LEMON/LEMON-official Changeset - r672:029a48052c67

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Changeset - r672:029a48052c67

« 665:b95898

673:58357e »

r672:029a48052c67

Sun, 26 Apr 2009 16:44:53

[Not Reviewed]

0 comments (0 inline)

kpeter (Peter Kovacs)
kpeter@inf.elte.hu

Modify the interface of MinCostArborescence + improvements (#267) - Rename arborescenceValue() to arborescenceCost(). - Rename DefXyz template named paramaters to SetXyz. - Rearrange public functions (for better doc). - Doc improvements. - Extend the test file with interface checking.

0 2 0

default

2 files changed with 279 insertions and 206 deletions:

lemon/min_cost_arborescence.h

210

197

test/min_cost_arborescence_test.cc

↑ Collapse diff ↑

lemon/min_cost_arborescence.h

Show inline comments

@@ -36,7 +36,7 @@
 		  ///
 		  /// Default traits class for MinCostArborescence class.
 		  /// \param GR Digraph type.
 		  /// \param CM Type of cost map.
+		  /// \param CM Type of the cost map.
 		  template <class GR, class CM>
 		  struct MinCostArborescenceDefaultTraits{
@@ -46,7 +46,7 @@
 		    /// \brief The type of the map that stores the arc costs.
 		    ///
 		    /// The type of the map that stores the arc costs.
-		    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
+		    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
 		    typedef CM CostMap;
 		    /// \brief The value type of the costs.
@@ -58,23 +58,26 @@
 		    /// arborescence.
 		    ///
 		    /// The type of the map that stores which arcs are in the
 		    /// arborescence.  It must meet the \ref concepts::WriteMap
 		    /// "WriteMap" concept.  Initially it will be set to false on each
-		    /// arc. After it will set all arborescence arcs once.
+		    /// arborescence.  It must conform to the \ref concepts::WriteMap
 		    /// "WriteMap" concept, and its value type must be \c bool
 		    /// (or convertible). Initially it will be set to \c false on each
 		    /// arc, then it will be set on each arborescence arc once.
 		    typedef typename Digraph::template ArcMap<bool> ArborescenceMap;
 		    /// \brief Instantiates a \c ArborescenceMap.
 		    ///
 		    /// This function instantiates a \c ArborescenceMap.
 		    /// \param digraph is the graph, to which we would like to
 		    /// calculate the \c ArborescenceMap.
 		    /// \param digraph The digraph to which we would like to calculate
 		    /// the \c ArborescenceMap.
 		    static ArborescenceMap *createArborescenceMap(const Digraph &digraph){
 		      return new ArborescenceMap(digraph);
+		    }
 		    /// \brief The type of the \c PredMap
 		    ///
-		    /// The type of the \c PredMap. It is a node map with an arc value type.
+		    /// The type of the \c PredMap. It must confrom to the
 		    /// \ref concepts::WriteMap "WriteMap" concept, and its value type
 		    /// must be the \c Arc type of the digraph.
 		    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
 		    /// \brief Instantiates a \c PredMap.
@@ -92,32 +95,29 @@
 		  ///
 		  /// \brief Minimum Cost Arborescence algorithm class.
 		  ///
 		  /// This class provides an efficient implementation of
+		  /// This class provides an efficient implementation of the
 		  /// Minimum Cost Arborescence algorithm. The arborescence is a tree
 		  /// which is directed from a given source node of the digraph. One or
 		  /// more sources should be given for the algorithm and it will calculate
 		  /// the minimum cost subgraph which are union of arborescences with the
 		  /// more sources should be given to the algorithm and it will calculate
 		  /// the minimum cost subgraph that is the union of arborescences with the
 		  /// given sources and spans all the nodes which are reachable from the
 		  /// sources. The time complexity of the algorithm is O(n<sup>2</sup>+e).
 		  ///
-		  /// The algorithm provides also an optimal dual solution, therefore
+		  /// The algorithm also provides an optimal dual solution, therefore
 		  /// the optimality of the solution can be checked.
