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+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef LEMON_KRUSKAL_H
+#define LEMON_KRUSKAL_H
+
+#include <algorithm>
+#include <vector>
+#include <lemon/unionfind.h>
+// #include <lemon/graph_utils.h>
+#include <lemon/maps.h>
+
+// #include <lemon/radix_sort.h>
+
+#include <lemon/bits/utility.h>
+#include <lemon/bits/traits.h>
+
+///\ingroup spantree
+///\file
+///\brief Kruskal's algorithm to compute a minimum cost tree
+///
+///Kruskal's algorithm to compute a minimum cost tree.
+///
+
+namespace lemon {
+
+  namespace _kruskal_bits {
+
+    // Kruskal for directed graphs.
+
+    template <typename Digraph, typename In, typename Out>
+    typename disable_if<lemon::UndirectedTagIndicator<Digraph>,
+		       typename In::value_type::second_type >::type
+    kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) {
+      typedef typename In::value_type::second_type Value;
+      typedef typename Digraph::template NodeMap<int> IndexMap;
+      typedef typename Digraph::Node Node;
+      
+      IndexMap index(digraph);
+      UnionFind<IndexMap> uf(index);
+      for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) {
+        uf.insert(it);
+      }
+      
+      Value tree_value = 0;
+      for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
+        if (uf.join(digraph.target(it->first),digraph.source(it->first))) {
+          out.set(it->first, true);
+          tree_value += it->second;
+        }
+        else {
+          out.set(it->first, false);
+        }
+      }
+      return tree_value;
+    }
+
+    // Kruskal for undirected graphs.
+
+    template <typename Graph, typename In, typename Out>
+    typename enable_if<lemon::UndirectedTagIndicator<Graph>,
+		       typename In::value_type::second_type >::type
+    kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) {
+      typedef typename In::value_type::second_type Value;
+      typedef typename Graph::template NodeMap<int> IndexMap;
+      typedef typename Graph::Node Node;
+      
+      IndexMap index(graph);
+      UnionFind<IndexMap> uf(index);
+      for (typename Graph::NodeIt it(graph); it != INVALID; ++it) {
+        uf.insert(it);
+      }
+      
+      Value tree_value = 0;
+      for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
+        if (uf.join(graph.u(it->first),graph.v(it->first))) {
+          out.set(it->first, true);
+          tree_value += it->second;
+        }
+        else {
+          out.set(it->first, false);
+        }
+      }
+      return tree_value;
+    }
+
+
+    template <typename Sequence>
+    struct PairComp {
+      typedef typename Sequence::value_type Value;
+      bool operator()(const Value& left, const Value& right) {
+	return left.second < right.second;
+      }
+    };
+
+    template <typename In, typename Enable = void>
+    struct SequenceInputIndicator {
+      static const bool value = false;
+    };
+
+    template <typename In>
+    struct SequenceInputIndicator<In, 
+      typename exists<typename In::value_type::first_type>::type> {
+      static const bool value = true;
+    };
+
+    template <typename In, typename Enable = void>
+    struct MapInputIndicator {
+      static const bool value = false;
+    };
+
+    template <typename In>
+    struct MapInputIndicator<In, 
+      typename exists<typename In::Value>::type> {
+      static const bool value = true;
+    };
+
+    template <typename In, typename Enable = void>
+    struct SequenceOutputIndicator {
+      static const bool value = false;
+    };
+ 
+    template <typename Out>
+    struct SequenceOutputIndicator<Out, 
+      typename exists<typename Out::value_type>::type> {
+      static const bool value = true;
+    };
+
+    template <typename Out, typename Enable = void>
+    struct MapOutputIndicator {
+      static const bool value = false;
+    };
+
+    template <typename Out>
+    struct MapOutputIndicator<Out, 
+      typename exists<typename Out::Value>::type> {
+      static const bool value = true;
+    };
+
+    template <typename In, typename InEnable = void>
+    struct KruskalValueSelector {};
+
+    template <typename In>
+    struct KruskalValueSelector<In,
+      typename enable_if<SequenceInputIndicator<In>, void>::type> 
+    {
+      typedef typename In::value_type::second_type Value;
+    };    
+
+    template <typename In>
+    struct KruskalValueSelector<In,
+      typename enable_if<MapInputIndicator<In>, void>::type> 
+    {
+      typedef typename In::Value Value;
+    };    
+    
+    template <typename Graph, typename In, typename Out,
+              typename InEnable = void>
+    struct KruskalInputSelector {};
+
+    template <typename Graph, typename In, typename Out,
+              typename InEnable = void>
+    struct KruskalOutputSelector {};
+    
+    template <typename Graph, typename In, typename Out>
+    struct KruskalInputSelector<Graph, In, Out,
+      typename enable_if<SequenceInputIndicator<In>, void>::type > 
