/* glpapi17.c (flow network problems) */

 /***********************************************************************

 *  This code is part of GLPK (GNU Linear Programming Kit).

 *

 *  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,

 *  2009, 2010 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 "glpapi.h"

 #include "glpnet.h"

 /***********************************************************************

 *  NAME

 *

 *  glp_mincost_lp - convert minimum cost flow problem to LP

 *

 *  SYNOPSIS

 *

 *  void glp_mincost_lp(glp_prob *lp, glp_graph *G, int names,

 *     int v_rhs, int a_low, int a_cap, int a_cost);

 *

 *  DESCRIPTION

 *

 *  The routine glp_mincost_lp builds an LP problem, which corresponds

 *  to the minimum cost flow problem on the specified network G. */

 void glp_mincost_lp(glp_prob *lp, glp_graph *G, int names, int v_rhs,

       int a_low, int a_cap, int a_cost)

 {     glp_vertex *v;

       glp_arc *a;

       int i, j, type, ind[1+2];

       double rhs, low, cap, cost, val[1+2];

       if (!(names == GLP_ON || names == GLP_OFF))

          xerror("glp_mincost_lp: names = %d; invalid parameter\n",

             names);

       if (v_rhs >= 0 && v_rhs > G->v_size - (int)sizeof(double))

          xerror("glp_mincost_lp: v_rhs = %d; invalid offset\n", v_rhs);

       if (a_low >= 0 && a_low > G->a_size - (int)sizeof(double))

          xerror("glp_mincost_lp: a_low = %d; invalid offset\n", a_low);

       if (a_cap >= 0 && a_cap > G->a_size - (int)sizeof(double))

          xerror("glp_mincost_lp: a_cap = %d; invalid offset\n", a_cap);

       if (a_cost >= 0 && a_cost > G->a_size - (int)sizeof(double))

          xerror("glp_mincost_lp: a_cost = %d; invalid offset\n", a_cost)

             ;

       glp_erase_prob(lp);

       if (names) glp_set_prob_name(lp, G->name);

       if (G->nv > 0) glp_add_rows(lp, G->nv);

       for (i = 1; i <= G->nv; i++)

       {  v = G->v[i];

          if (names) glp_set_row_name(lp, i, v->name);

          if (v_rhs >= 0)

             memcpy(&rhs, (char *)v->data + v_rhs, sizeof(double));

          else

             rhs = 0.0;

          glp_set_row_bnds(lp, i, GLP_FX, rhs, rhs);

       }

       if (G->na > 0) glp_add_cols(lp, G->na);

       for (i = 1, j = 0; i <= G->nv; i++)

       {  v = G->v[i];

          for (a = v->out; a != NULL; a = a->t_next)

          {  j++;

             if (names)

             {  char name[50+1];

                sprintf(name, "x[%d,%d]", a->tail->i, a->head->i);

                xassert(strlen(name) < sizeof(name));

                glp_set_col_name(lp, j, name);

             }

             if (a->tail->i != a->head->i)

             {  ind[1] = a->tail->i, val[1] = +1.0;

                ind[2] = a->head->i, val[2] = -1.0;

                glp_set_mat_col(lp, j, 2, ind, val);

             }

             if (a_low >= 0)

                memcpy(&low, (char *)a->data + a_low, sizeof(double));

             else

                low = 0.0;

             if (a_cap >= 0)

                memcpy(&cap, (char *)a->data + a_cap, sizeof(double));

             else

                cap = 1.0;

             if (cap == DBL_MAX)

                type = GLP_LO;

             else if (low != cap)

                type = GLP_DB;

             else

                type = GLP_FX;

             glp_set_col_bnds(lp, j, type, low, cap);

             if (a_cost >= 0)

                memcpy(&cost, (char *)a->data + a_cost, sizeof(double));

             else

                cost = 0.0;

             glp_set_obj_coef(lp, j, cost);

          }

       }

       xassert(j == G->na);

       return;

