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/* cpp.c (solve critical path problem) */
/***********************************************************************
* This code is part of GLPK (GNU Linear Programming Kit).
*
* Copyright (C) 2010-2016 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_cpp - solve critical path problem
*
* SYNOPSIS
*
* double glp_cpp(glp_graph *G, int v_t, int v_es, int v_ls);
*
* DESCRIPTION
*
* The routine glp_cpp solves the critical path problem represented in
* the form of the project network.
*
* The parameter G is a pointer to the graph object, which specifies
* the project network. This graph must be acyclic. Multiple arcs are
* allowed being considered as single arcs.
*
* The parameter v_t specifies an offset of the field of type double
* in the vertex data block, which contains time t[i] >= 0 needed to
* perform corresponding job j. If v_t < 0, it is assumed that t[i] = 1
* for all jobs.
*
* The parameter v_es specifies an offset of the field of type double
* in the vertex data block, to which the routine stores earliest start
* time for corresponding job. If v_es < 0, this time is not stored.
*
* The parameter v_ls specifies an offset of the field of type double
* in the vertex data block, to which the routine stores latest start
* time for corresponding job. If v_ls < 0, this time is not stored.
*
* RETURNS
*
* The routine glp_cpp returns the minimal project duration, that is,
* minimal time needed to perform all jobs in the project. */
static void sorting(glp_graph *G, int list[]);
double glp_cpp(glp_graph *G, int v_t, int v_es, int v_ls)
{ glp_vertex *v;
glp_arc *a;
int i, j, k, nv, *list;
double temp, total, *t, *es, *ls;
if (v_t >= 0 && v_t > G->v_size - (int)sizeof(double))
xerror("glp_cpp: v_t = %d; invalid offset\n", v_t);
if (v_es >= 0 && v_es > G->v_size - (int)sizeof(double))
xerror("glp_cpp: v_es = %d; invalid offset\n", v_es);
if (v_ls >= 0 && v_ls > G->v_size - (int)sizeof(double))
xerror("glp_cpp: v_ls = %d; invalid offset\n", v_ls);
nv = G->nv;
if (nv == 0)
{ total = 0.0;
goto done;
}
/* allocate working arrays */
t = xcalloc(1+nv, sizeof(double));
es = xcalloc(1+nv, sizeof(double));
ls = xcalloc(1+nv, sizeof(double));
list = xcalloc(1+nv, sizeof(int));
/* retrieve job times */
for (i = 1; i <= nv; i++)
{ v = G->v[i];
if (v_t >= 0)
{ memcpy(&t[i], (char *)v->data + v_t, sizeof(double));
if (t[i] < 0.0)
xerror("glp_cpp: t[%d] = %g; invalid time\n", i, t[i]);
}
else
t[i] = 1.0;
}
/* perform topological sorting to determine the list of nodes
(jobs) such that if list[k] = i and list[kk] = j and there
exists arc (i->j), then k < kk */
sorting(G, list);
/* FORWARD PASS */
/* determine earliest start times */
for (k = 1; k <= nv; k++)
{ j = list[k];
es[j] = 0.0;
for (a = G->v[j]->in; a != NULL; a = a->h_next)
{ i = a->tail->i;
/* there exists arc (i->j) in the project network */
temp = es[i] + t[i];
if (es[j] < temp) es[j] = temp;
}
}
/* determine the minimal project duration */
total = 0.0;
for (i = 1; i <= nv; i++)
{ temp = es[i] + t[i];
if (total < temp) total = temp;
}
/* BACKWARD PASS */
/* determine latest start times */
for (k = nv; k >= 1; k--)
{ i = list[k];
ls[i] = total - t[i];
for (a = G->v[i]->out; a != NULL; a = a->t_next)
{ j = a->head->i;
/* there exists arc (i->j) in the project network */
temp = ls[j] - t[i];
if (ls[i] > temp) ls[i] = temp;
}
/* avoid possible round-off errors */
if (ls[i] < es[i]) ls[i] = es[i];
}
/* store results, if necessary */
if (v_es >= 0)
{ for (i = 1; i <= nv; i++)
{ v = G->v[i];
memcpy((char *)v->data + v_es, &es[i], sizeof(double));
}
}
if (v_ls >= 0)
{ for (i = 1; i <= nv; i++)
{ v = G->v[i];
memcpy((char *)v->data + v_ls, &ls[i], sizeof(double));
}
}
/* free working arrays */
xfree(t);
xfree(es);
xfree(ls);
xfree(list);
done: return total;
}
static void sorting(glp_graph *G, int list[])
{ /* perform topological sorting to determine the list of nodes
(jobs) such that if list[k] = i and list[kk] = j and there
exists arc (i->j), then k < kk */
int i, k, nv, v_size, *num;
void **save;
nv = G->nv;
v_size = G->v_size;
save = xcalloc(1+nv, sizeof(void *));
num = xcalloc(1+nv, sizeof(int));
G->v_size = sizeof(int);
for (i = 1; i <= nv; i++)
{ save[i] = G->v[i]->data;
G->v[i]->data = &num[i];
list[i] = 0;
}
if (glp_top_sort(G, 0) != 0)
xerror("glp_cpp: project network is not acyclic\n");
G->v_size = v_size;
for (i = 1; i <= nv; i++)
{ G->v[i]->data = save[i];
k = num[i];
xassert(1 <= k && k <= nv);
xassert(list[k] == 0);
list[k] = i;
}
xfree(save);
xfree(num);
return;
}
/* eof */
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