test/min_cost_flow_test.cc
author Peter Kovacs <kpeter@inf.elte.hu>
Mon, 23 Mar 2009 23:54:42 +0100
changeset 603 425cc8328c0e
child 605 5232721b3f14
permissions -rw-r--r--
Internal restructuring and renamings in NetworkSimplex (#234)
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #include <iostream>
    20 #include <fstream>
    21 
    22 #include <lemon/list_graph.h>
    23 #include <lemon/smart_graph.h>
    24 #include <lemon/lgf_reader.h>
    25 
    26 //#include <lemon/cycle_canceling.h>
    27 //#include <lemon/capacity_scaling.h>
    28 //#include <lemon/cost_scaling.h>
    29 #include <lemon/network_simplex.h>
    30 //#include <lemon/min_cost_flow.h>
    31 //#include <lemon/min_cost_max_flow.h>
    32 
    33 #include <lemon/concepts/digraph.h>
    34 #include <lemon/concept_check.h>
    35 
    36 #include "test_tools.h"
    37 
    38 using namespace lemon;
    39 
    40 char test_lgf[] =
    41   "@nodes\n"
    42   "label  sup1 sup2 sup3\n"
    43   "    1    20   27    0\n"
    44   "    2    -4    0    0\n"
    45   "    3     0    0    0\n"
    46   "    4     0    0    0\n"
    47   "    5     9    0    0\n"
    48   "    6    -6    0    0\n"
    49   "    7     0    0    0\n"
    50   "    8     0    0    0\n"
    51   "    9     3    0    0\n"
    52   "   10    -2    0    0\n"
    53   "   11     0    0    0\n"
    54   "   12   -20  -27    0\n"
    55   "\n"
    56   "@arcs\n"
    57   "       cost  cap low1 low2\n"
    58   " 1  2    70   11    0    8\n"
    59   " 1  3   150    3    0    1\n"
    60   " 1  4    80   15    0    2\n"
    61   " 2  8    80   12    0    0\n"
    62   " 3  5   140    5    0    3\n"
    63   " 4  6    60   10    0    1\n"
    64   " 4  7    80    2    0    0\n"
    65   " 4  8   110    3    0    0\n"
    66   " 5  7    60   14    0    0\n"
    67   " 5 11   120   12    0    0\n"
    68   " 6  3     0    3    0    0\n"
    69   " 6  9   140    4    0    0\n"
    70   " 6 10    90    8    0    0\n"
    71   " 7  1    30    5    0    0\n"
    72   " 8 12    60   16    0    4\n"
    73   " 9 12    50    6    0    0\n"
    74   "10 12    70   13    0    5\n"
    75   "10  2   100    7    0    0\n"
    76   "10  7    60   10    0    0\n"
    77   "11 10    20   14    0    6\n"
    78   "12 11    30   10    0    0\n"
    79   "\n"
    80   "@attributes\n"
    81   "source 1\n"
    82   "target 12\n";
    83 
    84 
    85 // Check the interface of an MCF algorithm
    86 template <typename GR, typename Value>
    87 class McfClassConcept
    88 {
    89 public:
    90 
    91   template <typename MCF>
    92   struct Constraints {
    93     void constraints() {
    94       checkConcept<concepts::Digraph, GR>();
    95 
    96       MCF mcf_test1(g, lower, upper, cost, sup);
    97       MCF mcf_test2(g, upper, cost, sup);
    98       MCF mcf_test3(g, lower, upper, cost, n, n, k);
    99       MCF mcf_test4(g, upper, cost, n, n, k);
   100 
   101       // TODO: This part should be enabled and the next part
   102       // should be removed if map copying is supported
   103 /*
   104       flow = mcf_test1.flowMap();
   105       mcf_test1.flowMap(flow);
   106 
   107       pot = mcf_test1.potentialMap();
   108       mcf_test1.potentialMap(pot);
   109 */
   110 /**/
   111       const typename MCF::FlowMap &fm =
   112         mcf_test1.flowMap();
   113       mcf_test1.flowMap(flow);
   114       const typename MCF::PotentialMap &pm =
   115         mcf_test1.potentialMap();
   116       mcf_test1.potentialMap(pot);
   117       ignore_unused_variable_warning(fm);
   118       ignore_unused_variable_warning(pm);
   119 /**/
   120 
   121       mcf_test1.run();
   122 
   123       v = mcf_test1.totalCost();
   124       v = mcf_test1.flow(a);
   125       v = mcf_test1.potential(n);
   126     }
   127 
   128     typedef typename GR::Node Node;
