Added thirdparty: boost library

thirdparty/include/boost/graph/tiernan_all_cycles.hpp

@@ -0,0 +1,372 @@
+// (C) Copyright 2007-2009 Andrew Sutton
+//
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0 (See accompanying file
+// LICENSE_1_0.txt or http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_GRAPH_CYCLE_HPP
+#define BOOST_GRAPH_CYCLE_HPP
+
+#include <vector>
+
+#include <boost/config.hpp>
+#include <boost/graph/graph_concepts.hpp>
+#include <boost/graph/graph_traits.hpp>
+#include <boost/graph/properties.hpp>
+#include <boost/concept/assert.hpp>
+
+#include <boost/concept/detail/concept_def.hpp>
+namespace boost
+{
+namespace concepts
+{
+    BOOST_concept(CycleVisitor, (Visitor)(Path)(Graph))
+    {
+        BOOST_CONCEPT_USAGE(CycleVisitor) { vis.cycle(p, g); }
+
+    private:
+        Visitor vis;
+        Graph g;
+        Path p;
+    };
+} /* namespace concepts */
+using concepts::CycleVisitorConcept;
+} /* namespace boost */
+#include <boost/concept/detail/concept_undef.hpp>
+
+namespace boost
+{
+
+// The implementation of this algorithm is a reproduction of the Teirnan
+// approach for directed graphs: bibtex follows
+//
+//     @article{362819,
+//         author = {James C. Tiernan},
+//         title = {An efficient search algorithm to find the elementary
+//         circuits of a graph}, journal = {Commun. ACM}, volume = {13}, number
+//         = {12}, year = {1970}, issn = {0001-0782}, pages = {722--726}, doi =
+//         {http://doi.acm.org/10.1145/362814.362819},
+//             publisher = {ACM Press},
+//             address = {New York, NY, USA},
+//         }
+//
+// It should be pointed out that the author does not provide a complete analysis
+// for either time or space. This is in part, due to the fact that it's a fairly
+// input sensitive problem related to the density and construction of the graph,
+// not just its size.
+//
+// I've also taken some liberties with the interpretation of the algorithm -
+// I've basically modernized it to use real data structures (no more arrays and
+// matrices). Oh... and there's explicit control structures - not just gotos.
+//
+// The problem is definitely NP-complete, an unbounded implementation of this
+// will probably run for quite a while on a large graph. The conclusions
+// of this paper also reference a Paton algorithm for undirected graphs as being
+// much more efficient (apparently based on spanning trees). Although not
+// implemented, it can be found here:
+//
+//     @article{363232,
+//         author = {Keith Paton},
+//         title = {An algorithm for finding a fundamental set of cycles of a
+//         graph}, journal = {Commun. ACM}, volume = {12}, number = {9}, year =
+//         {1969}, issn = {0001-0782}, pages = {514--518}, doi =
+//         {http://doi.acm.org/10.1145/363219.363232},
+//             publisher = {ACM Press},
+//             address = {New York, NY, USA},
+//         }
+
+/**
+ * The default cycle visitor provides an empty visit function for cycle
+ * visitors.
+ */
+struct cycle_visitor
+{
+    template < typename Path, typename Graph >
+    inline void cycle(const Path& p, const Graph& g)
+    {
+    }
+};
+
+/**
+ * The min_max_cycle_visitor simultaneously records the minimum and maximum
+ * cycles in a graph.
+ */
+struct min_max_cycle_visitor
+{
+    min_max_cycle_visitor(std::size_t& min_, std::size_t& max_)
+    : minimum(min_), maximum(max_)
+    {
+    }
+
+    template < typename Path, typename Graph >
+    inline void cycle(const Path& p, const Graph& g)
+    {
+        BOOST_USING_STD_MIN();
+        BOOST_USING_STD_MAX();
+        std::size_t len = p.size();
+        minimum = min BOOST_PREVENT_MACRO_SUBSTITUTION(minimum, len);
+        maximum = max BOOST_PREVENT_MACRO_SUBSTITUTION(maximum, len);
+    }
+    std::size_t& minimum;
+    std::size_t& maximum;
+};
+
+inline min_max_cycle_visitor find_min_max_cycle(
+    std::size_t& min_, std::size_t& max_)
+{
+    return min_max_cycle_visitor(min_, max_);
+}
+
+namespace detail
+{
+    template < typename Graph, typename Path >
+    inline bool is_vertex_in_path(const Graph&,
+        typename graph_traits< Graph >::vertex_descriptor v, const Path& p)
+    {
+        return (std::find(p.begin(), p.end(), v) != p.end());
+    }
+
+    template < typename Graph, typename ClosedMatrix >
+    inline bool is_path_closed(const Graph& g,
+        typename graph_traits< Graph >::vertex_descriptor u,
+        typename graph_traits< Graph >::vertex_descriptor v,
+        const ClosedMatrix& closed)
+    {
+        // the path from u to v is closed if v can be found in the list
+        // of closed vertices associated with u.