 }

 /**********************************************************************/

 int glp_mincost_okalg(glp_graph *G, int v_rhs, int a_low, int a_cap,

       int a_cost, double *sol, int a_x, int v_pi)

 {     /* find minimum-cost flow with out-of-kilter algorithm */

       glp_vertex *v;

       glp_arc *a;

       int nv, na, i, k, s, t, *tail, *head, *low, *cap, *cost, *x, *pi,

          ret;

       double sum, temp;

       if (v_rhs >= 0 && v_rhs > G->v_size - (int)sizeof(double))

          xerror("glp_mincost_okalg: v_rhs = %d; invalid offset\n",

             v_rhs);

       if (a_low >= 0 && a_low > G->a_size - (int)sizeof(double))

          xerror("glp_mincost_okalg: a_low = %d; invalid offset\n",

             a_low);

       if (a_cap >= 0 && a_cap > G->a_size - (int)sizeof(double))

          xerror("glp_mincost_okalg: a_cap = %d; invalid offset\n",

             a_cap);

       if (a_cost >= 0 && a_cost > G->a_size - (int)sizeof(double))

          xerror("glp_mincost_okalg: a_cost = %d; invalid offset\n",

             a_cost);

       if (a_x >= 0 && a_x > G->a_size - (int)sizeof(double))

          xerror("glp_mincost_okalg: a_x = %d; invalid offset\n", a_x);

       if (v_pi >= 0 && v_pi > G->v_size - (int)sizeof(double))

          xerror("glp_mincost_okalg: v_pi = %d; invalid offset\n", v_pi);

       /* s is artificial source node */

       s = G->nv + 1;

       /* t is artificial sink node */

       t = s + 1;

       /* nv is the total number of nodes in the resulting network */

       nv = t;

       /* na is the total number of arcs in the resulting network */

       na = G->na + 1;

       for (i = 1; i <= G->nv; i++)

       {  v = G->v[i];

          if (v_rhs >= 0)

             memcpy(&temp, (char *)v->data + v_rhs, sizeof(double));

          else

             temp = 0.0;

          if (temp != 0.0) na++;

       }

       /* allocate working arrays */

       tail = xcalloc(1+na, sizeof(int));

       head = xcalloc(1+na, sizeof(int));

       low = xcalloc(1+na, sizeof(int));

       cap = xcalloc(1+na, sizeof(int));

       cost = xcalloc(1+na, sizeof(int));

       x = xcalloc(1+na, sizeof(int));

       pi = xcalloc(1+nv, sizeof(int));

       /* construct the resulting network */

       k = 0;

       /* (original arcs) */

       for (i = 1; i <= G->nv; i++)

       {  v = G->v[i];

          for (a = v->out; a != NULL; a = a->t_next)

          {  k++;

             tail[k] = a->tail->i;

             head[k] = a->head->i;

             if (tail[k] == head[k])

             {  ret = GLP_EDATA;

                goto done;

             }

             if (a_low >= 0)

                memcpy(&temp, (char *)a->data + a_low, sizeof(double));

             else

                temp = 0.0;

             if (!(0.0 <= temp && temp <= (double)INT_MAX &&

                   temp == floor(temp)))

             {  ret = GLP_EDATA;

                goto done;

             }

             low[k] = (int)temp;

             if (a_cap >= 0)

                memcpy(&temp, (char *)a->data + a_cap, sizeof(double));

             else

                temp = 1.0;

             if (!((double)low[k] <= temp && temp <= (double)INT_MAX &&

                   temp == floor(temp)))

             {  ret = GLP_EDATA;

                goto done;

             }

             cap[k] = (int)temp;

             if (a_cost >= 0)

                memcpy(&temp, (char *)a->data + a_cost, sizeof(double));

             else

                temp = 0.0;

             if (!(fabs(temp) <= (double)INT_MAX && temp == floor(temp)))

             {  ret = GLP_EDATA;

                goto done;

             }

             cost[k] = (int)temp;

          }

       }

       /* (artificial arcs) */

       sum = 0.0;

       for (i = 1; i <= G->nv; i++)