   129     typedef typename GR::Arc Arc;
   130     typedef concepts::ReadMap<Node, Value> NM;
   131     typedef concepts::ReadMap<Arc, Value> AM;
   132 
   133     const GR &g;
   134     const AM &lower;
   135     const AM &upper;
   136     const AM &cost;
   137     const NM &sup;
   138     const Node &n;
   139     const Arc &a;
   140     const Value &k;
   141     Value v;
   142 
   143     typename MCF::FlowMap &flow;
   144     typename MCF::PotentialMap &pot;
   145   };
   146 
   147 };
   148 
   149 
   150 // Check the feasibility of the given flow (primal soluiton)
   151 template < typename GR, typename LM, typename UM,
   152            typename SM, typename FM >
   153 bool checkFlow( const GR& gr, const LM& lower, const UM& upper,
   154                 const SM& supply, const FM& flow )
   155 {
   156   TEMPLATE_DIGRAPH_TYPEDEFS(GR);
   157 
   158   for (ArcIt e(gr); e != INVALID; ++e) {
   159     if (flow[e] < lower[e] || flow[e] > upper[e]) return false;
   160   }
   161 
   162   for (NodeIt n(gr); n != INVALID; ++n) {
   163     typename SM::Value sum = 0;
   164     for (OutArcIt e(gr, n); e != INVALID; ++e)
   165       sum += flow[e];
   166     for (InArcIt e(gr, n); e != INVALID; ++e)
   167       sum -= flow[e];
   168     if (sum != supply[n]) return false;
   169   }
   170 
   171   return true;
   172 }
   173 
   174 // Check the feasibility of the given potentials (dual soluiton)
   175 // using the Complementary Slackness optimality condition
   176 template < typename GR, typename LM, typename UM,
   177            typename CM, typename FM, typename PM >
   178 bool checkPotential( const GR& gr, const LM& lower, const UM& upper,
   179                      const CM& cost, const FM& flow, const PM& pi )
   180 {
   181   TEMPLATE_DIGRAPH_TYPEDEFS(GR);
   182 
   183   bool opt = true;
   184   for (ArcIt e(gr); opt && e != INVALID; ++e) {
   185     typename CM::Value red_cost =
   186       cost[e] + pi[gr.source(e)] - pi[gr.target(e)];
   187     opt = red_cost == 0 ||
   188           (red_cost > 0 && flow[e] == lower[e]) ||
   189           (red_cost < 0 && flow[e] == upper[e]);
   190   }
   191   return opt;
   192 }
   193 
   194 // Run a minimum cost flow algorithm and check the results
   195 template < typename MCF, typename GR,
   196            typename LM, typename UM,
   197            typename CM, typename SM >
   198 void checkMcf( const MCF& mcf, bool mcf_result,
   199                const GR& gr, const LM& lower, const UM& upper,
   200                const CM& cost, const SM& supply,
   201                bool result, typename CM::Value total,
   202                const std::string &test_id = "" )
   203 {
   204   check(mcf_result == result, "Wrong result " + test_id);
   205   if (result) {
   206     check(checkFlow(gr, lower, upper, supply, mcf.flowMap()),
   207           "The flow is not feasible " + test_id);
   208     check(mcf.totalCost() == total, "The flow is not optimal " + test_id);
   209     check(checkPotential(gr, lower, upper, cost, mcf.flowMap(),
   210                          mcf.potentialMap()),
   211           "Wrong potentials " + test_id);
   212   }
   213 }
   214 
   215 int main()
   216 {
   217   // Check the interfaces
   218   {
   219     typedef int Value;
   220     // This typedef should be enabled if the standard maps are
   221     // reference maps in the graph concepts
   222     //typedef concepts::Digraph GR;
   223     typedef ListDigraph GR;
   224     typedef concepts::ReadMap<GR::Node, Value> NM;
   225     typedef concepts::ReadMap<GR::Arc, Value> AM;
   226 
   227     //checkConcept< McfClassConcept<GR, Value>,
   228     //              CycleCanceling<GR, AM, AM, AM, NM> >();
   229     //checkConcept< McfClassConcept<GR, Value>,
   230     //              CapacityScaling<GR, AM, AM, AM, NM> >();