+        typedef typename ClosedMatrix::const_reference Row;
+        Row r = closed[get(vertex_index, g, u)];
+        if (find(r.begin(), r.end(), v) != r.end())
+        {
+            return true;
+        }
+        return false;
+    }
+
+    template < typename Graph, typename Path, typename ClosedMatrix >
+    inline bool can_extend_path(const Graph& g,
+        typename graph_traits< Graph >::edge_descriptor e, const Path& p,
+        const ClosedMatrix& m)
+    {
+        BOOST_CONCEPT_ASSERT((IncidenceGraphConcept< Graph >));
+        BOOST_CONCEPT_ASSERT((VertexIndexGraphConcept< Graph >));
+        typedef typename graph_traits< Graph >::vertex_descriptor Vertex;
+
+        // get the vertices in question
+        Vertex u = source(e, g), v = target(e, g);
+
+        // conditions for allowing a traversal along this edge are:
+        // 1. the index of v must be greater than that at which the
+        //    path is rooted (p.front()).
+        // 2. the vertex v cannot already be in the path
+        // 3. the vertex v cannot be closed to the vertex u
+
+        bool indices
+            = get(vertex_index, g, p.front()) < get(vertex_index, g, v);
+        bool path = !is_vertex_in_path(g, v, p);
+        bool closed = !is_path_closed(g, u, v, m);
+        return indices && path && closed;
+    }
+
+    template < typename Graph, typename Path >
+    inline bool can_wrap_path(const Graph& g, const Path& p)
+    {
+        BOOST_CONCEPT_ASSERT((IncidenceGraphConcept< Graph >));
+        typedef typename graph_traits< Graph >::vertex_descriptor Vertex;
+        typedef typename graph_traits< Graph >::out_edge_iterator OutIterator;
+
+        // iterate over the out-edges of the back, looking for the
+        // front of the path. also, we can't travel along the same
+        // edge that we did on the way here, but we don't quite have the
+        // stringent requirements that we do in can_extend_path().
+        Vertex u = p.back(), v = p.front();
+        OutIterator i, end;
+        for (boost::tie(i, end) = out_edges(u, g); i != end; ++i)
+        {
+            if ((target(*i, g) == v))
+            {
+                return true;
+            }
+        }
+        return false;
+    }
+
+    template < typename Graph, typename Path, typename ClosedMatrix >
+    inline typename graph_traits< Graph >::vertex_descriptor extend_path(
+        const Graph& g, Path& p, ClosedMatrix& closed)
+    {
+        BOOST_CONCEPT_ASSERT((IncidenceGraphConcept< Graph >));
+        typedef typename graph_traits< Graph >::vertex_descriptor Vertex;
+        typedef typename graph_traits< Graph >::out_edge_iterator OutIterator;
+
+        // get the current vertex
+        Vertex u = p.back();
+        Vertex ret = graph_traits< Graph >::null_vertex();
+
+        // AdjacencyIterator i, end;
+        OutIterator i, end;
+        for (boost::tie(i, end) = out_edges(u, g); i != end; ++i)
+        {
+            Vertex v = target(*i, g);
+
+            // if we can actually extend along this edge,
+            // then that's what we want to do
+            if (can_extend_path(g, *i, p, closed))
+            {
+                p.push_back(v); // add the vertex to the path
+                ret = v;
+                break;
+            }
+        }
+        return ret;
+    }
+
+    template < typename Graph, typename Path, typename ClosedMatrix >
+    inline bool exhaust_paths(const Graph& g, Path& p, ClosedMatrix& closed)
+    {
+        BOOST_CONCEPT_ASSERT((GraphConcept< Graph >));
+        typedef typename graph_traits< Graph >::vertex_descriptor Vertex;
+
+        // if there's more than one vertex in the path, this closes
+        // of some possible routes and returns true. otherwise, if there's
+        // only one vertex left, the vertex has been used up
+        if (p.size() > 1)
+        {
+            // get the last and second to last vertices, popping the last
+            // vertex off the path
+            Vertex last, prev;
+            last = p.back();
+            p.pop_back();
+            prev = p.back();
+
+            // reset the closure for the last vertex of the path and
