diff -r 70bee017b584 -r 4980b05606bd lemon/nagamochi_ibaraki.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/nagamochi_ibaraki.h	Tue Nov 16 07:46:01 2010 +0100
@@ -0,0 +1,697 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2010
+ * 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_NAGAMOCHI_IBARAKI_H
+#define LEMON_NAGAMOCHI_IBARAKI_H
+
+
+/// \ingroup min_cut
+/// \file
+/// \brief Implementation of the Nagamochi-Ibaraki algorithm.
+
+#include <lemon/core.h>
+#include <lemon/bin_heap.h>
+#include <lemon/bucket_heap.h>
+#include <lemon/maps.h>
+#include <lemon/radix_sort.h>
+#include <lemon/unionfind.h>
+
+#include <cassert>
+
+namespace lemon {
+
+  /// \brief Default traits class for NagamochiIbaraki class.
+  ///
+  /// Default traits class for NagamochiIbaraki class.
+  /// \param GR The undirected graph type.
+  /// \param CM Type of capacity map.
+  template <typename GR, typename CM>
+  struct NagamochiIbarakiDefaultTraits {
+    /// The type of the capacity map.
+    typedef typename CM::Value Value;
+
+    /// The undirected graph type the algorithm runs on.
+    typedef GR Graph;
+
+    /// \brief The type of the map that stores the edge capacities.
+    ///
+    /// The type of the map that stores the edge capacities.
+    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
+    typedef CM CapacityMap;
+
+    /// \brief Instantiates a CapacityMap.
+    ///
+    /// This function instantiates a \ref CapacityMap.
+#ifdef DOXYGEN
+    static CapacityMap *createCapacityMap(const Graph& graph)
+#else
+    static CapacityMap *createCapacityMap(const Graph&)
+#endif
+    {
+        LEMON_ASSERT(false, "CapacityMap is not initialized");
+        return 0; // ignore warnings
+    }
+
+    /// \brief The cross reference type used by heap.
+    ///
+    /// The cross reference type used by heap.
+    /// Usually \c Graph::NodeMap<int>.
+    typedef typename Graph::template NodeMap<int> HeapCrossRef;
+
+    /// \brief Instantiates a HeapCrossRef.
+    ///
+    /// This function instantiates a \ref HeapCrossRef.
+    /// \param g is the graph, to which we would like to define the
+    /// \ref HeapCrossRef.
+    static HeapCrossRef *createHeapCrossRef(const Graph& g) {
+      return new HeapCrossRef(g);
+    }
+
+    /// \brief The heap type used by NagamochiIbaraki algorithm.
+    ///
+    /// The heap type used by NagamochiIbaraki algorithm. It has to
+    /// maximize the priorities.
+    ///
+    /// \sa BinHeap
+    /// \sa NagamochiIbaraki
+    typedef BinHeap<Value, HeapCrossRef, std::greater<Value> > Heap;
+
+    /// \brief Instantiates a Heap.
+    ///
+    /// This function instantiates a \ref Heap.
+    /// \param r is the cross reference of the heap.
+    static Heap *createHeap(HeapCrossRef& r) {
+      return new Heap(r);
+    }
+  };
+
+  /// \ingroup min_cut
+  ///
+  /// \brief Calculates the minimum cut in an undirected graph.
+  ///
+  /// Calculates the minimum cut in an undirected graph with the
+  /// Nagamochi-Ibaraki algorithm. The algorithm separates the graph's
+  /// nodes into two partitions with the minimum sum of edge capacities
+  /// between the two partitions. The algorithm can be used to test
+  /// the network reliability, especially to test how many links have
+  /// to be destroyed in the network to split it to at least two
+  /// distinict subnetworks.
+  ///
+  /// The complexity of the algorithm is \f$ O(nm\log(n)) \f$ but with
+  /// \ref FibHeap "Fibonacci heap" it can be decreased to
+  /// \f$ O(nm+n^2\log(n)) \f$.  When the edges have unit capacities,
+  /// \c BucketHeap can be used which yields \f$ O(nm) \f$ time
+  /// complexity.
