diff -r c6acc34f98dc -r 1a7fe3bef514 lemon/gomory_hu.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/gomory_hu.h	Thu Nov 05 15:50:01 2009 +0100
@@ -0,0 +1,570 @@
+/* -*- 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_GOMORY_HU_TREE_H
+#define LEMON_GOMORY_HU_TREE_H
+
+#include <limits>
+
+#include <lemon/core.h>
+#include <lemon/preflow.h>
+#include <lemon/concept_check.h>
+#include <lemon/concepts/maps.h>
+
+/// \ingroup min_cut
+/// \file 
+/// \brief Gomory-Hu cut tree in graphs.
+
+namespace lemon {
+
+  /// \ingroup min_cut
+  ///
+  /// \brief Gomory-Hu cut tree algorithm
+  ///
+  /// The Gomory-Hu tree is a tree on the node set of a given graph, but it
+  /// may contain edges which are not in the original graph. It has the
+  /// property that the minimum capacity edge of the path between two nodes 
+  /// in this tree has the same weight as the minimum cut in the graph
+  /// between these nodes. Moreover the components obtained by removing
+  /// this edge from the tree determine the corresponding minimum cut.
+  /// Therefore once this tree is computed, the minimum cut between any pair
+  /// of nodes can easily be obtained.
+  /// 
+  /// The algorithm calculates \e n-1 distinct minimum cuts (currently with
+  /// the \ref Preflow algorithm), thus it has \f$O(n^3\sqrt{e})\f$ overall
+  /// time complexity. It calculates a rooted Gomory-Hu tree.
+  /// The structure of the tree and the edge weights can be
+  /// obtained using \c predNode(), \c predValue() and \c rootDist().
+  /// The functions \c minCutMap() and \c minCutValue() calculate
+  /// the minimum cut and the minimum cut value between any two nodes
+  /// in the graph. You can also list (iterate on) the nodes and the
+  /// edges of the cuts using \c MinCutNodeIt and \c MinCutEdgeIt.
+  ///
+  /// \tparam GR The type of the undirected graph the algorithm runs on.
+  /// \tparam CAP The type of the edge map containing the capacities.
+  /// The default map type is \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".
+#ifdef DOXYGEN
+  template <typename GR,
+	    typename CAP>
+#else
+  template <typename GR,
+	    typename CAP = typename GR::template EdgeMap<int> >
+#endif
+  class GomoryHu {
+  public:
+
+    /// The graph type of the algorithm
+    typedef GR Graph;
+    /// The capacity map type of the algorithm
+    typedef CAP Capacity;
+    /// The value type of capacities
+    typedef typename Capacity::Value Value;
+    
+  private:
+
+    TEMPLATE_GRAPH_TYPEDEFS(Graph);
+
+    const Graph& _graph;
+    const Capacity& _capacity;
+
+    Node _root;
+    typename Graph::template NodeMap<Node>* _pred;
+    typename Graph::template NodeMap<Value>* _weight;
+    typename Graph::template NodeMap<int>* _order;
+
+    void createStructures() {
+      if (!_pred) {
+	_pred = new typename Graph::template NodeMap<Node>(_graph);
+      }
+      if (!_weight) {
+	_weight = new typename Graph::template NodeMap<Value>(_graph);
+      }
+      if (!_order) {
+	_order = new typename Graph::template NodeMap<int>(_graph);
+      }
+    }
+
+    void destroyStructures() {
+      if (_pred) {
+	delete _pred;
+      }
+      if (_weight) {
+	delete _weight;
+      }
+      if (_order) {
+	delete _order;
+      }
+    }
+  
+  public:
+
+    /// \brief Constructor
+    ///
+    /// Constructor.
+    /// \param graph The undirected graph the algorithm runs on.
+    /// \param capacity The edge capacity map.
+    GomoryHu(const Graph& graph, const Capacity& capacity) 
+      : _graph(graph), _capacity(capacity),
+	_pred(0), _weight(0), _order(0) 
+    {
+      checkConcept<concepts::ReadMap<Edge, Value>, Capacity>();
+    }
+
+
+    /// \brief Destructor
+    ///
+    /// Destructor.