 		  ///
 		  /// \param GR The digraph type the algorithm runs on. The default value
 		  /// is \ref ListDigraph.
-		  /// \param CM This read-only ArcMap determines the costs of the
+		  /// \param GR The digraph type the algorithm runs on.
 		  /// \param CM A read-only arc map storing the costs of the
 		  /// arcs. It is read once for each arc, so the map may involve in
-		  /// relatively time consuming process to compute the arc cost if
+		  /// relatively time consuming process to compute the arc costs if
 		  /// it is necessary. The default map type is \ref
 		  /// concepts::Digraph::ArcMap "Digraph::ArcMap<int>".
 		  /// \param TR Traits class to set various data types used
 		  /// by the algorithm. The default traits class is
 		  /// \ref MinCostArborescenceDefaultTraits
 		  /// "MinCostArborescenceDefaultTraits<GR, CM>".  See \ref
 		  /// MinCostArborescenceDefaultTraits for the documentation of a
-		  /// MinCostArborescence traits class.
+		  /// "MinCostArborescenceDefaultTraits<GR, CM>".
 		#ifndef DOXYGEN
-		  template <typename GR = ListDigraph,
 		  template <typename GR,
 		            typename CM = typename GR::template ArcMap<int>,
 		            typename TR =
 		              MinCostArborescenceDefaultTraits<GR, CM> >
@@ -127,7 +127,8 @@
 		  class MinCostArborescence {
 		  public:
-		    /// The traits.
+		    /// \brief The \ref MinCostArborescenceDefaultTraits "traits class"
 		    /// of the algorithm.
 		    typedef TR Traits;
 		    /// The type of the underlying digraph.
 		    typedef typename Traits::Digraph Digraph;
@@ -395,7 +396,7 @@
 		    /// @{
 		    template <class T>
-		    struct DefArborescenceMapTraits : public Traits {
+		    struct SetArborescenceMapTraits : public Traits {
 		      typedef T ArborescenceMap;
 		      static ArborescenceMap *createArborescenceMap(const Digraph &)
+		      {
@@ -405,33 +406,40 @@
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for
 		    /// setting ArborescenceMap type
+		    /// setting \c ArborescenceMap type
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting
 		    /// ArborescenceMap type
+		    /// \c ArborescenceMap type.
 		    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept,
 		    /// and its value type must be \c bool (or convertible).
 		    /// Initially it will be set to \c false on each arc,
 		    /// then it will be set on each arborescence arc once.
 		    template <class T>
-		    struct DefArborescenceMap
+		    struct SetArborescenceMap
 		      : public MinCostArborescence<Digraph, CostMap,
-		                                   DefArborescenceMapTraits<T> > {
+		                                   SetArborescenceMapTraits<T> > {
 		    };
 		    template <class T>
-		    struct DefPredMapTraits : public Traits {
+		    struct SetPredMapTraits : public Traits {
 		      typedef T PredMap;
 		      static PredMap *createPredMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "PredMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for
 		    /// setting PredMap type
+		    /// setting \c PredMap type
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting
 		    /// PredMap type
+		    /// \c PredMap type.
 		    /// It must meet the \ref concepts::WriteMap "WriteMap" concept,
 		    /// and its value type must be the \c Arc type of the digraph.
 		    template <class T>
 		    struct DefPredMap
 		      : public MinCostArborescence<Digraph, CostMap, DefPredMapTraits<T> > {
 		    struct SetPredMap
 		      : public MinCostArborescence<Digraph, CostMap, SetPredMapTraits<T> > {
 		    };
 		    /// @}
@@ -464,9 +472,9 @@
 		      return *this;
+		    }
-		    /// \brief Sets the arborescence map.
+		    /// \brief Sets the predecessor map.
 		    ///
-		    /// Sets the arborescence map.
+		    /// Sets the predecessor map.
 		    /// \return <tt>(*this)</tt>
 		    MinCostArborescence& predMap(PredMap& m) {
 		      if (local_pred) {
@@ -477,159 +485,6 @@
 		      return *this;
+		    }
 		    /// \name Query Functions
