//Tests dijsktra.h with two heap implementations:

 //the default binary heap of bin_heap.h, and the 

 //Fibonacci heap of fib_heap.h.

 //The input is a graph in standard dimacs format from the standard input (like

 //in /hugo_loc/testfiles/dimacs). It runs dijkstra.h on this graph with both

 //heaps, checking two postconditions:

 //- if the edges e=uv of the shortest path tree reported by dijkstra.h have

 //dist(v)-dist(u)=length(e)

 // - if all edges e=uv with u reachable from the root have

 //dist(v)-dist(u)>=length(e)

 #include <iostream>

 #include <math.h>

 #include <hugo/smart_graph.h>

 #include <hugo/dimacs.h>

 #include <hugo/dijkstra.h>

 #include <hugo/time_measure.h>

 #include <hugo/bin_heap.h>

 #include <hugo/fib_heap.h>

 using namespace hugo;

 int main(int, char **) {

   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 cap(G);

   readDimacsMaxFlow(std::cin, G, s, t, cap);

   Timer ts;

   std::cout <<

     "\n  Testing dijkstra.h with binary heap implementation bin_heap.h,"

 	    <<std::endl;

   std::cout<<"  on a graph with " << 

     G.nodeNum() << " nodes and " << G.edgeNum() << " edges..."

 	   << std::endl<<std::endl;

   Dijkstra<Graph, LengthMap> 

     dijkstra_test(G, cap);

   ts.reset();

   dijkstra_test.run(s);

   std::cout << "elapsed time: " << ts << std::endl;

   int error1=0;

   int error2=0;

   EdgeIt e;

   for(G.first(e); G.valid(e); G.next(e)) {

     Node u=G.tail(e);

     Node v=G.head(e);

     if ( dijkstra_test.dist(v) - dijkstra_test.dist(u) > cap[e] )

       if ( dijkstra_test.reached(u) ) {

 	std::cout<<"Error! dist(head)-dist(tail)- edge_length= " 

 		 <<dijkstra_test.dist(v) - dijkstra_test.dist(u) 

 	  - cap[e]<<std::endl;

 	++error1;

       }

   }

   NodeIt v;

   for(G.first(v); G.valid(v); G.next(v)) {

     if ( dijkstra_test.reached(v) ) {

       Edge e=dijkstra_test.pred(v);

       Node u=G.tail(e);

       if ( dijkstra_test.dist(v) - dijkstra_test.dist(u) != cap[e] ) {

 	std::cout<<"Error in a shortest path tree edge! Difference: " 

 		 <<std::abs(dijkstra_test.dist(v) - dijkstra_test.dist(u) 

 			    - cap[e])<<std::endl;

 	++error2;

       }

     }

   }

   std::cout << error1 << " non-tree and " << error2 

 	    << " shortest path tree edge is erroneous."<<std::endl;

   std::cout <<

     "\n\n  Testing dijkstra.h with Fibonacci heap implementation fib_heap.h,"

 	    <<std::endl;

   std::cout<<"  on a graph with " << 

     G.nodeNum() << " nodes and " << G.edgeNum() << " edges..."

 	   << std::endl<<std::endl;

   Dijkstra<Graph, LengthMap, FibHeap> 

     dijkstra_test2(G, cap);

   ts.reset();

   dijkstra_test2.run(s);

   std::cout << "elapsed time: " << ts << std::endl;

   error1=0;

   error2=0;

   for(G.first(e); G.valid(e); G.next(e)) {

     Node u=G.tail(e);

     Node v=G.head(e);

     if ( dijkstra_test2.dist(v) - dijkstra_test2.dist(u) > cap[e] )

       if ( dijkstra_test2.reached(u) ) {

 	std::cout<<"Error! dist(head)-dist(tail)- edge_length= " 

 		 <<dijkstra_test2.dist(v) - dijkstra_test2.dist(u) 

 	  - cap[e]<<std::endl;

 	++error1;

       }

   }

   for(G.first(v); G.valid(v); G.next(v)) {

     if ( dijkstra_test2.reached(v) ) {

       Edge e=dijkstra_test2.pred(v);

       Node u=G.tail(e);

       if ( dijkstra_test2.dist(v) - dijkstra_test2.dist(u) != cap[e] ) {

 	std::cout<<"Error in a shortest path tree edge! Difference: " 

 		 <<std::abs(dijkstra_test2.dist(v) - dijkstra_test2.dist(u) 

 			    - cap[e])<<std::endl;

 	++error2;

       }

     }

   }

   std::cout << error1 << " non-tree and " << error2 

 	    << " shortest path tree edge is erroneous."<<std::endl;

   return 0;

 }