text: // Copyright Michael Drexl 2005, 2006.
  // Distributed under the Boost Software License, Version 1.0.
  // (See accompanying file LICENSE_1_0.txt or copy at
  // http://boost.org/LICENSE_1_0.txt)
  
  // Example use of the resource-constrained shortest paths algorithm.
  #include <boost/config.hpp>
  
  #ifdef BOOST_MSVC
  #pragma warning(disable : 4267)
  #endif
  
  #include <boost/graph/adjacency_list.hpp>
  
  #include <boost/graph/r_c_shortest_paths.hpp>
  #include <iostream>
  
  using namespace boost;
  
  struct SPPRC_Example_Graph_Vert_Prop
  {
      SPPRC_Example_Graph_Vert_Prop(int n = 0, int e = 0, int l = 0)
      : num(n), eat(e), lat(l)
      {
      }
      int num;
      // earliest arrival time
      int eat;
      // latest arrival time
      int lat;
  };
  
  struct SPPRC_Example_Graph_Arc_Prop
  {
      SPPRC_Example_Graph_Arc_Prop(int n = 0, int c = 0, int t = 0)
      : num(n), cost(c), time(t)
      {
      }
      int num;
      // traversal cost
      int cost;
      // traversal time
      int time;
  };
  
  typedef adjacency_list< vecS, vecS, directedS, SPPRC_Example_Graph_Vert_Prop,
      SPPRC_Example_Graph_Arc_Prop >
      SPPRC_Example_Graph;
  
  // data structures for spp without resource constraints:
  // ResourceContainer model
  struct spp_no_rc_res_cont
  {
      spp_no_rc_res_cont(int c = 0) : cost(c) {};
      spp_no_rc_res_cont& operator=(const spp_no_rc_res_cont& other)
      {
          if (this == &other)
              return *this;
          this->~spp_no_rc_res_cont();
          new (this) spp_no_rc_res_cont(other);
          return *this;
      }
      int cost;
  };
  
  bool operator==(
      const spp_no_rc_res_cont& res_cont_1, const spp_no_rc_res_cont& res_cont_2)
  {
      return (res_cont_1.cost == res_cont_2.cost);
  }
  
  bool operator<(
      const spp_no_rc_res_cont& res_cont_1, const spp_no_rc_res_cont& res_cont_2)
  {
      return (res_cont_1.cost < res_cont_2.cost);
  }
  
  // ResourceExtensionFunction model
  class ref_no_res_cont
  {
  public:
      inline bool operator()(const SPPRC_Example_Graph& g,
          spp_no_rc_res_cont& new_cont, const spp_no_rc_res_cont& old_cont,
          graph_traits< SPPRC_Example_Graph >::edge_descriptor ed) const
      {
          new_cont.cost = old_cont.cost + g[ed].cost;
          return true;
      }
  };
  
  // DominanceFunction model
  class dominance_no_res_cont
  {
  public:
      inline bool operator()(const spp_no_rc_res_cont& res_cont_1,
          const spp_no_rc_res_cont& res_cont_2) const
      {
          // must be "<=" here!!!
          // must NOT be "<"!!!
          return res_cont_1.cost <= res_cont_2.cost;
          // this is not a contradiction to the documentation
          // the documentation says:
          // "A label $l_1$ dominates a label $l_2$ if and only if both are
          // resident at the same vertex, and if, for each resource, the resource
          // consumption of $l_1$ is less than or equal to the resource
          // consumption of $l_2$, and if there is at least one resource where
          // $l_1$ has a lower resource consumption than $l_2$." one can think of
          // a new label with a resource consumption equal to that of an old label
          // as being dominated by that old label, because the new one will have a
          // higher number and is created at a later point in time, so one can
          // implicitly use the number or the creation time as a resource for
          // tie-breaking
      }
  };
  // end data structures for spp without resource constraints:
  
  // data structures for shortest path problem with time windows (spptw)
  // ResourceContainer model
  struct spp_spptw_res_cont
  {
      spp_spptw_res_cont(int c = 0, int t = 0) : cost(c), time(t) {}
      spp_spptw_res_cont& operator=(const spp_spptw_res_cont& other)
      {
          if (this == &other)
              return *this;
          this->~spp_spptw_res_cont();
          new (this) spp_spptw_res_cont(other);
          return *this;
      }
      int cost;
      int time;
  };
  
  bool operator==(
      const spp_spptw_res_cont& res_cont_1, const spp_spptw_res_cont& res_cont_2)
  {
      return (res_cont_1.cost == res_cont_2.cost
          && res_cont_1.time == res_cont_2.time);
  }
  
  bool operator<(
      const spp_spptw_res_cont& res_cont_1, const spp_spptw_res_cont& res_cont_2)
  {
      if (res_cont_1.cost > res_cont_2.cost)
          return false;
      if (res_cont_1.cost == res_cont_2.cost)
          return res_cont_1.time < res_cont_2.time;
      return true;
  }
  
