// -*- c++ -*-

 // Use a DIMACS max flow file as stdin.

 // sub_graph_wrapper_demo < dimacs_max_flow_file

 // This program computes a maximum number of edge-disjoint shortest paths

 // between s and t.

 #include <iostream>

 #include <fstream>

 #include <lemon/smart_graph.h>

 #include <lemon/dijkstra.h>

 #include <lemon/maps.h>

 #include <lemon/graph_wrapper.h>

 #include <lemon/dimacs.h>

 #include <lemon/preflow.h>

 #include <lemon/tight_edge_filter_map.h>

 using namespace lemon;

 using std::cout;

 using std::endl;

 int main()

 {    

   typedef SmartGraph Graph;

   typedef Graph::Edge Edge;

   typedef Graph::Node Node;

   typedef Graph::EdgeIt EdgeIt;

   typedef Graph::NodeIt NodeIt;

   typedef Graph::EdgeMap<int> LengthMap;

   Graph g;

   Node s, t;

   LengthMap length(g);

   readDimacs(std::cin, g, length, s, t);

   cout << "edges with lengths (of form tail--length->head): " << endl;

   for(EdgeIt e(g); e!=INVALID; ++e) 

     cout << " " << g.id(g.tail(e)) << "--" 

 	 << length[e] << "->" << g.id(g.head(e)) << endl;

   cout << "s: " << g.id(s) << " t: " << g.id(t) << endl;

   typedef Dijkstra<Graph, LengthMap> Dijkstra;

   Dijkstra dijkstra(g, length);

   dijkstra.run(s);

   // This map returns true exactly for those edges which are 

   // tight w.r.t the length funcion and the potential 

   // given by the dijkstra algorithm.

   typedef TightEdgeFilterMap<Graph, const Dijkstra::DistMap, LengthMap> 

     TightEdgeFilter;

   TightEdgeFilter tight_edge_filter(g, dijkstra.distMap(), length);

   ConstMap<Node, bool> const_true_map(true);

   // This graph contains exaclty the tight edges.

   typedef SubGraphWrapper<Graph, ConstMap<Node, bool>, TightEdgeFilter> SubGW;

   SubGW gw(g, const_true_map, tight_edge_filter);

   ConstMap<Edge, int> const_1_map(1);

   Graph::EdgeMap<int> flow(g, 0);

   // Max flow between s and t in the graph of tight edges.

   Preflow<SubGW, int, ConstMap<Edge, int>, Graph::EdgeMap<int> > 

     preflow(gw, s, t, const_1_map, flow);

   preflow.run();

   cout << "edges of the maximum number of edge-disjoint shortest s-t paths: " 

        << endl;

   for(EdgeIt e(g); e!=INVALID; ++e) 

     if (flow[e])

       cout << " " << g.id(g.tail(e)) << "--" 

 	   << length[e] << "->" << g.id(g.head(e)) << endl;

   return 0;

 }