 		    /// The result of the %MinCostArborescence algorithm can be obtained
 		    /// using these functions.\n
 		    /// Before the use of these functions,
 		    /// either run() or start() must be called.
 		    /// @{
 		    /// \brief Returns a reference to the arborescence map.
 		    ///
 		    /// Returns a reference to the arborescence map.
 		    const ArborescenceMap& arborescenceMap() const {
 		      return *_arborescence;
+		    }
 		    /// \brief Returns true if the arc is in the arborescence.
 		    ///
 		    /// Returns true if the arc is in the arborescence.
 		    /// \param arc The arc of the digraph.
 		    /// \pre \ref run() must be called before using this function.
 		    bool arborescence(Arc arc) const {
 		      return (*_pred)[_digraph->target(arc)] == arc;
+		    }
 		    /// \brief Returns a reference to the pred map.
 		    ///
 		    /// Returns a reference to the pred map.
 		    const PredMap& predMap() const {
 		      return *_pred;
+		    }
 		    /// \brief Returns the predecessor arc of the given node.
 		    ///
 		    /// Returns the predecessor arc of the given node.
 		    Arc pred(Node node) const {
 		      return (*_pred)[node];
+		    }
 		    /// \brief Returns the cost of the arborescence.
 		    ///
 		    /// Returns the cost of the arborescence.
 		    Value arborescenceValue() const {
 		      Value sum = 0;
 		      for (ArcIt it(*_digraph); it != INVALID; ++it) {
 		        if (arborescence(it)) {
 		          sum += (*_cost)[it];
+		        }
+		      }
 		      return sum;
+		    }
 		    /// \brief Indicates that a node is reachable from the sources.
 		    ///
 		    /// Indicates that a node is reachable from the sources.
 		    bool reached(Node node) const {
 		      return (*_node_order)[node] != -3;
+		    }
 		    /// \brief Indicates that a node is processed.
 		    ///
 		    /// Indicates that a node is processed. The arborescence path exists
 		    /// from the source to the given node.
 		    bool processed(Node node) const {
 		      return (*_node_order)[node] == -1;
+		    }
 		    /// \brief Returns the number of the dual variables in basis.
 		    ///
 		    /// Returns the number of the dual variables in basis.
 		    int dualNum() const {
 		      return _dual_variables.size();
+		    }
 		    /// \brief Returns the value of the dual solution.
 		    ///
 		    /// Returns the value of the dual solution. It should be
 		    /// equal to the arborescence value.
 		    Value dualValue() const {
 		      Value sum = 0;
 		      for (int i = 0; i < int(_dual_variables.size()); ++i) {
 		        sum += _dual_variables[i].value;
+		      }
 		      return sum;
+		    }
 		    /// \brief Returns the number of the nodes in the dual variable.
 		    ///
 		    /// Returns the number of the nodes in the dual variable.
 		    int dualSize(int k) const {
 		      return _dual_variables[k].end - _dual_variables[k].begin;
+		    }
 		    /// \brief Returns the value of the dual variable.
 		    ///
 		    /// Returns the the value of the dual variable.
 		    const Value& dualValue(int k) const {
 		      return _dual_variables[k].value;
+		    }
 		    /// \brief Lemon iterator for get a dual variable.
 		    ///
 		    /// Lemon iterator for get a dual variable. This class provides
 		    /// a common style lemon iterator which gives back a subset of
 		    /// the nodes.
 		    class DualIt {
 		    public:
 		      /// \brief Constructor.
 		      ///
 		      /// Constructor for get the nodeset of the variable.
 		      DualIt(const MinCostArborescence& algorithm, int variable)
 		        : _algorithm(&algorithm)
+		      {
 		        _index = _algorithm->_dual_variables[variable].begin;
 		        _last = _algorithm->_dual_variables[variable].end;
+		      }
 		      /// \brief Conversion to node.
 		      ///
 		      /// Conversion to node.
 		      operator Node() const {
 		        return _algorithm->_dual_node_list[_index];
+		      }
 		      /// \brief Increment operator.
 		      ///
 		      /// Increment operator.