+    {
+      typedef typename In::value_type::second_type Value;
+
+      static Value kruskal(const Graph& graph, const In& in, Out& out) {
+        return KruskalOutputSelector<Graph, In, Out>::
+          kruskal(graph, in, out);
+      }
+
+    };
+
+    template <typename Graph, typename In, typename Out>
+    struct KruskalInputSelector<Graph, In, Out,
+      typename enable_if<MapInputIndicator<In>, void>::type > 
+    {
+      typedef typename In::Value Value;
+      static Value kruskal(const Graph& graph, const In& in, Out& out) {
+        typedef typename In::Key MapArc;
+        typedef typename In::Value Value;
+        typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt;
+        typedef std::vector<std::pair<MapArc, Value> > Sequence;
+        Sequence seq;
+        
+        for (MapArcIt it(graph); it != INVALID; ++it) {
+          seq.push_back(std::make_pair(it, in[it]));
+        }
+
+        std::sort(seq.begin(), seq.end(), PairComp<Sequence>());
+        return KruskalOutputSelector<Graph, Sequence, Out>::
+          kruskal(graph, seq, out);
+      }
+    };
+
+    template <typename Graph, typename In, typename Out>
+    struct KruskalOutputSelector<Graph, In, Out,
+      typename enable_if<SequenceOutputIndicator<Out>, void>::type > 
+    {
+      typedef typename In::value_type::second_type Value;
+
+      static Value kruskal(const Graph& graph, const In& in, Out& out) {
+        typedef StoreBoolMap<Out> Map;
+        Map map(out);
+        return _kruskal_bits::kruskal(graph, in, map);
+      }
+
+    };
+
+    template <typename Graph, typename In, typename Out>
+    struct KruskalOutputSelector<Graph, In, Out,
+      typename enable_if<MapOutputIndicator<Out>, void>::type > 
+    {
+      typedef typename In::value_type::second_type Value;
+
+      static Value kruskal(const Graph& graph, const In& in, Out& out) {
+        return _kruskal_bits::kruskal(graph, in, out);
+      }
+    };
+
+  }
+
+  /// \ingroup spantree
+  ///
+  /// \brief Kruskal's algorithm to find a minimum cost tree of a graph.
+  ///
+  /// This function runs Kruskal's algorithm to find a minimum cost tree.
+  /// Due to some C++ hacking, it accepts various input and output types.
+  ///
+  /// \param g The graph the algorithm runs on.
+  /// It can be either \ref concepts::Digraph "directed" or 
+  /// \ref concepts::Graph "undirected".
+  /// If the graph is directed, the algorithm consider it to be 
+  /// undirected by disregarding the direction of the arcs.
+  ///
+  /// \param in This object is used to describe the arc costs. It can be one
+  /// of the following choices.
+  /// - An STL compatible 'Forward Container' with
+  /// <tt>std::pair<GR::Edge,X></tt> or
+  /// <tt>std::pair<GR::Arc,X></tt> as its <tt>value_type</tt>, where
+  /// \c X is the type of the costs. The pairs indicates the arcs
+  /// along with the assigned cost. <em>They must be in a
+  /// cost-ascending order.</em>
+  /// - Any readable Arc map. The values of the map indicate the arc costs.
+  ///
+  /// \retval out Here we also have a choise.
+  /// - It can be a writable \c bool arc map.  After running the
+  /// algorithm this will contain the found minimum cost spanning
+  /// tree: the value of an arc will be set to \c true if it belongs
+  /// to the tree, otherwise it will be set to \c false. The value of
+  /// each arc will be set exactly once.
+  /// - It can also be an iteraror of an STL Container with
+  /// <tt>GR::Edge</tt> or <tt>GR::Arc</tt> as its
+  /// <tt>value_type</tt>.  The algorithm copies the elements of the
+  /// found tree into this sequence.  For example, if we know that the
+  /// spanning tree of the graph \c g has say 53 arcs, then we can
+  /// put its arcs into an STL vector \c tree with a code like this.
+  ///\code
+  /// std::vector<Arc> tree(53);
+  /// kruskal(g,cost,tree.begin());
+  ///\endcode
+  /// Or if we don't know in advance the size of the tree, we can
+  /// write this.  
+  ///\code std::vector<Arc> tree;
+  /// kruskal(g,cost,std::back_inserter(tree)); 
+  ///\endcode
+  ///
+  /// \return The total cost of the found tree.
+  ///
+  /// \warning If kruskal runs on an be consistent of using the same
+  /// Arc type for input and output.
+  ///
+
+#ifdef DOXYGEN
+  template <class Graph, class In, class Out>
+  Value kruskal(GR const& g, const In& in, Out& out)
+#else 
+  template <class Graph, class In, class Out>
+  inline typename _kruskal_bits::KruskalValueSelector<In>::Value 
+  kruskal(const Graph& graph, const In& in, Out& out) 
+#endif
+  {
+    return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::
+      kruskal(graph, in, out);
+  }
+
+ 
+  
+
+  template <class Graph, class In, class Out>
+  inline typename _kruskal_bits::KruskalValueSelector<In>::Value
+  kruskal(const Graph& graph, const In& in, const Out& out)
+  {
+    return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::
+      kruskal(graph, in, out);
+  }  
+
+} //namespace lemon
+
+#endif //LEMON_KRUSKAL_H