+  ///
+  /// \warning The value type of the capacity map should be able to
+  /// hold any cut value of the graph, otherwise the result can
+  /// overflow.
+  /// \note This capacity is supposed to be integer type.
+#ifdef DOXYGEN
+  template <typename GR, typename CM, typename TR>
+#else
+  template <typename GR,
+            typename CM = typename GR::template EdgeMap<int>,
+            typename TR = NagamochiIbarakiDefaultTraits<GR, CM> >
+#endif
+  class NagamochiIbaraki {
+  public:
+
+    typedef TR Traits;
+    /// The type of the underlying graph.
+    typedef typename Traits::Graph Graph;
+
+    /// The type of the capacity map.
+    typedef typename Traits::CapacityMap CapacityMap;
+    /// The value type of the capacity map.
+    typedef typename Traits::CapacityMap::Value Value;
+
+    /// The heap type used by the algorithm.
+    typedef typename Traits::Heap Heap;
+    /// The cross reference type used for the heap.
+    typedef typename Traits::HeapCrossRef HeapCrossRef;
+
+    ///\name Named template parameters
+
+    ///@{
+
+    struct SetUnitCapacityTraits : public Traits {
+      typedef ConstMap<typename Graph::Edge, Const<int, 1> > CapacityMap;
+      static CapacityMap *createCapacityMap(const Graph&) {
+        return new CapacityMap();
+      }
+    };
+
+    /// \brief \ref named-templ-param "Named parameter" for setting
+    /// the capacity map to a constMap<Edge, int, 1>() instance
+    ///
+    /// \ref named-templ-param "Named parameter" for setting
+    /// the capacity map to a constMap<Edge, int, 1>() instance
+    struct SetUnitCapacity
+      : public NagamochiIbaraki<Graph, CapacityMap,
+                                SetUnitCapacityTraits> {
+      typedef NagamochiIbaraki<Graph, CapacityMap,
+                               SetUnitCapacityTraits> Create;
+    };
+
+
+    template <class H, class CR>
+    struct SetHeapTraits : public Traits {
+      typedef CR HeapCrossRef;
+      typedef H Heap;
+      static HeapCrossRef *createHeapCrossRef(int num) {
+        LEMON_ASSERT(false, "HeapCrossRef is not initialized");
+        return 0; // ignore warnings
+      }
+      static Heap *createHeap(HeapCrossRef &) {
+        LEMON_ASSERT(false, "Heap is not initialized");
+        return 0; // ignore warnings
+      }
+    };
+
+    /// \brief \ref named-templ-param "Named parameter" for setting
+    /// heap and cross reference type
+    ///
+    /// \ref named-templ-param "Named parameter" for setting heap and
+    /// cross reference type. The heap has to maximize the priorities.
+    template <class H, class CR = RangeMap<int> >
+    struct SetHeap
+      : public NagamochiIbaraki<Graph, CapacityMap, SetHeapTraits<H, CR> > {
+      typedef NagamochiIbaraki< Graph, CapacityMap, SetHeapTraits<H, CR> >
+      Create;
+    };
+
+    template <class H, class CR>
+    struct SetStandardHeapTraits : public Traits {
+      typedef CR HeapCrossRef;
+      typedef H Heap;
+      static HeapCrossRef *createHeapCrossRef(int size) {
+        return new HeapCrossRef(size);
+      }
+      static Heap *createHeap(HeapCrossRef &crossref) {
+        return new Heap(crossref);
+      }
+    };
+
+    /// \brief \ref named-templ-param "Named parameter" for setting
+    /// heap and cross reference type with automatic allocation
+    ///
+    /// \ref named-templ-param "Named parameter" for setting heap and
+    /// cross reference type with automatic allocation. They should
+    /// have standard constructor interfaces to be able to
+    /// automatically created by the algorithm (i.e. the graph should
+    /// be passed to the constructor of the cross reference and the
+    /// cross reference should be passed to the constructor of the
+    /// heap). However, external heap and cross reference objects
+    /// could also be passed to the algorithm using the \ref heap()
+    /// function before calling \ref run() or \ref init(). The heap
+    /// has to maximize the priorities.