 		      DualIt& operator++() {
 		        ++_index;
 		        return *this;
+		      }
 		      /// \brief Validity checking
 		      ///
 		      /// Checks whether the iterator is invalid.
 		      bool operator==(Invalid) const {
 		        return _index == _last;
+		      }
 		      /// \brief Validity checking
 		      ///
 		      /// Checks whether the iterator is valid.
 		      bool operator!=(Invalid) const {
 		        return _index != _last;
+		      }
 		    private:
 		      const MinCostArborescence* _algorithm;
 		      int _index, _last;
 		    };
 		    /// @}
 		    /// \name Execution Control
 		    /// The simplest way to execute the algorithm is to use
 		    /// one of the member functions called \c run(...). \n
@@ -689,7 +544,7 @@
 		    ///
 		    /// \return The processed node.
 		    ///
-		    /// \warning The queue must not be empty!
+		    /// \warning The queue must not be empty.
 		    Node processNextNode() {
 		      Node node = queue.back();
 		      queue.pop_back();
@@ -712,7 +567,8 @@
 		    /// \brief Returns the number of the nodes to be processed.
 		    ///
-		    /// Returns the number of the nodes to be processed.
+		    /// Returns the number of the nodes to be processed in the priority
 		    /// queue.
 		    int queueSize() const {
 		      return queue.size();
+		    }
@@ -754,14 +610,170 @@
 		    /// mca.addSource(s);
 		    /// mca.start();
 		    /// \endcode
-		    void run(Node node) {
+		    void run(Node s) {
 		      init();
-		      addSource(node);
+		      addSource(s);
 		      start();
+		    }
 		    ///@}
 		    /// \name Query Functions
 		    /// The result of the %MinCostArborescence algorithm can be obtained
 		    /// using these functions.\n
 		    /// Either run() or start() must be called before using them.
 		    /// @{
 		    /// \brief Returns the cost of the arborescence.
 		    ///
 		    /// Returns the cost of the arborescence.
 		    Value arborescenceCost() const {
 		      Value sum = 0;
 		      for (ArcIt it(*_digraph); it != INVALID; ++it) {
 		        if (arborescence(it)) {
 		          sum += (*_cost)[it];
+		        }
+		      }
 		      return sum;
+		    }
 		    /// \brief Returns \c true if the arc is in the arborescence.
 		    ///
 		    /// Returns \c true if the given arc is in the arborescence.
 		    /// \param arc An arc of the digraph.
 		    /// \pre \ref run() must be called before using this function.
 		    bool arborescence(Arc arc) const {
 		      return (*_pred)[_digraph->target(arc)] == arc;
+		    }
 		    /// \brief Returns a const reference to the arborescence map.
 		    ///
 		    /// Returns a const reference to the arborescence map.
 		    /// \pre \ref run() must be called before using this function.
 		    const ArborescenceMap& arborescenceMap() const {
 		      return *_arborescence;
+		    }
 		    /// \brief Returns the predecessor arc of the given node.
 		    ///
 		    /// Returns the predecessor arc of the given node.
 		    /// \pre \ref run() must be called before using this function.
 		    Arc pred(Node node) const {
 		      return (*_pred)[node];
+		    }
 		    /// \brief Returns a const reference to the pred map.
 		    ///
 		    /// Returns a const reference to the pred map.
 		    /// \pre \ref run() must be called before using this function.
 		    const PredMap& predMap() const {
 		      return *_pred;
+		    }
 		    /// \brief Indicates that a node is reachable from the sources.
 		    ///
 		    /// Indicates that a node is reachable from the sources.
 		    bool reached(Node node) const {
 		      return (*_node_order)[node] != -3;
+		    }
 		    /// \brief Indicates that a node is processed.
 		    ///
 		    /// Indicates that a node is processed. The arborescence path exists
 		    /// from the source to the given node.
 		    bool processed(Node node) const {
 		      return (*_node_order)[node] == -1;
+		    }
 		    /// \brief Returns the number of the dual variables in basis.
 		    ///
 		    /// Returns the number of the dual variables in basis.