       {  v = G->v[i];

          if (v_rhs >= 0)

             memcpy(&temp, (char *)v->data + v_rhs, sizeof(double));

          else

             temp = 0.0;

          if (!(fabs(temp) <= (double)INT_MAX && temp == floor(temp)))

          {  ret = GLP_EDATA;

             goto done;

          }

          if (temp > 0.0)

          {  /* artificial arc from s to original source i */

             k++;

             tail[k] = s;

             head[k] = i;

             low[k] = cap[k] = (int)(+temp); /* supply */

             cost[k] = 0;

             sum += (double)temp;

          }

          else if (temp < 0.0)

          {  /* artificial arc from original sink i to t */

             k++;

             tail[k] = i;

             head[k] = t;

             low[k] = cap[k] = (int)(-temp); /* demand */

             cost[k] = 0;

          }

       }

       /* (feedback arc from t to s) */

       k++;

       xassert(k == na);

       tail[k] = t;

       head[k] = s;

       if (sum > (double)INT_MAX)

       {  ret = GLP_EDATA;

          goto done;

       }

       low[k] = cap[k] = (int)sum; /* total supply/demand */

       cost[k] = 0;

       /* find minimal-cost circulation in the resulting network */

       ret = okalg(nv, na, tail, head, low, cap, cost, x, pi);

       switch (ret)

       {  case 0:

             /* optimal circulation found */

             ret = 0;

             break;

          case 1:

             /* no feasible circulation exists */

             ret = GLP_ENOPFS;

             break;

          case 2:

             /* integer overflow occured */

             ret = GLP_ERANGE;

             goto done;

          case 3:

             /* optimality test failed (logic error) */

             ret = GLP_EFAIL;

             goto done;

          default:

             xassert(ret != ret);

       }

       /* store solution components */

       /* (objective function = the total cost) */

       if (sol != NULL)

       {  temp = 0.0;

          for (k = 1; k <= na; k++)

             temp += (double)cost[k] * (double)x[k];

          *sol = temp;

       }

       /* (arc flows) */

       if (a_x >= 0)

       {  k = 0;

          for (i = 1; i <= G->nv; i++)

          {  v = G->v[i];

             for (a = v->out; a != NULL; a = a->t_next)

             {  temp = (double)x[++k];

                memcpy((char *)a->data + a_x, &temp, sizeof(double));

             }

          }

       }

       /* (node potentials = Lagrange multipliers) */

       if (v_pi >= 0)

       {  for (i = 1; i <= G->nv; i++)

          {  v = G->v[i];

             temp = - (double)pi[i];

             memcpy((char *)v->data + v_pi, &temp, sizeof(double));

          }

       }

 done: /* free working arrays */

       xfree(tail);

       xfree(head);

       xfree(low);

       xfree(cap);

       xfree(cost);

       xfree(x);

       xfree(pi);

       return ret;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_maxflow_lp - convert maximum flow problem to LP

 *

 *  SYNOPSIS

 *

 *  void glp_maxflow_lp(glp_prob *lp, glp_graph *G, int names, int s,

 *     int t, int a_cap);

 *

 *  DESCRIPTION

 *

 *  The routine glp_maxflow_lp builds an LP problem, which corresponds

 *  to the maximum flow problem on the specified network G. */

 void glp_maxflow_lp(glp_prob *lp, glp_graph *G, int names, int s,

       int t, int a_cap)

 {     glp_vertex *v;

       glp_arc *a;

       int i, j, type, ind[1+2];

       double cap, val[1+2];

       if (!(names == GLP_ON || names == GLP_OFF))

          xerror("glp_maxflow_lp: names = %d; invalid parameter\n",

             names);

       if (!(1 <= s && s <= G->nv))

          xerror("glp_maxflow_lp: s = %d; source node number out of rang"

             "e\n", s);

       if (!(1 <= t && t <= G->nv))

          xerror("glp_maxflow_lp: t = %d: sink node number out of range "

             "\n", t);

       if (s == t)

          xerror("glp_maxflow_lp: s = t = %d; source and sink nodes must"

