// -*- C++ -*-
/* 
 *template <Graph, T, Heap=FibHeap, LengthMap=Graph::EdgeMap<T> >
 *
 *Constructor: 
 *
 *Prim(Graph G, LengthMap weight)
 *
 *
 *Methods:
 *
 *void run() : Runs the Prim-algorithm from a random node
 *
 *void run(Node r) : Runs the Prim-algorithm from node s
 *
 *T weight() : After run(r) was run, it returns the minimum 
 *   weight of a spanning tree of the component of the root. 
 *
 *Edge tree(Node v) : After run(r) was run, it returns the 
 *   first edge in the path from v to the root. Returns 
 *   INVALID if v=r or v is not reachable from the root.
 *
 *bool conn() : After run(r) was run, it is true iff G is connected
 *
 *bool reached(Node v) : After run(r) was run, it is true 
 *   iff v is in the same component as the root
 *
 *Node root() : returns the root
 *
 */

#ifndef HUGO_PRIM_H
#define HUGO_PRIM_H

#include <fib_heap.h>
#include <invalid.h>

namespace hugo {

  template <typename Graph, typename T, 
    typename Heap=FibHeap<typename Graph::Node, T, 
    typename Graph::NodeMap<int> >, 
    typename LengthMap=typename Graph::EdgeMap<T> >
    class Prim{
      typedef typename Graph::Node Node;
      typedef typename Graph::NodeIt NodeIt;
      typedef typename Graph::Edge Edge;
      typedef typename Graph::OutEdgeIt OutEdgeIt;
      typedef typename Graph::InEdgeIt InEdgeIt;  

      const Graph& G;
      const LengthMap& edge_weight;
      typename Graph::NodeMap<Edge> tree_edge;
      typename Graph::NodeMap<T> min_weight;
      typename Graph::NodeMap<bool> reach;
          
  public :

      Prim(Graph& _G, LengthMap& _edge_weight) : 
	G(_G), edge_weight(_edge_weight), 
	tree_edge(_G,INVALID), min_weight(_G), reach(_G, false) { }


      void run() {
	NodeIt _r;	
	G.first(_r);
	run(_r);
      }


      void run(Node r) {

	NodeIt u;
	for ( G.first(u) ; G.valid(u) ; G.next(u) ) {
	  tree_edge.set(u,INVALID);
	  min_weight.set(u,0);
	  reach.set(u,false);
	}


	typename Graph::NodeMap<bool> scanned(G, false);
	typename Graph::NodeMap<int> heap_map(G,-1);
	
	Heap heap(heap_map);

	heap.push(r,0); 
	reach.set(r, true);

	while ( !heap.empty() ) {

	  Node v=heap.top(); 
	  min_weight.set(v, heap.get(v));
	  heap.pop();
	  scanned.set(v,true);

	  OutEdgeIt e;
	  for( G.first(e,v); G.valid(e); G.next(e)) {
	    Node w=G.head(e); 
	    
	    if ( !scanned[w] ) {
	      if ( !reach[w] ) {
		reach.set(w,true);
		heap.push(w, edge_weight[e]); 
		tree_edge.set(w,e);
	      } else if ( edge_weight[e] < heap.get(w) ) {
		tree_edge.set(w,e);
		heap.decrease(w, edge_weight[e]); 
	      }
	    }
	  }

	  InEdgeIt f;
	  for( G.first(f,v); G.valid(f); G.next(f)) {
	    Node w=G.tail(f); 
	    
	    if ( !scanned[w] ) {
	      if ( !reach[w] ) {
		reach.set(w,true);
		heap.push(w, edge_weight[f]); 
		tree_edge.set(w,f);
	      } else if ( edge_weight[f] < heap.get(w) ) {
		tree_edge.set(w,f);
		heap.decrease(w, edge_weight[f]); 
	      }
	    }
	  }
	}
      } 
 

      T weight() {
	T w=0;
	NodeIt u;
	for ( G.first(u) ; G.valid(u) ; G.next(u) ) w+=min_weight[u];
	return w;
      }
     

      Edge tree(Node v) {
	return tree_edge[v];
      } 


      bool conn() {
	bool c=true;
	NodeIt u;
	for ( G.first(u) ; G.valid(u) ; G.next(u) ) 
	  if ( !reached[u] ) { 
	    c=false;
	    break;
	  }
	return c;
      }


      bool reached(Node v) {
	return reached[v];
      }


      Node root() {
	return r;
      }

    };

}

#endif