+            // indicate that the last vertex in p is now closed to
+            // the next-to-last vertex in p
+            closed[get(vertex_index, g, last)].clear();
+            closed[get(vertex_index, g, prev)].push_back(last);
+            return true;
+        }
+        else
+        {
+            return false;
+        }
+    }
+
+    template < typename Graph, typename Visitor >
+    inline void all_cycles_from_vertex(const Graph& g,
+        typename graph_traits< Graph >::vertex_descriptor v, Visitor vis,
+        std::size_t minlen, std::size_t maxlen)
+    {
+        BOOST_CONCEPT_ASSERT((VertexListGraphConcept< Graph >));
+        typedef typename graph_traits< Graph >::vertex_descriptor Vertex;
+        typedef std::vector< Vertex > Path;
+        BOOST_CONCEPT_ASSERT((CycleVisitorConcept< Visitor, Path, Graph >));
+        typedef std::vector< Vertex > VertexList;
+        typedef std::vector< VertexList > ClosedMatrix;
+
+        Path p;
+        ClosedMatrix closed(num_vertices(g), VertexList());
+        Vertex null = graph_traits< Graph >::null_vertex();
+
+        // each path investigation starts at the ith vertex
+        p.push_back(v);
+
+        while (1)
+        {
+            // extend the path until we've reached the end or the
+            // maxlen-sized cycle
+            Vertex j = null;
+            while (((j = detail::extend_path(g, p, closed)) != null)
+                && (p.size() < maxlen))
+                ; // empty loop
+
+            // if we're done extending the path and there's an edge
+            // connecting the back to the front, then we should have
+            // a cycle.
+            if (detail::can_wrap_path(g, p) && p.size() >= minlen)
+            {
+                vis.cycle(p, g);
+            }
+
+            if (!detail::exhaust_paths(g, p, closed))
+            {
+                break;
+            }
+        }
+    }
+
+    // Select the minimum allowable length of a cycle based on the directedness
+    // of the graph - 2 for directed, 3 for undirected.
+    template < typename D > struct min_cycles
+    {
+        enum
+        {
+            value = 2
+        };
+    };
+    template <> struct min_cycles< undirected_tag >
+    {
+        enum
+        {
+            value = 3
+        };
+    };
+} /* namespace detail */
+
+template < typename Graph, typename Visitor >
+inline void tiernan_all_cycles(
+    const Graph& g, Visitor vis, std::size_t minlen, std::size_t maxlen)
+{
+    BOOST_CONCEPT_ASSERT((VertexListGraphConcept< Graph >));
+    typedef typename graph_traits< Graph >::vertex_iterator VertexIterator;
+
+    VertexIterator i, end;
+    for (boost::tie(i, end) = vertices(g); i != end; ++i)
+    {
+        detail::all_cycles_from_vertex(g, *i, vis, minlen, maxlen);
+    }
+}
+
+template < typename Graph, typename Visitor >
+inline void tiernan_all_cycles(const Graph& g, Visitor vis, std::size_t maxlen)
+{
+    typedef typename graph_traits< Graph >::directed_category Dir;
+    tiernan_all_cycles(g, vis, detail::min_cycles< Dir >::value, maxlen);
+}
+
+template < typename Graph, typename Visitor >
+inline void tiernan_all_cycles(const Graph& g, Visitor vis)
+{
+    typedef typename graph_traits< Graph >::directed_category Dir;
+    tiernan_all_cycles(g, vis, detail::min_cycles< Dir >::value,
+        (std::numeric_limits< std::size_t >::max)());
+}
+
+template < typename Graph >
+inline std::pair< std::size_t, std::size_t > tiernan_girth_and_circumference(
+    const Graph& g)
+{
+    std::size_t min_ = (std::numeric_limits< std::size_t >::max)(), max_ = 0;
+    tiernan_all_cycles(g, find_min_max_cycle(min_, max_));
+
+    // if this is the case, the graph is acyclic...
+    if (max_ == 0)
+        max_ = min_;
+
+    return std::make_pair(min_, max_);
+}
+
+template < typename Graph > inline std::size_t tiernan_girth(const Graph& g)
+{
+    return tiernan_girth_and_circumference(g).first;
+}
+
+template < typename Graph >
+inline std::size_t tiernan_circumference(const Graph& g)
+{
+    return tiernan_girth_and_circumference(g).second;
+}
+
+} /* namespace boost */
+
+#endif