             " be distinct\n", s);

       if (a_cap >= 0 && a_cap > G->a_size - (int)sizeof(double))

          xerror("glp_maxflow_lp: a_cap = %d; invalid offset\n", a_cap);

       glp_erase_prob(lp);

       if (names) glp_set_prob_name(lp, G->name);

       glp_set_obj_dir(lp, GLP_MAX);

       glp_add_rows(lp, G->nv);

       for (i = 1; i <= G->nv; i++)

       {  v = G->v[i];

          if (names) glp_set_row_name(lp, i, v->name);

          if (i == s)

             type = GLP_LO;

          else if (i == t)

             type = GLP_UP;

          else

             type = GLP_FX;

          glp_set_row_bnds(lp, i, type, 0.0, 0.0);

       }

       if (G->na > 0) glp_add_cols(lp, G->na);

       for (i = 1, j = 0; i <= G->nv; i++)

       {  v = G->v[i];

          for (a = v->out; a != NULL; a = a->t_next)

          {  j++;

             if (names)

             {  char name[50+1];

                sprintf(name, "x[%d,%d]", a->tail->i, a->head->i);

                xassert(strlen(name) < sizeof(name));

                glp_set_col_name(lp, j, name);

             }

             if (a->tail->i != a->head->i)

             {  ind[1] = a->tail->i, val[1] = +1.0;

                ind[2] = a->head->i, val[2] = -1.0;

                glp_set_mat_col(lp, j, 2, ind, val);

             }

             if (a_cap >= 0)

                memcpy(&cap, (char *)a->data + a_cap, sizeof(double));

             else

                cap = 1.0;

             if (cap == DBL_MAX)

                type = GLP_LO;

             else if (cap != 0.0)

                type = GLP_DB;

             else

                type = GLP_FX;

             glp_set_col_bnds(lp, j, type, 0.0, cap);

             if (a->tail->i == s)

                glp_set_obj_coef(lp, j, +1.0);

             else if (a->head->i == s)

                glp_set_obj_coef(lp, j, -1.0);

          }

       }

       xassert(j == G->na);

       return;

 }

 int glp_maxflow_ffalg(glp_graph *G, int s, int t, int a_cap,

       double *sol, int a_x, int v_cut)

 {     /* find maximal flow with Ford-Fulkerson algorithm */

       glp_vertex *v;

       glp_arc *a;

       int nv, na, i, k, flag, *tail, *head, *cap, *x, ret;

       char *cut;

       double temp;

       if (!(1 <= s && s <= G->nv))

          xerror("glp_maxflow_ffalg: s = %d; source node number out of r"

             "ange\n", s);

       if (!(1 <= t && t <= G->nv))

          xerror("glp_maxflow_ffalg: t = %d: sink node number out of ran"

             "ge\n", t);

       if (s == t)

          xerror("glp_maxflow_ffalg: s = t = %d; source and sink nodes m"

             "ust be distinct\n", s);

       if (a_cap >= 0 && a_cap > G->a_size - (int)sizeof(double))

          xerror("glp_maxflow_ffalg: a_cap = %d; invalid offset\n",

             a_cap);

       if (v_cut >= 0 && v_cut > G->v_size - (int)sizeof(int))

          xerror("glp_maxflow_ffalg: v_cut = %d; invalid offset\n",

             v_cut);

       /* allocate working arrays */

       nv = G->nv;

       na = G->na;

       tail = xcalloc(1+na, sizeof(int));

       head = xcalloc(1+na, sizeof(int));

       cap = xcalloc(1+na, sizeof(int));

       x = xcalloc(1+na, sizeof(int));

       if (v_cut < 0)

          cut = NULL;

       else

          cut = xcalloc(1+nv, sizeof(char));

       /* copy the flow network */

       k = 0;

       for (i = 1; i <= G->nv; i++)

       {  v = G->v[i];

          for (a = v->out; a != NULL; a = a->t_next)

          {  k++;

             tail[k] = a->tail->i;

             head[k] = a->head->i;

             if (tail[k] == head[k])