+    ~GomoryHu() {
+      destroyStructures();
+    }
+
+  private:
+  
+    // Initialize the internal data structures
+    void init() {
+      createStructures();
+
+      _root = NodeIt(_graph);
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        (*_pred)[n] = _root;
+        (*_order)[n] = -1;
+      }
+      (*_pred)[_root] = INVALID;
+      (*_weight)[_root] = std::numeric_limits<Value>::max(); 
+    }
+
+
+    // Start the algorithm
+    void start() {
+      Preflow<Graph, Capacity> fa(_graph, _capacity, _root, INVALID);
+
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+	if (n == _root) continue;
+
+	Node pn = (*_pred)[n];
+	fa.source(n);
+	fa.target(pn);
+
+	fa.runMinCut();
+
+	(*_weight)[n] = fa.flowValue();
+
+	for (NodeIt nn(_graph); nn != INVALID; ++nn) {
+	  if (nn != n && fa.minCut(nn) && (*_pred)[nn] == pn) {
+	    (*_pred)[nn] = n;
+	  }
+	}
+	if ((*_pred)[pn] != INVALID && fa.minCut((*_pred)[pn])) {
+	  (*_pred)[n] = (*_pred)[pn];
+	  (*_pred)[pn] = n;
+	  (*_weight)[n] = (*_weight)[pn];
+	  (*_weight)[pn] = fa.flowValue();
+	}
+      }
+
+      (*_order)[_root] = 0;
+      int index = 1;
+
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+	std::vector<Node> st;
+	Node nn = n;
+	while ((*_order)[nn] == -1) {
+	  st.push_back(nn);
+	  nn = (*_pred)[nn];
+	}
+	while (!st.empty()) {
+	  (*_order)[st.back()] = index++;
+	  st.pop_back();
+	}
+      }
+    }
+
+  public:
+
+    ///\name Execution Control
+ 
+    ///@{
+
+    /// \brief Run the Gomory-Hu algorithm.
+    ///
+    /// This function runs the Gomory-Hu algorithm.
+    void run() {
+      init();
+      start();
+    }
+    
+    /// @}
+
+    ///\name Query Functions
+    ///The results of the algorithm can be obtained using these
+    ///functions.\n
+    ///\ref run() should be called before using them.\n
+    ///See also \ref MinCutNodeIt and \ref MinCutEdgeIt.
+
+    ///@{
+
+    /// \brief Return the predecessor node in the Gomory-Hu tree.
+    ///
+    /// This function returns the predecessor node of the given node
+    /// in the Gomory-Hu tree.
+    /// If \c node is the root of the tree, then it returns \c INVALID.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    Node predNode(const Node& node) const {
+      return (*_pred)[node];
+    }
+
+    /// \brief Return the weight of the predecessor edge in the
+    /// Gomory-Hu tree.
+    ///
+    /// This function returns the weight of the predecessor edge of the 
+    /// given node in the Gomory-Hu tree.
+    /// If \c node is the root of the tree, the result is undefined.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    Value predValue(const Node& node) const {
+      return (*_weight)[node];
+    }
+
+    /// \brief Return the distance from the root node in the Gomory-Hu tree.
+    ///
+    /// This function returns the distance of the given node from the root
+    /// node in the Gomory-Hu tree.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    int rootDist(const Node& node) const {
+      return (*_order)[node];
+    }
+
+    /// \brief Return the minimum cut value between two nodes
+    ///
+    /// This function returns the minimum cut value between the nodes
+    /// \c s and \c t. 
+    /// It finds the nearest common ancestor of the given nodes in the
+    /// Gomory-Hu tree and calculates the minimum weight edge on the
+    /// paths to the ancestor.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    Value minCutValue(const Node& s, const Node& t) const {
+      Node sn = s, tn = t;
+      Value value = std::numeric_limits<Value>::max();
+      
+      while (sn != tn) {
+	if ((*_order)[sn] < (*_order)[tn]) {
+	  if ((*_weight)[tn] <= value) value = (*_weight)[tn];
+	  tn = (*_pred)[tn];
+	} else {
+	  if ((*_weight)[sn] <= value) value = (*_weight)[sn];
+	  sn = (*_pred)[sn];
+	}
+      }
+      return value;
+    }
+
+    /// \brief Return the minimum cut between two nodes
+    ///
+    /// This function returns the minimum cut between the nodes \c s and \c t
+    /// in the \c cutMap parameter by setting the nodes in the component of
+    /// \c s to \c true and the other nodes to \c false.
+    ///
+    /// For higher level interfaces see MinCutNodeIt and MinCutEdgeIt.
+    ///
+    /// \param s The base node.
+    /// \param t The node you want to separate from node \c s.
+    /// \param cutMap The cut will be returned in this map.
+    /// It must be a \c bool (or convertible) \ref concepts::ReadWriteMap
+    /// "ReadWriteMap" on the graph nodes.
