// Copyright Louis Dionne 2013

// Use, modification and distribution is subject to the Boost Software
// License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy
// at http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_GRAPH_HAWICK_CIRCUITS_HPP
#define BOOST_GRAPH_HAWICK_CIRCUITS_HPP

#include <algorithm>
#include <boost/assert.hpp>
#include <boost/foreach.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/one_bit_color_map.hpp>
#include <boost/graph/properties.hpp>
#include <boost/move/utility.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/range/begin.hpp>
#include <boost/range/end.hpp>
#include <boost/range/iterator.hpp>
#include <boost/tuple/tuple.hpp> // for boost::tie
#include <boost/type_traits/remove_reference.hpp>
#include <boost/utility/result_of.hpp>
#include <set>
#include <utility> // for std::pair
#include <vector>


namespace boost {
namespace hawick_circuits_detail {
//! @internal Functor returning all the vertices adjacent to a vertex.
struct get_all_adjacent_vertices {
    template <typename Sig>
    struct result;

    template <typename This, typename Vertex, typename Graph>
    struct result<This(Vertex, Graph)> {
    private:
        typedef typename remove_reference<Graph>::type RawGraph;
        typedef graph_traits<RawGraph> Traits;
        typedef typename Traits::adjacency_iterator AdjacencyIterator;

    public:
        typedef std::pair<AdjacencyIterator, AdjacencyIterator> type;
    };

    template <typename Vertex, typename Graph>
    typename result<
        get_all_adjacent_vertices(BOOST_FWD_REF(Vertex), BOOST_FWD_REF(Graph))
    >::type
    operator()(BOOST_FWD_REF(Vertex) v, BOOST_FWD_REF(Graph) g) const {
        return adjacent_vertices(boost::forward<Vertex>(v),
                                 boost::forward<Graph>(g));
    }
};

//! @internal Functor returning a set of the vertices adjacent to a vertex.
struct get_unique_adjacent_vertices {
    template <typename Sig>
    struct result;

    template <typename This, typename Vertex, typename Graph>
    struct result<This(Vertex, Graph)> {
        typedef std::set<typename remove_reference<Vertex>::type> type;
    };

    template <typename Vertex, typename Graph>
    typename result<get_unique_adjacent_vertices(Vertex, Graph const&)>::type
    operator()(Vertex v, Graph const& g) const {
        typedef typename result<
                    get_unique_adjacent_vertices(Vertex, Graph const&)
                >::type Set;
        return Set(adjacent_vertices(v, g).first,
                   adjacent_vertices(v, g).second);
    }
};

//! @internal
//! Return whether a container contains a given value.
//! This is not meant as a general purpose membership testing function; it
//! would have to be more clever about possible optimizations.
template <typename Container, typename Value>
bool contains(Container const& c, Value const& v) {
    return std::find(boost::begin(c), boost::end(c), v) != boost::end(c);
}

/*!
 * @internal
 * Algorithm finding all the cycles starting from a given vertex.
 *
 * The search is only done in the subgraph induced by the starting vertex
 * and the vertices with an index higher than the starting vertex.
 */
template <
    typename Graph,
    typename Visitor,
    typename VertexIndexMap,
    typename Stack,
    typename ClosedMatrix,
    typename GetAdjacentVertices
>
struct hawick_circuits_from {
private:
    typedef graph_traits<Graph> Traits;
    typedef typename Traits::vertex_descriptor Vertex;
    typedef typename Traits::edge_descriptor Edge;
    typedef typename Traits::vertices_size_type VerticesSize;
    typedef typename property_traits<VertexIndexMap>::value_type VertexIndex;

    typedef typename result_of<
                GetAdjacentVertices(Vertex, Graph const&)
            >::type AdjacentVertices;
    typedef typename range_iterator<AdjacentVertices const>::type AdjacencyIterator;

    // The one_bit_color_map starts all white, i.e. not blocked.
    // Since we make that assumption (I looked at the implementation, but
    // I can't find anything that documents this behavior), we're gonna
    // assert it in the constructor.
    typedef one_bit_color_map<VertexIndexMap> BlockedMap;
    typedef typename property_traits<BlockedMap>::value_type BlockedColor;

    static BlockedColor blocked_false_color()
    { return color_traits<BlockedColor>::white(); }

    static BlockedColor blocked_true_color()
    { return color_traits<BlockedColor>::black(); }

    // This is used by the constructor to secure the assumption
    // documented above.
    bool blocked_map_starts_all_unblocked() const {
        BOOST_FOREACH(Vertex v, vertices(graph_))
            if (is_blocked(v))
                return false;
        return true;
    }