             {  ret = GLP_EDATA;

                goto done;

             }

             if (a_cap >= 0)

                memcpy(&temp, (char *)a->data + a_cap, sizeof(double));

             else

                temp = 1.0;

             if (!(0.0 <= temp && temp <= (double)INT_MAX &&

                   temp == floor(temp)))

             {  ret = GLP_EDATA;

                goto done;

             }

             cap[k] = (int)temp;

          }

       }

       xassert(k == na);

       /* find maximal flow in the flow network */

       ffalg(nv, na, tail, head, s, t, cap, x, cut);

       ret = 0;

       /* store solution components */

       /* (objective function = total flow through the network) */

       if (sol != NULL)

       {  temp = 0.0;

          for (k = 1; k <= na; k++)

          {  if (tail[k] == s)

                temp += (double)x[k];

             else if (head[k] == s)

                temp -= (double)x[k];

          }

          *sol = temp;

       }

       /* (arc flows) */

       if (a_x >= 0)

       {  k = 0;

          for (i = 1; i <= G->nv; i++)

          {  v = G->v[i];

             for (a = v->out; a != NULL; a = a->t_next)

             {  temp = (double)x[++k];

                memcpy((char *)a->data + a_x, &temp, sizeof(double));

             }

          }

       }

       /* (node flags) */

       if (v_cut >= 0)

       {  for (i = 1; i <= G->nv; i++)

          {  v = G->v[i];

             flag = cut[i];

             memcpy((char *)v->data + v_cut, &flag, sizeof(int));

          }

       }

 done: /* free working arrays */

       xfree(tail);

       xfree(head);

       xfree(cap);

       xfree(x);

       if (cut != NULL) xfree(cut);

       return ret;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_check_asnprob - check correctness of assignment problem data

 *

 *  SYNOPSIS

 *

 *  int glp_check_asnprob(glp_graph *G, int v_set);

 *

 *  RETURNS

 *

 *  If the specified assignment problem data are correct, the routine

 *  glp_check_asnprob returns zero, otherwise, non-zero. */

 int glp_check_asnprob(glp_graph *G, int v_set)

 {     glp_vertex *v;

       int i, k, ret = 0;

       if (v_set >= 0 && v_set > G->v_size - (int)sizeof(int))

          xerror("glp_check_asnprob: v_set = %d; invalid offset\n",

             v_set);

       for (i = 1; i <= G->nv; i++)

       {  v = G->v[i];

          if (v_set >= 0)

          {  memcpy(&k, (char *)v->data + v_set, sizeof(int));

             if (k == 0)

             {  if (v->in != NULL)

                {  ret = 1;

                   break;

                }

             }

             else if (k == 1)

             {  if (v->out != NULL)

                {  ret = 2;

                   break;

                }

             }

             else

             {  ret = 3;

                break;

             }

          }

          else

          {  if (v->in != NULL && v->out != NULL)

             {  ret = 4;

                break;

             }

          }

       }

       return ret;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_asnprob_lp - convert assignment problem to LP

 *

 *  SYNOPSIS

 *

 *  int glp_asnprob_lp(glp_prob *P, int form, glp_graph *G, int names,

 *     int v_set, int a_cost);

 *

 *  DESCRIPTION

 *

 *  The routine glp_asnprob_lp builds an LP problem, which corresponds

 *  to the assignment problem on the specified graph G.

 *

 *  RETURNS

 *

 *  If the LP problem has been successfully built, the routine returns

 *  zero, otherwise, non-zero. */

 int glp_asnprob_lp(glp_prob *P, int form, glp_graph *G, int names,

       int v_set, int a_cost)