  // ResourceExtensionFunction model
  class ref_spptw
  {
  public:
      inline bool operator()(const SPPRC_Example_Graph& g,
          spp_spptw_res_cont& new_cont, const spp_spptw_res_cont& old_cont,
          graph_traits< SPPRC_Example_Graph >::edge_descriptor ed) const
      {
          const SPPRC_Example_Graph_Arc_Prop& arc_prop = get(edge_bundle, g)[ed];
          const SPPRC_Example_Graph_Vert_Prop& vert_prop
              = get(vertex_bundle, g)[target(ed, g)];
          new_cont.cost = old_cont.cost + arc_prop.cost;
          int& i_time = new_cont.time;
          i_time = old_cont.time + arc_prop.time;
          i_time < vert_prop.eat ? i_time = vert_prop.eat : 0;
          return i_time <= vert_prop.lat ? true : false;
      }
  };
  
  // DominanceFunction model
  class dominance_spptw
  {
  public:
      inline bool operator()(const spp_spptw_res_cont& res_cont_1,
          const spp_spptw_res_cont& res_cont_2) const
      {
          // must be "<=" here!!!
          // must NOT be "<"!!!
          return res_cont_1.cost <= res_cont_2.cost
              && res_cont_1.time <= res_cont_2.time;
          // this is not a contradiction to the documentation
          // the documentation says:
          // "A label $l_1$ dominates a label $l_2$ if and only if both are
          // resident at the same vertex, and if, for each resource, the resource
          // consumption of $l_1$ is less than or equal to the resource
          // consumption of $l_2$, and if there is at least one resource where
          // $l_1$ has a lower resource consumption than $l_2$." one can think of
          // a new label with a resource consumption equal to that of an old label
          // as being dominated by that old label, because the new one will have a
          // higher number and is created at a later point in time, so one can
          // implicitly use the number or the creation time as a resource for
          // tie-breaking
      }
  };
  // end data structures for shortest path problem with time windows (spptw)
  
  // example graph structure and cost from
  // http://www.boost.org/libs/graph/example/dijkstra-example.cpp
  enum nodes
  {
      A,
      B,
      C,
      D,
      E
  };
  char name[] = "ABCDE";
  
  int main()
  {
      SPPRC_Example_Graph g;
  
      add_vertex(SPPRC_Example_Graph_Vert_Prop(A, 0, 0), g);
      add_vertex(SPPRC_Example_Graph_Vert_Prop(B, 5, 20), g);
      add_vertex(SPPRC_Example_Graph_Vert_Prop(C, 6, 10), g);
      add_vertex(SPPRC_Example_Graph_Vert_Prop(D, 3, 12), g);
      add_vertex(SPPRC_Example_Graph_Vert_Prop(E, 0, 100), g);
  
      add_edge(A, C, SPPRC_Example_Graph_Arc_Prop(0, 1, 5), g);
      add_edge(B, B, SPPRC_Example_Graph_Arc_Prop(1, 2, 5), g);
      add_edge(B, D, SPPRC_Example_Graph_Arc_Prop(2, 1, 2), g);
      add_edge(B, E, SPPRC_Example_Graph_Arc_Prop(3, 2, 7), g);
      add_edge(C, B, SPPRC_Example_Graph_Arc_Prop(4, 7, 3), g);
      add_edge(C, D, SPPRC_Example_Graph_Arc_Prop(5, 3, 8), g);
      add_edge(D, E, SPPRC_Example_Graph_Arc_Prop(6, 1, 3), g);
      add_edge(E, A, SPPRC_Example_Graph_Arc_Prop(7, 1, 5), g);
      add_edge(E, B, SPPRC_Example_Graph_Arc_Prop(8, 1, 4), g);
  
      // the unique shortest path from A to E in the dijkstra-example.cpp is
      // A -> C -> D -> E
      // its length is 5
      // the following code also yields this result
  
      // with the above time windows, this path is infeasible
      // now, there are two shortest paths that are also feasible with respect to
      // the vertex time windows:
      // A -> C -> B -> D -> E and
      // A -> C -> B -> E
      // however, the latter has a longer total travel time and is therefore not
      // pareto-optimal, i.e., it is dominated by the former path
      // therefore, the code below returns only the former path
  
