// -*- 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;

}