+    /// \sa SetHeap
+    template <class H, class CR = RangeMap<int> >
+    struct SetStandardHeap
+      : public NagamochiIbaraki<Graph, CapacityMap,
+                                SetStandardHeapTraits<H, CR> > {
+      typedef NagamochiIbaraki<Graph, CapacityMap,
+                               SetStandardHeapTraits<H, CR> > Create;
+    };
+
+    ///@}
+
+
+  private:
+
+    const Graph &_graph;
+    const CapacityMap *_capacity;
+    bool _local_capacity; // unit capacity
+
+    struct ArcData {
+      typename Graph::Node target;
+      int prev, next;
+    };
+    struct EdgeData {
+      Value capacity;
+      Value cut;
+    };
+
+    struct NodeData {
+      int first_arc;
+      typename Graph::Node prev, next;
+      int curr_arc;
+      typename Graph::Node last_rep;
+      Value sum;
+    };
+
+    typename Graph::template NodeMap<NodeData> *_nodes;
+    std::vector<ArcData> _arcs;
+    std::vector<EdgeData> _edges;
+
+    typename Graph::Node _first_node;
+    int _node_num;
+
+    Value _min_cut;
+
+    HeapCrossRef *_heap_cross_ref;
+    bool _local_heap_cross_ref;
+    Heap *_heap;
+    bool _local_heap;
+
+    typedef typename Graph::template NodeMap<typename Graph::Node> NodeList;
+    NodeList *_next_rep;
+
+    typedef typename Graph::template NodeMap<bool> MinCutMap;
+    MinCutMap *_cut_map;
+
+    void createStructures() {
+      if (!_nodes) {
+        _nodes = new (typename Graph::template NodeMap<NodeData>)(_graph);
+      }
+      if (!_capacity) {
+        _local_capacity = true;
+        _capacity = Traits::createCapacityMap(_graph);
+      }
+      if (!_heap_cross_ref) {
+        _local_heap_cross_ref = true;
+        _heap_cross_ref = Traits::createHeapCrossRef(_graph);
+      }
+      if (!_heap) {
+        _local_heap = true;
+        _heap = Traits::createHeap(*_heap_cross_ref);
+      }
+      if (!_next_rep) {
+        _next_rep = new NodeList(_graph);
+      }
+      if (!_cut_map) {
+        _cut_map = new MinCutMap(_graph);
+      }
+    }
+
+  public :
+
+    typedef NagamochiIbaraki Create;
+
+
+    /// \brief Constructor.
+    ///
+    /// \param graph The graph the algorithm runs on.
+    /// \param capacity The capacity map used by the algorithm.
+    NagamochiIbaraki(const Graph& graph, const CapacityMap& capacity)
+      : _graph(graph), _capacity(&capacity), _local_capacity(false),
+        _nodes(0), _arcs(), _edges(), _min_cut(),
+        _heap_cross_ref(0), _local_heap_cross_ref(false),
+        _heap(0), _local_heap(false),
+        _next_rep(0), _cut_map(0) {}
+
+    /// \brief Constructor.
+    ///
+    /// This constructor can be used only when the Traits class
+    /// defines how can the local capacity map be instantiated.
+    /// If the SetUnitCapacity used the algorithm automatically
+    /// constructs the capacity map.
+    ///
+    ///\param graph The graph the algorithm runs on.
+    NagamochiIbaraki(const Graph& graph)
+      : _graph(graph), _capacity(0), _local_capacity(false),
+        _nodes(0), _arcs(), _edges(), _min_cut(),
+        _heap_cross_ref(0), _local_heap_cross_ref(false),
+        _heap(0), _local_heap(false),
+        _next_rep(0), _cut_map(0) {}
+
+    /// \brief Destructor.
+    ///
+    /// Destructor.
+    ~NagamochiIbaraki() {
+      if (_local_capacity) delete _capacity;
+      if (_nodes) delete _nodes;
+      if (_local_heap) delete _heap;
+      if (_local_heap_cross_ref) delete _heap_cross_ref;
+      if (_next_rep) delete _next_rep;
+      if (_cut_map) delete _cut_map;
+    }
+
+    /// \brief Sets the heap and the cross reference used by algorithm.