      // spp without resource constraints
      graph_traits< SPPRC_Example_Graph >::vertex_descriptor s = A;
      graph_traits< SPPRC_Example_Graph >::vertex_descriptor t = E;
  
      std::vector<
          std::vector< graph_traits< SPPRC_Example_Graph >::edge_descriptor > >
          opt_solutions;
      std::vector< spp_no_rc_res_cont > pareto_opt_rcs_no_rc;
  
      r_c_shortest_paths(g, get(&SPPRC_Example_Graph_Vert_Prop::num, g),
          get(&SPPRC_Example_Graph_Arc_Prop::num, g), s, t, opt_solutions,
          pareto_opt_rcs_no_rc, spp_no_rc_res_cont(0), ref_no_res_cont(),
          dominance_no_res_cont(),
          std::allocator< r_c_shortest_paths_label< SPPRC_Example_Graph,
              spp_no_rc_res_cont > >(),
          default_r_c_shortest_paths_visitor());
  
      std::cout << "SPP without resource constraints:" << std::endl;
      std::cout << "Number of optimal solutions: ";
      std::cout << static_cast< int >(opt_solutions.size()) << std::endl;
      for (int i = 0; i < static_cast< int >(opt_solutions.size()); ++i)
      {
          std::cout << "The " << i << "th shortest path from A to E is: ";
          std::cout << std::endl;
          for (int j = static_cast< int >(opt_solutions[i].size()) - 1; j >= 0;
               --j)
              std::cout << name[source(opt_solutions[i][j], g)] << std::endl;
          std::cout << "E" << std::endl;
          std::cout << "Length: " << pareto_opt_rcs_no_rc[i].cost << std::endl;
      }
      std::cout << std::endl;
  
      // spptw
      std::vector<
          std::vector< graph_traits< SPPRC_Example_Graph >::edge_descriptor > >
          opt_solutions_spptw;
      std::vector< spp_spptw_res_cont > pareto_opt_rcs_spptw;
  
      r_c_shortest_paths(g, get(&SPPRC_Example_Graph_Vert_Prop::num, g),
          get(&SPPRC_Example_Graph_Arc_Prop::num, g), s, t, opt_solutions_spptw,
          pareto_opt_rcs_spptw, spp_spptw_res_cont(0, 0), ref_spptw(),
          dominance_spptw(),
          std::allocator< r_c_shortest_paths_label< SPPRC_Example_Graph,
              spp_spptw_res_cont > >(),
          default_r_c_shortest_paths_visitor());
  
      std::cout << "SPP with time windows:" << std::endl;
      std::cout << "Number of optimal solutions: ";
      std::cout << static_cast< int >(opt_solutions.size()) << std::endl;
      for (int i = 0; i < static_cast< int >(opt_solutions.size()); ++i)
      {
          std::cout << "The " << i << "th shortest path from A to E is: ";
          std::cout << std::endl;
          for (int j = static_cast< int >(opt_solutions_spptw[i].size()) - 1;
               j >= 0; --j)
              std::cout << name[source(opt_solutions_spptw[i][j], g)]
                        << std::endl;
          std::cout << "E" << std::endl;
          std::cout << "Length: " << pareto_opt_rcs_spptw[i].cost << std::endl;
          std::cout << "Time: " << pareto_opt_rcs_spptw[i].time << std::endl;
      }
  
      // utility function check_r_c_path example
      std::cout << std::endl;
      bool b_is_a_path_at_all = false;
      bool b_feasible = false;
      bool b_correctly_extended = false;
      spp_spptw_res_cont actual_final_resource_levels(0, 0);
      graph_traits< SPPRC_Example_Graph >::edge_descriptor ed_last_extended_arc;
      check_r_c_path(g, opt_solutions_spptw[0], spp_spptw_res_cont(0, 0), true,
          pareto_opt_rcs_spptw[0], actual_final_resource_levels, ref_spptw(),
          b_is_a_path_at_all, b_feasible, b_correctly_extended,
          ed_last_extended_arc);
      if (!b_is_a_path_at_all)
          std::cout << "Not a path." << std::endl;
      if (!b_feasible)
          std::cout << "Not a feasible path." << std::endl;
      if (!b_correctly_extended)
          std::cout << "Not correctly extended." << std::endl;
      if (b_is_a_path_at_all && b_feasible && b_correctly_extended)
      {
          std::cout << "Actual final resource levels:" << std::endl;
          std::cout << "Length: " << actual_final_resource_levels.cost
                    << std::endl;
          std::cout << "Time: " << actual_final_resource_levels.time << std::endl;
          std::cout << "OK." << std::endl;
      }
  
      return 0;
  }
  