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boost/graph/tiernan_all_cycles.hpp

// (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/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 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 providse 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)
    {
        function_requires< IncidenceGraphConcept<Graph> >();
        function_requires< 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
        //    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)
    {
        function_requires< 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(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)
    {
        function_requires< IncidenceGraphConcept<Graph> >();
        typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
        typedef typename graph_traits<Graph>::edge_descriptor Edge;
        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(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)
    {
        function_requires< 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)
    {
        function_requires< VertexListGraphConcept<Graph> >();
        typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
        typedef std::vector<Vertex> Path;
        function_requires< 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)
{
    function_requires< VertexListGraphConcept<Graph> >();
    typedef typename graph_traits<Graph>::vertex_iterator VertexIterator;

    VertexIterator i, end;
    for(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