 {     glp_vertex *v;

       glp_arc *a;

       int i, j, ret, ind[1+2];

       double cost, val[1+2];

       if (!(form == GLP_ASN_MIN || form == GLP_ASN_MAX ||

             form == GLP_ASN_MMP))

          xerror("glp_asnprob_lp: form = %d; invalid parameter\n",

             form);

       if (!(names == GLP_ON || names == GLP_OFF))

          xerror("glp_asnprob_lp: names = %d; invalid parameter\n",

             names);

       if (v_set >= 0 && v_set > G->v_size - (int)sizeof(int))

          xerror("glp_asnprob_lp: v_set = %d; invalid offset\n",

             v_set);

       if (a_cost >= 0 && a_cost > G->a_size - (int)sizeof(double))

          xerror("glp_asnprob_lp: a_cost = %d; invalid offset\n",

             a_cost);

       ret = glp_check_asnprob(G, v_set);

       if (ret != 0) goto done;

       glp_erase_prob(P);

       if (names) glp_set_prob_name(P, G->name);

       glp_set_obj_dir(P, form == GLP_ASN_MIN ? GLP_MIN : GLP_MAX);

       if (G->nv > 0) glp_add_rows(P, G->nv);

       for (i = 1; i <= G->nv; i++)

       {  v = G->v[i];

          if (names) glp_set_row_name(P, i, v->name);

          glp_set_row_bnds(P, i, form == GLP_ASN_MMP ? GLP_UP : GLP_FX,

             1.0, 1.0);

       }

       if (G->na > 0) glp_add_cols(P, G->na);

       for (i = 1, j = 0; i <= G->nv; i++)

       {  v = G->v[i];

          for (a = v->out; a != NULL; a = a->t_next)

          {  j++;

             if (names)

             {  char name[50+1];

                sprintf(name, "x[%d,%d]", a->tail->i, a->head->i);

                xassert(strlen(name) < sizeof(name));

                glp_set_col_name(P, j, name);

             }

             ind[1] = a->tail->i, val[1] = +1.0;

             ind[2] = a->head->i, val[2] = +1.0;

             glp_set_mat_col(P, j, 2, ind, val);

             glp_set_col_bnds(P, j, GLP_DB, 0.0, 1.0);

             if (a_cost >= 0)

                memcpy(&cost, (char *)a->data + a_cost, sizeof(double));

             else

                cost = 1.0;

             glp_set_obj_coef(P, j, cost);

          }

       }

       xassert(j == G->na);

 done: return ret;

 }

 /**********************************************************************/

 int glp_asnprob_okalg(int form, glp_graph *G, int v_set, int a_cost,

       double *sol, int a_x)

 {     /* solve assignment problem with out-of-kilter algorithm */

       glp_vertex *v;

       glp_arc *a;

       int nv, na, i, k, *tail, *head, *low, *cap, *cost, *x, *pi, ret;

       double temp;

       if (!(form == GLP_ASN_MIN || form == GLP_ASN_MAX ||

             form == GLP_ASN_MMP))

          xerror("glp_asnprob_okalg: form = %d; invalid parameter\n",

             form);

       if (v_set >= 0 && v_set > G->v_size - (int)sizeof(int))

          xerror("glp_asnprob_okalg: v_set = %d; invalid offset\n",

             v_set);

       if (a_cost >= 0 && a_cost > G->a_size - (int)sizeof(double))

          xerror("glp_asnprob_okalg: a_cost = %d; invalid offset\n",

             a_cost);

       if (a_x >= 0 && a_x > G->a_size - (int)sizeof(int))

          xerror("glp_asnprob_okalg: a_x = %d; invalid offset\n", a_x);

       if (glp_check_asnprob(G, v_set))

          return GLP_EDATA;

       /* nv is the total number of nodes in the resulting network */

       nv = G->nv + 1;

       /* na is the total number of arcs in the resulting network */

       na = G->na + G->nv;

       /* allocate working arrays */

       tail = xcalloc(1+na, sizeof(int));

       head = xcalloc(1+na, sizeof(int));

       low = xcalloc(1+na, sizeof(int));

       cap = xcalloc(1+na, sizeof(int));

       cost = xcalloc(1+na, sizeof(int));

       x = xcalloc(1+na, sizeof(int));

       pi = xcalloc(1+nv, sizeof(int));

       /* construct the resulting network */

       k = 0;

