc(1+nv, sizeof(int));
/* if vertex i is unlabelled, prev[i] is the index of previous
unlabelled vertex, and next[i] is the index of next unlabelled
vertex; if vertex i is labelled, then prev[i] < 0, and next[i]
is the connected component number */
/* initially all vertices are unlabelled */
f = 1;
for (i = 1; i <= nv; i++)
prev[i] = i - 1, next[i] = i + 1;
next[nv] = 0;
/* main loop (until all vertices have been labelled) */
nc = 0;
while (f != 0)
{ /* take an unlabelled vertex */
i = f;
/* and remove it from the list of unlabelled vertices */
f = next[i];
if (f != 0) prev[f] = 0;
/* label the vertex; it begins a new component */
prev[i] = -1, next[i] = ++nc;
/* breadth first search */
list[1] = i, pos1 = pos2 = 1;
while (pos1 <= pos2)
{ /* dequeue vertex i */
i = list[pos1++];
/* consider all arcs incoming to vertex i */
for (a = G->v[i]->in; a != NULL; a = a->h_next)
{ /* vertex j is adjacent to vertex i */
j = a->tail->i;
if (prev[j] >= 0)
{ /* vertex j is unlabelled */
/* remove it from the list of unlabelled vertices */
if (prev[j] == 0)
f = next[j];
else
next[prev[j]] = next[j];
if (next[j] == 0)
;
else
prev[next[j]] = prev[j];
/* label the vertex */
prev[j] = -1, next[j] = nc;
/* and enqueue it for further consideration */
list[++pos2] = j;
}
}
/* consider all arcs outgoing from vertex i */
for (a = G->v[i]->out; a != NULL; a = a->t_next)
{ /* vertex j is adjacent to vertex i */
j = a->head->i;
if (prev[j] >= 0)
{ /* vertex j is unlabelled */
/* remove it from the list of unlabelled vertices */
if (prev[j] == 0)
f = next[j];
else
next[prev[j]] = next[j];
if (next[j] == 0)
;
else
prev[next[j]] = prev[j];
/* label the vertex */
prev[j] = -1, next[j] = nc;
/* and enqueue it for further consideration */
list[++pos2] = j;
}
}
}
}
/* store component numbers */
if (v_num >= 0)
{ for (i = 1; i <= nv; i++)
{ v = G->v[i];
memcpy((char *)v->data + v_num, &next[i], sizeof(int));
}
}
/* free working arrays */
xfree(prev);
xfree(next);
xfree(list);
done: return nc;
}
/* eof */
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