 		    int dualNum() const {
 		      return _dual_variables.size();
+		    }
 		    /// \brief Returns the value of the dual solution.
 		    ///
 		    /// Returns the value of the dual solution. It should be
 		    /// equal to the arborescence value.
 		    Value dualValue() const {
 		      Value sum = 0;
 		      for (int i = 0; i < int(_dual_variables.size()); ++i) {
 		        sum += _dual_variables[i].value;
+		      }
 		      return sum;
+		    }
 		    /// \brief Returns the number of the nodes in the dual variable.
 		    ///
 		    /// Returns the number of the nodes in the dual variable.
 		    int dualSize(int k) const {
 		      return _dual_variables[k].end - _dual_variables[k].begin;
+		    }
 		    /// \brief Returns the value of the dual variable.
 		    ///
 		    /// Returns the the value of the dual variable.
 		    Value dualValue(int k) const {
 		      return _dual_variables[k].value;
+		    }
 		    /// \brief LEMON iterator for getting a dual variable.
 		    ///
 		    /// This class provides a common style LEMON iterator for getting a
 		    /// dual variable of \ref MinCostArborescence algorithm.
 		    /// It iterates over a subset of the nodes.
 		    class DualIt {
 		    public:
 		      /// \brief Constructor.
 		      ///
 		      /// Constructor for getting the nodeset of the dual variable
 		      /// of \ref MinCostArborescence algorithm.
 		      DualIt(const MinCostArborescence& algorithm, int variable)
 		        : _algorithm(&algorithm)
+		      {
 		        _index = _algorithm->_dual_variables[variable].begin;
 		        _last = _algorithm->_dual_variables[variable].end;
+		      }
 		      /// \brief Conversion to \c Node.
 		      ///
 		      /// Conversion to \c Node.
 		      operator Node() const {
 		        return _algorithm->_dual_node_list[_index];
+		      }
 		      /// \brief Increment operator.
 		      ///
 		      /// Increment operator.
 		      DualIt& operator++() {
 		        ++_index;
 		        return *this;
+		      }
 		      /// \brief Validity checking
 		      ///
 		      /// Checks whether the iterator is invalid.
 		      bool operator==(Invalid) const {
 		        return _index == _last;
+		      }
 		      /// \brief Validity checking
 		      ///
 		      /// Checks whether the iterator is valid.
 		      bool operator!=(Invalid) const {
 		        return _index != _last;
+		      }
 		    private:
 		      const MinCostArborescence* _algorithm;
 		      int _index, _last;
 		    };
 		    /// @}
 		  };
 		  /// \ingroup spantree
@@ -769,11 +781,12 @@
 		  /// \brief Function type interface for MinCostArborescence algorithm.
 		  ///
 		  /// Function type interface for MinCostArborescence algorithm.
 		  /// \param digraph The Digraph that the algorithm runs on.
 		  /// \param cost The CostMap of the arcs.
 		  /// \param source The source of the arborescence.
 		  /// \retval arborescence The bool ArcMap which stores the arborescence.
-		  /// \return The cost of the arborescence.
+		  /// \param digraph The digraph the algorithm runs on.
 		  /// \param cost An arc map storing the costs.
 		  /// \param source The source node of the arborescence.
 		  /// \retval arborescence An arc map with \c bool (or convertible) value
 		  /// type that stores the arborescence.
 		  /// \return The total cost of the arborescence.
 		  ///
 		  /// \sa MinCostArborescence
 		  template <typename Digraph, typename CostMap, typename ArborescenceMap>
@@ -782,11 +795,11 @@
 		                                              typename Digraph::Node source,
 		                                              ArborescenceMap& arborescence) {
 		    typename MinCostArborescence<Digraph, CostMap>
-		      ::template DefArborescenceMap<ArborescenceMap>
+		      ::template SetArborescenceMap<ArborescenceMap>
 		      ::Create mca(digraph, cost);
 		    mca.arborescenceMap(arborescence);
 		    mca.run(source);
-		    return mca.arborescenceValue();
+		    return mca.arborescenceCost();
+		  }
+		}