       /* (original arcs) */

       for (i = 1; i <= G->nv; i++)

       {  v = G->v[i];

          for (a = v->out; a != NULL; a = a->t_next)

          {  k++;

             tail[k] = a->tail->i;

             head[k] = a->head->i;

             low[k] = 0;

             cap[k] = 1;

             if (a_cost >= 0)

                memcpy(&temp, (char *)a->data + a_cost, sizeof(double));

             else

                temp = 1.0;

             if (!(fabs(temp) <= (double)INT_MAX && temp == floor(temp)))

             {  ret = GLP_EDATA;

                goto done;

             }

             cost[k] = (int)temp;

             if (form != GLP_ASN_MIN) cost[k] = - cost[k];

          }

       }

       /* (artificial arcs) */

       for (i = 1; i <= G->nv; i++)

       {  v = G->v[i];

          k++;

          if (v->out == NULL)

             tail[k] = i, head[k] = nv;

          else if (v->in == NULL)

             tail[k] = nv, head[k] = i;

          else

             xassert(v != v);

          low[k] = (form == GLP_ASN_MMP ? 0 : 1);

          cap[k] = 1;

          cost[k] = 0;

       }

       xassert(k == na);

       /* find minimal-cost circulation in the resulting network */

       ret = okalg(nv, na, tail, head, low, cap, cost, x, pi);

       switch (ret)

       {  case 0:

             /* optimal circulation found */

             ret = 0;

             break;

          case 1:

             /* no feasible circulation exists */

             ret = GLP_ENOPFS;

             break;

          case 2:

             /* integer overflow occured */

             ret = GLP_ERANGE;

             goto done;

          case 3:

             /* optimality test failed (logic error) */

             ret = GLP_EFAIL;

             goto done;

          default:

             xassert(ret != ret);

       }

       /* store solution components */

       /* (objective function = the total cost) */

       if (sol != NULL)

       {  temp = 0.0;

          for (k = 1; k <= na; k++)

             temp += (double)cost[k] * (double)x[k];

          if (form != GLP_ASN_MIN) temp = - temp;

          *sol = temp;

       }

       /* (arc flows) */

       if (a_x >= 0)

       {  k = 0;

          for (i = 1; i <= G->nv; i++)

          {  v = G->v[i];

             for (a = v->out; a != NULL; a = a->t_next)

             {  k++;

                if (ret == 0)

                   xassert(x[k] == 0 || x[k] == 1);

                memcpy((char *)a->data + a_x, &x[k], sizeof(int));

             }

          }

       }

 done: /* free working arrays */

       xfree(tail);

       xfree(head);

       xfree(low);

       xfree(cap);

       xfree(cost);

       xfree(x);

       xfree(pi);

       return ret;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_asnprob_hall - find bipartite matching of maximum cardinality

 *

 *  SYNOPSIS

 *

 *  int glp_asnprob_hall(glp_graph *G, int v_set, int a_x);

 *

 *  DESCRIPTION

 *

 *  The routine glp_asnprob_hall finds a matching of maximal cardinality

 *  in the specified bipartite graph G. It uses a version of the Fortran

 *  routine MC21A developed by I.S.Duff [1], which implements Hall's

 *  algorithm [2].

 *

 *  RETURNS

 *

 *  The routine glp_asnprob_hall returns the cardinality of the matching

 *  found. However, if the specified graph is incorrect (as detected by

 *  the routine glp_check_asnprob), the routine returns negative value.

 *

 *  REFERENCES

 *

 *  1. I.S.Duff, Algorithm 575: Permutations for zero-free diagonal, ACM

 *     Trans. on Math. Softw. 7 (1981), 387-390.

 *

 *  2. M.Hall, "An Algorithm for distinct representatives," Amer. Math.