   231     //checkConcept< McfClassConcept<GR, Value>,
   232     //              CostScaling<GR, AM, AM, AM, NM> >();
   233     checkConcept< McfClassConcept<GR, Value>,
   234                   NetworkSimplex<GR, AM, AM, AM, NM> >();
   235     //checkConcept< MinCostFlow<GR, Value>,
   236     //              NetworkSimplex<GR, AM, AM, AM, NM> >();
   237   }
   238 
   239   // Run various MCF tests
   240   typedef ListDigraph Digraph;
   241   DIGRAPH_TYPEDEFS(ListDigraph);
   242 
   243   // Read the test digraph
   244   Digraph gr;
   245   Digraph::ArcMap<int> c(gr), l1(gr), l2(gr), u(gr);
   246   Digraph::NodeMap<int> s1(gr), s2(gr), s3(gr);
   247   Node v, w;
   248 
   249   std::istringstream input(test_lgf);
   250   DigraphReader<Digraph>(gr, input)
   251     .arcMap("cost", c)
   252     .arcMap("cap", u)
   253     .arcMap("low1", l1)
   254     .arcMap("low2", l2)
   255     .nodeMap("sup1", s1)
   256     .nodeMap("sup2", s2)
   257     .nodeMap("sup3", s3)
   258     .node("source", v)
   259     .node("target", w)
   260     .run();
   261 
   262 /*
   263   // A. Test CapacityScaling with scaling
   264   {
   265     CapacityScaling<Digraph> mcf1(gr, u, c, s1);
   266     CapacityScaling<Digraph> mcf2(gr, u, c, v, w, 27);
   267     CapacityScaling<Digraph> mcf3(gr, u, c, s3);
   268     CapacityScaling<Digraph> mcf4(gr, l2, u, c, s1);
   269     CapacityScaling<Digraph> mcf5(gr, l2, u, c, v, w, 27);
   270     CapacityScaling<Digraph> mcf6(gr, l2, u, c, s3);
   271 
   272     checkMcf(mcf1, mcf1.run(), gr, l1, u, c, s1, true,  5240, "#A1");
   273     checkMcf(mcf2, mcf2.run(), gr, l1, u, c, s2, true,  7620, "#A2");
   274     checkMcf(mcf3, mcf3.run(), gr, l1, u, c, s3, true,     0, "#A3");
   275     checkMcf(mcf4, mcf4.run(), gr, l2, u, c, s1, true,  5970, "#A4");
   276     checkMcf(mcf5, mcf5.run(), gr, l2, u, c, s2, true,  8010, "#A5");
   277     checkMcf(mcf6, mcf6.run(), gr, l2, u, c, s3, false,    0, "#A6");
   278   }
   279 
   280   // B. Test CapacityScaling without scaling
   281   {
   282     CapacityScaling<Digraph> mcf1(gr, u, c, s1);
   283     CapacityScaling<Digraph> mcf2(gr, u, c, v, w, 27);
   284     CapacityScaling<Digraph> mcf3(gr, u, c, s3);
   285     CapacityScaling<Digraph> mcf4(gr, l2, u, c, s1);
   286     CapacityScaling<Digraph> mcf5(gr, l2, u, c, v, w, 27);
   287     CapacityScaling<Digraph> mcf6(gr, l2, u, c, s3);
   288 
   289     checkMcf(mcf1, mcf1.run(false), gr, l1, u, c, s1, true,  5240, "#B1");
   290     checkMcf(mcf2, mcf2.run(false), gr, l1, u, c, s2, true,  7620, "#B2");
   291     checkMcf(mcf3, mcf3.run(false), gr, l1, u, c, s3, true,     0, "#B3");
   292     checkMcf(mcf4, mcf4.run(false), gr, l2, u, c, s1, true,  5970, "#B4");
   293     checkMcf(mcf5, mcf5.run(false), gr, l2, u, c, s2, true,  8010, "#B5");
   294     checkMcf(mcf6, mcf6.run(false), gr, l2, u, c, s3, false,    0, "#B6");
   295   }
   296 
   297   // C. Test CostScaling using partial augment-relabel method
   298   {
   299     CostScaling<Digraph> mcf1(gr, u, c, s1);
   300     CostScaling<Digraph> mcf2(gr, u, c, v, w, 27);
   301     CostScaling<Digraph> mcf3(gr, u, c, s3);
   302     CostScaling<Digraph> mcf4(gr, l2, u, c, s1);
   303     CostScaling<Digraph> mcf5(gr, l2, u, c, v, w, 27);
   304     CostScaling<Digraph> mcf6(gr, l2, u, c, s3);
   305 
   306     checkMcf(mcf1, mcf1.run(), gr, l1, u, c, s1, true,  5240, "#C1");
   307     checkMcf(mcf2, mcf2.run(), gr, l1, u, c, s2, true,  7620, "#C2");
   308     checkMcf(mcf3, mcf3.run(), gr, l1, u, c, s3, true,     0, "#C3");
   309     checkMcf(mcf4, mcf4.run(), gr, l2, u, c, s1, true,  5970, "#C4");
   310     checkMcf(mcf5, mcf5.run(), gr, l2, u, c, s2, true,  8010, "#C5");
   311     checkMcf(mcf6, mcf6.run(), gr, l2, u, c, s3, false,    0, "#C6");
   312   }
   313 