+    ///
+    /// Sets the heap and the cross reference used by algorithm.
+    /// If you don't use this function before calling \ref run(),
+    /// it will allocate one. The destuctor deallocates this
+    /// automatically allocated heap and cross reference, of course.
+    /// \return <tt> (*this) </tt>
+    NagamochiIbaraki &heap(Heap& hp, HeapCrossRef &cr)
+    {
+      if (_local_heap_cross_ref) {
+        delete _heap_cross_ref;
+        _local_heap_cross_ref = false;
+      }
+      _heap_cross_ref = &cr;
+      if (_local_heap) {
+        delete _heap;
+        _local_heap = false;
+      }
+      _heap = &hp;
+      return *this;
+    }
+
+    /// \name Execution control
+    /// The simplest way to execute the algorithm is to use
+    /// one of the member functions called \c run().
+    /// \n
+    /// If you need more control on the execution,
+    /// first you must call \ref init() and then call the start()
+    /// or proper times the processNextPhase() member functions.
+
+    ///@{
+
+    /// \brief Initializes the internal data structures.
+    ///
+    /// Initializes the internal data structures.
+    void init() {
+      createStructures();
+
+      int edge_num = countEdges(_graph);
+      _edges.resize(edge_num);
+      _arcs.resize(2 * edge_num);
+
+      typename Graph::Node prev = INVALID;
+      _node_num = 0;
+      for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
+        (*_cut_map)[n] = false;
+        (*_next_rep)[n] = INVALID;
+        (*_nodes)[n].last_rep = n;
+        (*_nodes)[n].first_arc = -1;
+        (*_nodes)[n].curr_arc = -1;
+        (*_nodes)[n].prev = prev;
+        if (prev != INVALID) {
+          (*_nodes)[prev].next = n;
+        }
+        (*_nodes)[n].next = INVALID;
+        (*_nodes)[n].sum = 0;
+        prev = n;
+        ++_node_num;
+      }
+
+      _first_node = typename Graph::NodeIt(_graph);
+
+      int index = 0;
+      for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
+        for (typename Graph::OutArcIt a(_graph, n); a != INVALID; ++a) {
+          typename Graph::Node m = _graph.target(a);
+          
+          if (!(n < m)) continue;
+
+          (*_nodes)[n].sum += (*_capacity)[a];
+          (*_nodes)[m].sum += (*_capacity)[a];
+          
+          int c = (*_nodes)[m].curr_arc;
+          if (c != -1 && _arcs[c ^ 1].target == n) {
+            _edges[c >> 1].capacity += (*_capacity)[a];
+          } else {
+            _edges[index].capacity = (*_capacity)[a];
+            
+            _arcs[index << 1].prev = -1;
+            if ((*_nodes)[n].first_arc != -1) {
+              _arcs[(*_nodes)[n].first_arc].prev = (index << 1);
+            }
+            _arcs[index << 1].next = (*_nodes)[n].first_arc;
+            (*_nodes)[n].first_arc = (index << 1);
+            _arcs[index << 1].target = m;
+
+            (*_nodes)[m].curr_arc = (index << 1);
+            
+            _arcs[(index << 1) | 1].prev = -1;
+            if ((*_nodes)[m].first_arc != -1) {
+              _arcs[(*_nodes)[m].first_arc].prev = ((index << 1) | 1);
+            }
+            _arcs[(index << 1) | 1].next = (*_nodes)[m].first_arc;
+            (*_nodes)[m].first_arc = ((index << 1) | 1);
+            _arcs[(index << 1) | 1].target = n;
+            
+            ++index;
+          }
+        }
+      }
+
+      typename Graph::Node cut_node = INVALID;
+      _min_cut = std::numeric_limits<Value>::max();
+
+      for (typename Graph::Node n = _first_node; 
+           n != INVALID; n = (*_nodes)[n].next) {
+        if ((*_nodes)[n].sum < _min_cut) {
+          cut_node = n;
+          _min_cut = (*_nodes)[n].sum;
+        }
+      }
+      (*_cut_map)[cut_node] = true;
+      if (_min_cut == 0) {
+        _first_node = INVALID;
+      }
+    }
+
+  public:
+
+    /// \brief Processes the next phase
+    ///
+    /// Processes the next phase in the algorithm. It must be called
+    /// at most one less the number of the nodes in the graph.
