/* strong.c (find all strongly 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"
#include "mc13d.h"

/***********************************************************************
*  NAME
*
*  glp_strong_comp - find all strongly connected components of graph
*
*  SYNOPSIS
*
*  int glp_strong_comp(glp_graph *G, int v_num);
*
*  DESCRIPTION
*
*  The routine glp_strong_comp finds all strongly 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 strongly 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|. However,
*  the component numbering has the property that for every arc (i->j)
*  in the graph the condition num(i) >= num(j) holds.
*
*  RETURNS
*
*  The routine returns nc, the total number of components found. */

int glp_strong_comp(glp_graph *G, int v_num)
{     glp_vertex *v;
      glp_arc *a;
      int i, k, last, n, na, nc, *icn, *ip, *lenr, *ior, *ib, *lowl,
         *numb, *prev;
      if (v_num >= 0 && v_num > G->v_size - (int)sizeof(int))
         xerror("glp_strong_comp: v_num = %d; invalid offset\n",
            v_num);
      n = G->nv;
      if (n == 0)
      {  nc = 0;
         goto done;
      }
      na = G->na;
      icn = xcalloc(1+na, sizeof(int));
      ip = xcalloc(1+n, sizeof(int));
      lenr = xcalloc(1+n, sizeof(int));
      ior = xcalloc(1+n, sizeof(int));
      ib = xcalloc(1+n, sizeof(int));
      lowl = xcalloc(1+n, sizeof(int));
      numb = xcalloc(1+n, sizeof(int));
      prev = xcalloc(1+n, sizeof(int));
      k = 1;
      for (i = 1; i <= n; i++)
      {  v = G->v[i];
         ip[i] = k;
         for (a = v->out; a != NULL; a = a->t_next)
            icn[k++] = a->head->i;
         lenr[i] = k - ip[i];
      }
      xassert(na == k-1);
      nc = mc13d(n, icn, ip, lenr, ior, ib, lowl, numb, prev);
      if (v_num >= 0)
      {  xassert(ib[1] == 1);
         for (k = 1; k <= nc; k++)
         {  last = (k < nc ? ib[k+1] : n+1);
            xassert(ib[k] < last);
            for (i = ib[k]; i < last; i++)
            {  v = G->v[ior[i]];
               memcpy((char *)v->data + v_num, &k, sizeof(int));
            }
         }
      }
      xfree(icn);
      xfree(ip);
      xfree(lenr);
      xfree(ior);
      xfree(ib);
      xfree(lowl);
      xfree(numb);
      xfree(prev);
done: return nc;
}

/* eof */