 *     Monthly 63 (1956), 716-717. */

 int glp_asnprob_hall(glp_graph *G, int v_set, int a_x)

 {     glp_vertex *v;

       glp_arc *a;

       int card, i, k, loc, n, n1, n2, xij;

       int *num, *icn, *ip, *lenr, *iperm, *pr, *arp, *cv, *out;

       if (v_set >= 0 && v_set > G->v_size - (int)sizeof(int))

          xerror("glp_asnprob_hall: v_set = %d; invalid offset\n",

             v_set);

       if (a_x >= 0 && a_x > G->a_size - (int)sizeof(int))

          xerror("glp_asnprob_hall: a_x = %d; invalid offset\n", a_x);

       if (glp_check_asnprob(G, v_set))

          return -1;

       /* determine the number of vertices in sets R and S and renumber

          vertices in S which correspond to columns of the matrix; skip

          all isolated vertices */

       num = xcalloc(1+G->nv, sizeof(int));

       n1 = n2 = 0;

       for (i = 1; i <= G->nv; i++)

       {  v = G->v[i];

          if (v->in == NULL && v->out != NULL)

             n1++, num[i] = 0; /* vertex in R */

          else if (v->in != NULL && v->out == NULL)

             n2++, num[i] = n2; /* vertex in S */

          else

          {  xassert(v->in == NULL && v->out == NULL);

             num[i] = -1; /* isolated vertex */

          }

       }

       /* the matrix must be square, thus, if it has more columns than

          rows, extra rows will be just empty, and vice versa */

       n = (n1 >= n2 ? n1 : n2);

       /* allocate working arrays */

       icn = xcalloc(1+G->na, sizeof(int));

       ip = xcalloc(1+n, sizeof(int));

       lenr = xcalloc(1+n, sizeof(int));

       iperm = xcalloc(1+n, sizeof(int));

       pr = xcalloc(1+n, sizeof(int));

       arp = xcalloc(1+n, sizeof(int));

       cv = xcalloc(1+n, sizeof(int));

       out = xcalloc(1+n, sizeof(int));

       /* build the adjacency matrix of the bipartite graph in row-wise

          format (rows are vertices in R, columns are vertices in S) */

       k = 0, loc = 1;

       for (i = 1; i <= G->nv; i++)

       {  if (num[i] != 0) continue;

          /* vertex i in R */

          ip[++k] = loc;

          v = G->v[i];

          for (a = v->out; a != NULL; a = a->t_next)

          {  xassert(num[a->head->i] != 0);

             icn[loc++] = num[a->head->i];

          }

          lenr[k] = loc - ip[k];

       }

       xassert(loc-1 == G->na);

       /* make all extra rows empty (all extra columns are empty due to

          the row-wise format used) */

       for (k++; k <= n; k++)

          ip[k] = loc, lenr[k] = 0;

       /* find a row permutation that maximizes the number of non-zeros

          on the main diagonal */

       card = mc21a(n, icn, ip, lenr, iperm, pr, arp, cv, out);

 #if 1 /* 18/II-2010 */

       /* FIXED: if card = n, arp remains clobbered on exit */

       for (i = 1; i <= n; i++)

          arp[i] = 0;

       for (i = 1; i <= card; i++)

       {  k = iperm[i];

          xassert(1 <= k && k <= n);

          xassert(arp[k] == 0);

          arp[k] = i;

       }

 #endif

       /* store solution, if necessary */

       if (a_x < 0) goto skip;

       k = 0;

       for (i = 1; i <= G->nv; i++)

       {  if (num[i] != 0) continue;

          /* vertex i in R */

          k++;

          v = G->v[i];

          for (a = v->out; a != NULL; a = a->t_next)

          {  /* arp[k] is the number of matched column or zero */

             if (arp[k] == num[a->head->i])

             {  xassert(arp[k] != 0);

                xij = 1;

             }

             else

                xij = 0;

             memcpy((char *)a->data + a_x, &xij, sizeof(int));

          }

       }

 skip: /* free working arrays */

       xfree(num);

       xfree(icn);

       xfree(ip);

       xfree(lenr);

       xfree(iperm);

       xfree(pr);

       xfree(arp);

       xfree(cv);

       xfree(out);

       return card;

 }

 /***********************************************************************

 *  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 */