   314   // D. Test CostScaling using push-relabel method
   315   {
   316     CostScaling<Digraph> mcf1(gr, u, c, s1);
   317     CostScaling<Digraph> mcf2(gr, u, c, v, w, 27);
   318     CostScaling<Digraph> mcf3(gr, u, c, s3);
   319     CostScaling<Digraph> mcf4(gr, l2, u, c, s1);
   320     CostScaling<Digraph> mcf5(gr, l2, u, c, v, w, 27);
   321     CostScaling<Digraph> mcf6(gr, l2, u, c, s3);
   322 
   323     checkMcf(mcf1, mcf1.run(false), gr, l1, u, c, s1, true,  5240, "#D1");
   324     checkMcf(mcf2, mcf2.run(false), gr, l1, u, c, s2, true,  7620, "#D2");
   325     checkMcf(mcf3, mcf3.run(false), gr, l1, u, c, s3, true,     0, "#D3");
   326     checkMcf(mcf4, mcf4.run(false), gr, l2, u, c, s1, true,  5970, "#D4");
   327     checkMcf(mcf5, mcf5.run(false), gr, l2, u, c, s2, true,  8010, "#D5");
   328     checkMcf(mcf6, mcf6.run(false), gr, l2, u, c, s3, false,    0, "#D6");
   329   }
   330 */
   331 
   332   // E. Test NetworkSimplex with FIRST_ELIGIBLE_PIVOT
   333   {
   334     NetworkSimplex<Digraph>::PivotRuleEnum pr =
   335       NetworkSimplex<Digraph>::FIRST_ELIGIBLE_PIVOT;
   336     NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
   337     NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
   338     NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
   339     NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
   340     NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
   341     NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
   342 
   343     checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true,  5240, "#E1");
   344     checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true,  7620, "#E2");
   345     checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true,     0, "#E3");
   346     checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true,  5970, "#E4");
   347     checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true,  8010, "#E5");
   348     checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false,    0, "#E6");
   349   }
   350 
   351   // F. Test NetworkSimplex with BEST_ELIGIBLE_PIVOT
   352   {
   353     NetworkSimplex<Digraph>::PivotRuleEnum pr =
   354       NetworkSimplex<Digraph>::BEST_ELIGIBLE_PIVOT;
   355     NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
   356     NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
   357     NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
   358     NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
   359     NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
   360     NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
   361 
   362     checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true,  5240, "#F1");
   363     checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true,  7620, "#F2");
   364     checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true,     0, "#F3");
   365     checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true,  5970, "#F4");
   366     checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true,  8010, "#F5");
   367     checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false,    0, "#F6");
   368   }
   369 
   370   // G. Test NetworkSimplex with BLOCK_SEARCH_PIVOT
   371   {
   372     NetworkSimplex<Digraph>::PivotRuleEnum pr =
   373       NetworkSimplex<Digraph>::BLOCK_SEARCH_PIVOT;
   374     NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
   375     NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
   376     NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
   377     NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
   378     NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
   379     NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
   380 
   381     checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true,  5240, "#G1");