+    ///
+    ///\return %True when the algorithm finished.
+    bool processNextPhase() {
+      if (_first_node == INVALID) return true;
+
+      _heap->clear();
+      for (typename Graph::Node n = _first_node; 
+           n != INVALID; n = (*_nodes)[n].next) {
+        (*_heap_cross_ref)[n] = Heap::PRE_HEAP;
+      }
+
+      std::vector<typename Graph::Node> order;
+      order.reserve(_node_num);
+      int sep = 0;
+
+      Value alpha = 0;
+      Value pmc = std::numeric_limits<Value>::max();
+
+      _heap->push(_first_node, static_cast<Value>(0));
+      while (!_heap->empty()) {
+        typename Graph::Node n = _heap->top();
+        Value v = _heap->prio();
+
+        _heap->pop();
+        for (int a = (*_nodes)[n].first_arc; a != -1; a = _arcs[a].next) {
+          switch (_heap->state(_arcs[a].target)) {
+          case Heap::PRE_HEAP: 
+            {
+              Value nv = _edges[a >> 1].capacity;
+              _heap->push(_arcs[a].target, nv);
+              _edges[a >> 1].cut = nv;
+            } break;
+          case Heap::IN_HEAP:
+            {
+              Value nv = _edges[a >> 1].capacity + (*_heap)[_arcs[a].target];
+              _heap->decrease(_arcs[a].target, nv);
+              _edges[a >> 1].cut = nv;
+            } break;
+          case Heap::POST_HEAP:
+            break;
+          }
+        }
+
+        alpha += (*_nodes)[n].sum;
+        alpha -= 2 * v;
+
+        order.push_back(n);
+        if (!_heap->empty()) {
+          if (alpha < pmc) {
+            pmc = alpha;
+            sep = order.size();
+          }
+        }
+      }
+
+      if (static_cast<int>(order.size()) < _node_num) {
+        _first_node = INVALID;
+        for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
+          (*_cut_map)[n] = false;
+        }
+        for (int i = 0; i < static_cast<int>(order.size()); ++i) {
+          typename Graph::Node n = order[i];
+          while (n != INVALID) {
+            (*_cut_map)[n] = true;
+            n = (*_next_rep)[n];
+          }
+        }
+        _min_cut = 0;
+        return true;
+      }
+
+      if (pmc < _min_cut) {
+        for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
+          (*_cut_map)[n] = false;
+        }
+        for (int i = 0; i < sep; ++i) {
+          typename Graph::Node n = order[i];
+          while (n != INVALID) {
+            (*_cut_map)[n] = true;
+            n = (*_next_rep)[n];
+          }
+        }
+        _min_cut = pmc;
+      }
+
+      for (typename Graph::Node n = _first_node;
+           n != INVALID; n = (*_nodes)[n].next) {
+        bool merged = false;
+        for (int a = (*_nodes)[n].first_arc; a != -1; a = _arcs[a].next) {
+          if (!(_edges[a >> 1].cut < pmc)) {
+            if (!merged) {
+              for (int b = (*_nodes)[n].first_arc; b != -1; b = _arcs[b].next) {
+                (*_nodes)[_arcs[b].target].curr_arc = b;          
+              }
+              merged = true;
+            }
+            typename Graph::Node m = _arcs[a].target;
+            int nb = 0;
+            for (int b = (*_nodes)[m].first_arc; b != -1; b = nb) {
+              nb = _arcs[b].next;
+              if ((b ^ a) == 1) continue;
+              typename Graph::Node o = _arcs[b].target;
+              int c = (*_nodes)[o].curr_arc; 
+              if (c != -1 && _arcs[c ^ 1].target == n) {
+                _edges[c >> 1].capacity += _edges[b >> 1].capacity;
+                (*_nodes)[n].sum += _edges[b >> 1].capacity;