test/min_cost_arborescence_test.cc

Show inline comments

@@ -24,6 +24,7 @@
 		#include <lemon/smart_graph.h>
 		#include <lemon/min_cost_arborescence.h>
 		#include <lemon/lgf_reader.h>
 		#include <lemon/concepts/digraph.h>
 		#include "test_tools.h"
@@ -70,6 +71,65 @@
 		  "@attributes\n"
 		  "source 0\n";
 		void checkMinCostArborescenceCompile()
+		{
 		  typedef double VType;
 		  typedef concepts::Digraph Digraph;
 		  typedef concepts::ReadMap<Digraph::Arc, VType> CostMap;
 		  typedef Digraph::Node Node;
 		  typedef Digraph::Arc Arc;
 		  typedef concepts::WriteMap<Digraph::Arc, bool> ArbMap;
 		  typedef concepts::ReadWriteMap<Digraph::Node, Digraph::Arc> PredMap;
 		  typedef MinCostArborescence<Digraph, CostMap>::
 		            SetArborescenceMap<ArbMap>::
 		            SetPredMap<PredMap>::Create MinCostArbType;
 		  Digraph g;
 		  Node s, n;
 		  Arc e;
 		  VType c;
 		  bool b;
 		  int i;
 		  CostMap cost;
 		  ArbMap arb;
 		  PredMap pred;
 		  MinCostArbType mcarb_test(g, cost);
 		  const MinCostArbType& const_mcarb_test = mcarb_test;
 		  mcarb_test
 		    .arborescenceMap(arb)
 		    .predMap(pred)
 		    .run(s);
 		  mcarb_test.init();
 		  mcarb_test.addSource(s);
 		  mcarb_test.start();
 		  n = mcarb_test.processNextNode();
 		  b = const_mcarb_test.emptyQueue();
 		  i = const_mcarb_test.queueSize();
 		  c = const_mcarb_test.arborescenceCost();
 		  b = const_mcarb_test.arborescence(e);
 		  e = const_mcarb_test.pred(n);
 		  const MinCostArbType::ArborescenceMap &am =
 		    const_mcarb_test.arborescenceMap();
 		  const MinCostArbType::PredMap &pm =
 		    const_mcarb_test.predMap();
 		  b = const_mcarb_test.reached(n);
 		  b = const_mcarb_test.processed(n);
 		  i = const_mcarb_test.dualNum();
 		  c = const_mcarb_test.dualValue();
 		  i = const_mcarb_test.dualSize(i);
 		  c = const_mcarb_test.dualValue(i);
 		  ignore_unused_variable_warning(am);
 		  ignore_unused_variable_warning(pm);
+		}
 		int main() {
 		  typedef SmartDigraph Digraph;
 		  DIGRAPH_TYPEDEFS(Digraph);
@@ -110,19 +170,19 @@
+		        }
+		      }
 		      if (mca.arborescence(it)) {
-		        check(sum == cost[it], "INVALID DUAL");
+		        check(sum == cost[it], "Invalid dual solution");
+		      }
-		      check(sum <= cost[it], "INVALID DUAL");
+		      check(sum <= cost[it], "Invalid dual solution");
+		    }
+		  }
-		  check(mca.dualValue() == mca.arborescenceValue(), "INVALID DUAL");
+		  check(mca.dualValue() == mca.arborescenceCost(), "Invalid dual solution");
-		  check(mca.reached(source), "INVALID ARBORESCENCE");
+		  check(mca.reached(source), "Invalid arborescence");
 		  for (ArcIt a(digraph); a != INVALID; ++a) {
 		    check(!mca.reached(digraph.source(a)) ||
-		          mca.reached(digraph.target(a)), "INVALID ARBORESCENCE");
+		          mca.reached(digraph.target(a)), "Invalid arborescence");
+		  }
 		  for (NodeIt n(digraph); n != INVALID; ++n) {
@@ -130,17 +190,17 @@
 		    int cnt = 0;
 		    for (InArcIt a(digraph, n); a != INVALID; ++a) {
 		      if (mca.arborescence(a)) {
-		        check(mca.pred(n) == a, "INVALID ARBORESCENCE");
+		        check(mca.pred(n) == a, "Invalid arborescence");
 		        ++cnt;
+		      }
+		    }
-		    check((n == source ? cnt == 0 : cnt == 1), "INVALID ARBORESCENCE");
+		    check((n == source ? cnt == 0 : cnt == 1), "Invalid arborescence");
+		  }
 		  Digraph::ArcMap<bool> arborescence(digraph);
-		  check(mca.arborescenceValue() ==
+		  check(mca.arborescenceCost() ==
 		        minCostArborescence(digraph, cost, source, arborescence),
-		        "WRONG FUNCTION");
+		        "Wrong result of the function interface");
 		  return 0;
+		}

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