   382     checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true,  7620, "#G2");
   383     checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true,     0, "#G3");
   384     checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true,  5970, "#G4");
   385     checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true,  8010, "#G5");
   386     checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false,    0, "#G6");
   387   }
   388 
   389   // H. Test NetworkSimplex with CANDIDATE_LIST_PIVOT
   390   {
   391     NetworkSimplex<Digraph>::PivotRuleEnum pr =
   392       NetworkSimplex<Digraph>::CANDIDATE_LIST_PIVOT;
   393     NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
   394     NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
   395     NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
   396     NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
   397     NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
   398     NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
   399 
   400     checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true,  5240, "#H1");
   401     checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true,  7620, "#H2");
   402     checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true,     0, "#H3");
   403     checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true,  5970, "#H4");
   404     checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true,  8010, "#H5");
   405     checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false,    0, "#H6");
   406   }
   407 
   408   // I. Test NetworkSimplex with ALTERING_LIST_PIVOT
   409   {
   410     NetworkSimplex<Digraph>::PivotRuleEnum pr =
   411       NetworkSimplex<Digraph>::ALTERING_LIST_PIVOT;
   412     NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
   413     NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
   414     NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
   415     NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
   416     NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
   417     NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
   418 
   419     checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true,  5240, "#I1");
   420     checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true,  7620, "#I2");
   421     checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true,     0, "#I3");
   422     checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true,  5970, "#I4");
   423     checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true,  8010, "#I5");
   424     checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false,    0, "#I6");
   425   }
   426 
   427 /*
   428   // J. Test MinCostFlow
   429   {
   430     MinCostFlow<Digraph> mcf1(gr, u, c, s1);
   431     MinCostFlow<Digraph> mcf2(gr, u, c, v, w, 27);
   432     MinCostFlow<Digraph> mcf3(gr, u, c, s3);
   433     MinCostFlow<Digraph> mcf4(gr, l2, u, c, s1);
   434     MinCostFlow<Digraph> mcf5(gr, l2, u, c, v, w, 27);
   435     MinCostFlow<Digraph> mcf6(gr, l2, u, c, s3);
   436 
   437     checkMcf(mcf1, mcf1.run(), gr, l1, u, c, s1, true,  5240, "#J1");
   438     checkMcf(mcf2, mcf2.run(), gr, l1, u, c, s2, true,  7620, "#J2");
   439     checkMcf(mcf3, mcf3.run(), gr, l1, u, c, s3, true,     0, "#J3");
   440     checkMcf(mcf4, mcf4.run(), gr, l2, u, c, s1, true,  5970, "#J4");
   441     checkMcf(mcf5, mcf5.run(), gr, l2, u, c, s2, true,  8010, "#J5");
   442     checkMcf(mcf6, mcf6.run(), gr, l2, u, c, s3, false,    0, "#J6");
   443   }
   444 */
   445 /*
   446   // K. Test MinCostMaxFlow
   447   {
   448     MinCostMaxFlow<Digraph> mcmf(gr, u, c, v, w);
   449     mcmf.run();
   450     checkMcf(mcmf, true, gr, l1, u, c, s3, true, 7620, "#K1");
   451   }
   452 */
   453 
   454   return 0;
   455 }