+    ///
+    /// \return The value of the minimum cut between \c s and \c t.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    template <typename CutMap>
+    Value minCutMap(const Node& s, ///< 
+                    const Node& t,
+                    ///< 
+                    CutMap& cutMap
+                    ///< 
+                    ) const {
+      Node sn = s, tn = t;
+      bool s_root=false;
+      Node rn = INVALID;
+      Value value = std::numeric_limits<Value>::max();
+      
+      while (sn != tn) {
+	if ((*_order)[sn] < (*_order)[tn]) {
+	  if ((*_weight)[tn] <= value) {
+	    rn = tn;
+            s_root = false;
+	    value = (*_weight)[tn];
+	  }
+	  tn = (*_pred)[tn];
+	} else {
+	  if ((*_weight)[sn] <= value) {
+	    rn = sn;
+            s_root = true;
+	    value = (*_weight)[sn];
+	  }
+	  sn = (*_pred)[sn];
+	}
+      }
+
+      typename Graph::template NodeMap<bool> reached(_graph, false);
+      reached[_root] = true;
+      cutMap.set(_root, !s_root);
+      reached[rn] = true;
+      cutMap.set(rn, s_root);
+
+      std::vector<Node> st;
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+	st.clear();
+        Node nn = n;
+	while (!reached[nn]) {
+	  st.push_back(nn);
+	  nn = (*_pred)[nn];
+	}
+	while (!st.empty()) {
+	  cutMap.set(st.back(), cutMap[nn]);
+	  st.pop_back();
+	}
+      }
+      
+      return value;
+    }
+
+    ///@}
+
+    friend class MinCutNodeIt;
+
+    /// Iterate on the nodes of a minimum cut
+    
+    /// This iterator class lists the nodes of a minimum cut found by
+    /// GomoryHu. Before using it, you must allocate a GomoryHu class
+    /// and call its \ref GomoryHu::run() "run()" method.
+    ///
+    /// This example counts the nodes in the minimum cut separating \c s from
+    /// \c t.
+    /// \code
+    /// GomoryHu<Graph> gom(g, capacities);
+    /// gom.run();
+    /// int cnt=0;
+    /// for(GomoryHu<Graph>::MinCutNodeIt n(gom,s,t); n!=INVALID; ++n) ++cnt;
+    /// \endcode
+    class MinCutNodeIt
+    {
+      bool _side;
+      typename Graph::NodeIt _node_it;
+      typename Graph::template NodeMap<bool> _cut;
+    public:
+      /// Constructor
+
+      /// Constructor.
+      ///
+      MinCutNodeIt(GomoryHu const &gomory,
+                   ///< The GomoryHu class. You must call its
+                   ///  run() method
+                   ///  before initializing this iterator.
+                   const Node& s, ///< The base node.
+                   const Node& t,
+                   ///< The node you want to separate from node \c s.
+                   bool side=true
+                   ///< If it is \c true (default) then the iterator lists
+                   ///  the nodes of the component containing \c s,
+                   ///  otherwise it lists the other component.
+                   /// \note As the minimum cut is not always unique,
+                   /// \code
+                   /// MinCutNodeIt(gomory, s, t, true);
+                   /// \endcode
+                   /// and
+                   /// \code
+                   /// MinCutNodeIt(gomory, t, s, false);
+                   /// \endcode
+                   /// does not necessarily give the same set of nodes.
+                   /// However it is ensured that
+                   /// \code
+                   /// MinCutNodeIt(gomory, s, t, true);
+                   /// \endcode
+                   /// and
+                   /// \code
+                   /// MinCutNodeIt(gomory, s, t, false);
+                   /// \endcode
+                   /// together list each node exactly once.
+                   )
+        : _side(side), _cut(gomory._graph)
+      {
+        gomory.minCutMap(s,t,_cut);
+        for(_node_it=typename Graph::NodeIt(gomory._graph);
+            _node_it!=INVALID && _cut[_node_it]!=_side;
+            ++_node_it) {}
+      }
+      /// Conversion to \c Node
+
+      /// Conversion to \c Node.
+      ///
+      operator typename Graph::Node() const
+      {
+        return _node_it;
+      }
+      bool operator==(Invalid) { return _node_it==INVALID; }
+      bool operator!=(Invalid) { return _node_it!=INVALID; }
+      /// Next node
+
+      /// Next node.
+      ///
+      MinCutNodeIt &operator++()
+      {
+        for(++_node_it;_node_it!=INVALID&&_cut[_node_it]!=_side;++_node_it) {}
+        return *this;
+      }
+      /// Postfix incrementation
+
+      /// Postfix incrementation.