+                if (_edges[b >> 1].cut < _edges[c >> 1].cut) {
+                  _edges[b >> 1].cut = _edges[c >> 1].cut;
+                }
+                if (_arcs[b ^ 1].prev != -1) {
+                  _arcs[_arcs[b ^ 1].prev].next = _arcs[b ^ 1].next;
+                } else {
+                  (*_nodes)[o].first_arc = _arcs[b ^ 1].next;
+                }
+                if (_arcs[b ^ 1].next != -1) {
+                  _arcs[_arcs[b ^ 1].next].prev = _arcs[b ^ 1].prev;
+                }
+              } else {
+                if (_arcs[a].next != -1) {
+                  _arcs[_arcs[a].next].prev = b;
+                }
+                _arcs[b].next = _arcs[a].next;
+                _arcs[b].prev = a;
+                _arcs[a].next = b;
+                _arcs[b ^ 1].target = n;
+
+                (*_nodes)[n].sum += _edges[b >> 1].capacity;
+                (*_nodes)[o].curr_arc = b;
+              }
+            }
+
+            if (_arcs[a].prev != -1) {
+              _arcs[_arcs[a].prev].next = _arcs[a].next;
+            } else {
+              (*_nodes)[n].first_arc = _arcs[a].next;
+            }            
+            if (_arcs[a].next != -1) {
+              _arcs[_arcs[a].next].prev = _arcs[a].prev;
+            }
+
+            (*_nodes)[n].sum -= _edges[a >> 1].capacity;
+            (*_next_rep)[(*_nodes)[n].last_rep] = m;
+            (*_nodes)[n].last_rep = (*_nodes)[m].last_rep;
+            
+            if ((*_nodes)[m].prev != INVALID) {
+              (*_nodes)[(*_nodes)[m].prev].next = (*_nodes)[m].next;
+            } else{
+              _first_node = (*_nodes)[m].next;
+            }
+            if ((*_nodes)[m].next != INVALID) {
+              (*_nodes)[(*_nodes)[m].next].prev = (*_nodes)[m].prev;
+            }
+            --_node_num;
+          }
+        }
+      }
+
+      if (_node_num == 1) {
+        _first_node = INVALID;
+        return true;
+      }
+
+      return false;
+    }
+
+    /// \brief Executes the algorithm.
+    ///
+    /// Executes the algorithm.
+    ///
+    /// \pre init() must be called
+    void start() {
+      while (!processNextPhase()) {}
+    }
+
+
+    /// \brief Runs %NagamochiIbaraki algorithm.
+    ///
+    /// This method runs the %Min cut algorithm
+    ///
+    /// \note mc.run(s) is just a shortcut of the following code.
+    ///\code
+    ///  mc.init();
+    ///  mc.start();
+    ///\endcode
+    void run() {
+      init();
+      start();
+    }
+
+    ///@}
+
+    /// \name Query Functions
+    ///
+    /// The result of the %NagamochiIbaraki
+    /// algorithm can be obtained using these functions.\n
+    /// Before the use of these functions, either run() or start()
+    /// must be called.
+
+    ///@{
+
+    /// \brief Returns the min cut value.
+    ///
+    /// Returns the min cut value if the algorithm finished.
+    /// After the first processNextPhase() it is a value of a
+    /// valid cut in the graph.
+    Value minCutValue() const {
+      return _min_cut;
+    }
+
+    /// \brief Returns a min cut in a NodeMap.
+    ///
+    /// It sets the nodes of one of the two partitions to true and
+    /// the other partition to false.
+    /// \param cutMap A \ref concepts::WriteMap "writable" node map with
+    /// \c bool (or convertible) value type.
+    template <typename CutMap>
+    Value minCutMap(CutMap& cutMap) const {
+      for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
+        cutMap.set(n, (*_cut_map)[n]);
+      }
+      return minCutValue();
+    }
+
+    ///@}
+
+  };
+}
+
+#endif