+      ///
+      /// \warning This incrementation
+      /// returns a \c Node, not a \c MinCutNodeIt, as one may
+      /// expect.
+      typename Graph::Node operator++(int)
+      {
+        typename Graph::Node n=*this;
+        ++(*this);
+        return n;
+      }
+    };
+    
+    friend class MinCutEdgeIt;
+    
+    /// Iterate on the edges of a minimum cut
+    
+    /// This iterator class lists the edges of a minimum cut found by
+    /// GomoryHu. Before using it, you must allocate a GomoryHu class
+    /// and call its \ref GomoryHu::run() "run()" method.
+    ///
+    /// This example computes the value of the minimum cut separating \c s from
+    /// \c t.
+    /// \code
+    /// GomoryHu<Graph> gom(g, capacities);
+    /// gom.run();
+    /// int value=0;
+    /// for(GomoryHu<Graph>::MinCutEdgeIt e(gom,s,t); e!=INVALID; ++e)
+    ///   value+=capacities[e];
+    /// \endcode
+    /// The result will be the same as the value returned by
+    /// \ref GomoryHu::minCutValue() "gom.minCutValue(s,t)".
+    class MinCutEdgeIt
+    {
+      bool _side;
+      const Graph &_graph;
+      typename Graph::NodeIt _node_it;
+      typename Graph::OutArcIt _arc_it;
+      typename Graph::template NodeMap<bool> _cut;
+      void step()
+      {
+        ++_arc_it;
+        while(_node_it!=INVALID && _arc_it==INVALID)
+          {
+            for(++_node_it;_node_it!=INVALID&&!_cut[_node_it];++_node_it) {}
+            if(_node_it!=INVALID)
+              _arc_it=typename Graph::OutArcIt(_graph,_node_it);
+          }
+      }
+      
+    public:
+      /// Constructor
+
+      /// Constructor.
+      ///
+      MinCutEdgeIt(GomoryHu const &gomory,
+                   ///< The GomoryHu class. You must call its
+                   ///  run() method
+                   ///  before initializing this iterator.
+                   const Node& s,  ///< The base node.
+                   const Node& t,
+                   ///< The node you want to separate from node \c s.
+                   bool side=true
+                   ///< If it is \c true (default) then the listed arcs
+                   ///  will be oriented from the
+                   ///  nodes of the component containing \c s,
+                   ///  otherwise they will be oriented in the opposite
+                   ///  direction.
+                   )
+        : _graph(gomory._graph), _cut(_graph)
+      {
+        gomory.minCutMap(s,t,_cut);
+        if(!side)
+          for(typename Graph::NodeIt n(_graph);n!=INVALID;++n)
+            _cut[n]=!_cut[n];
+
+        for(_node_it=typename Graph::NodeIt(_graph);
+            _node_it!=INVALID && !_cut[_node_it];
+            ++_node_it) {}
+        _arc_it = _node_it!=INVALID ?
+          typename Graph::OutArcIt(_graph,_node_it) : INVALID;
+        while(_node_it!=INVALID && _arc_it == INVALID)
+          {
+            for(++_node_it; _node_it!=INVALID&&!_cut[_node_it]; ++_node_it) {}
+            if(_node_it!=INVALID)
+              _arc_it= typename Graph::OutArcIt(_graph,_node_it);
+          }
+        while(_arc_it!=INVALID && _cut[_graph.target(_arc_it)]) step();
+      }
+      /// Conversion to \c Arc
+
+      /// Conversion to \c Arc.
+      ///
+      operator typename Graph::Arc() const
+      {
+        return _arc_it;
+      }
+      /// Conversion to \c Edge
+
+      /// Conversion to \c Edge.
+      ///
+      operator typename Graph::Edge() const
+      {
+        return _arc_it;
+      }
+      bool operator==(Invalid) { return _node_it==INVALID; }
+      bool operator!=(Invalid) { return _node_it!=INVALID; }
+      /// Next edge
+
+      /// Next edge.
+      ///
+      MinCutEdgeIt &operator++()
+      {
+        step();
+        while(_arc_it!=INVALID && _cut[_graph.target(_arc_it)]) step();
+        return *this;
+      }
+      /// Postfix incrementation
+      
+      /// Postfix incrementation.
+      ///
+      /// \warning This incrementation
+      /// returns an \c Arc, not a \c MinCutEdgeIt, as one may expect.
+      typename Graph::Arc operator++(int)
+      {
+        typename Graph::Arc e=*this;
+        ++(*this);
+        return e;
+      }
+    };
+
+  };
+
+}
+
+#endif