    // This is only used in the constructor to make sure the optimization of
    // sharing data structures between iterations does not break the code.
    bool all_closed_rows_are_empty() const {
        BOOST_FOREACH(typename ClosedMatrix::reference row, closed_)
            if (!row.empty())
                return false;
        return true;
    }

public:
    hawick_circuits_from(Graph const& graph, Visitor& visitor,
                         VertexIndexMap const& vim,
                         Stack& stack, ClosedMatrix& closed,
                         VerticesSize n_vertices)
        : graph_(graph), visitor_(visitor), vim_(vim), stack_(stack),
          closed_(closed), blocked_(n_vertices, vim_)
        {
            BOOST_ASSERT(blocked_map_starts_all_unblocked());

            // Since sharing the data structures between iterations is
            // just an optimization, it must always be equivalent to
            // constructing new ones in this constructor.
            BOOST_ASSERT(stack_.empty());
            BOOST_ASSERT(closed_.size() == n_vertices);
            BOOST_ASSERT(all_closed_rows_are_empty());
        }

private:
    //! @internal Return the index of a given vertex.
    VertexIndex index_of(Vertex v) const {
        return get(vim_, v);
    }


    //! @internal Return whether a vertex `v` is closed to a vertex `u`.
    bool is_closed_to(Vertex u, Vertex v) const {
        typedef typename ClosedMatrix::const_reference VertexList;
        VertexList closed_to_u = closed_[index_of(u)];
        return contains(closed_to_u, v);
    }

    //! @internal Close a vertex `v` to a vertex `u`.
    void close_to(Vertex u, Vertex v) {
        BOOST_ASSERT(!is_closed_to(u, v));
        closed_[index_of(u)].push_back(v);
    }


    //! @internal Return whether a given vertex is blocked.
    bool is_blocked(Vertex v) const {
        return get(blocked_, v) == blocked_true_color();
    }

    //! @internal Block a given vertex.
    void block(Vertex v) {
        put(blocked_, v, blocked_true_color());
    }

    //! @internal Unblock a given vertex.
    void unblock(Vertex u) {
        typedef typename ClosedMatrix::reference VertexList;

        put(blocked_, u, blocked_false_color());
        VertexList closed_to_u = closed_[index_of(u)];

        while (!closed_to_u.empty()) {
            Vertex const w = closed_to_u.back();
            closed_to_u.pop_back();
            if (is_blocked(w))
                unblock(w);
        }
        BOOST_ASSERT(closed_to_u.empty());
    }

    //! @internal Main procedure as described in the paper.
    bool circuit(Vertex start, Vertex v) {
        bool found_circuit = false;
        stack_.push_back(v);
        block(v);

        // Cache some values that are used more than once in the function.
        VertexIndex const index_of_start = index_of(start);
        AdjacentVertices const adj_vertices = GetAdjacentVertices()(v, graph_);
        AdjacencyIterator const w_end = boost::end(adj_vertices);

        for (AdjacencyIterator w_it = boost::begin(adj_vertices);
             w_it != w_end;
             ++w_it)
        {
            Vertex const w = *w_it;
            // Since we're only looking in the subgraph induced by `start`
            // and the vertices with an index higher than `start`, we skip
            // any vertex that does not satisfy that.
            if (index_of(w) < index_of_start)
                continue;

            // If the last vertex is equal to `start`, we have a circuit.
            else if (w == start) {
                // const_cast to ensure the visitor does not modify the stack
                visitor_.cycle(const_cast<Stack const&>(stack_), graph_);
                found_circuit = true;
            }

            // If `w` is not blocked, we continue searching further down the
            // same path for a cycle with `w` in it.
            else if (!is_blocked(w) && circuit(start, w))
                found_circuit = true;
        }

        if (found_circuit)
            unblock(v);
        else
            for (AdjacencyIterator w_it = boost::begin(adj_vertices);
                 w_it != w_end;
                 ++w_it)
            {
                Vertex const w = *w_it;
                // Like above, we skip vertices that are not in the subgraph
                // we're considering.
                if (index_of(w) < index_of_start)
                    continue;

                // If `v` is not closed to `w`, we make it so.
                if (!is_closed_to(w, v))
                    close_to(w, v);
            }

        BOOST_ASSERT(v == stack_.back());
        stack_.pop_back();
        return found_circuit;
    }

public:
    void operator()(Vertex start) {
        circuit(start, start);
    }

private:
    Graph const& graph_;
    Visitor& visitor_;
    VertexIndexMap const& vim_;
    Stack& stack_;
    ClosedMatrix& closed_;
    BlockedMap blocked_;
};

template <
    typename GetAdjacentVertices,
    typename Graph, typename Visitor, typename VertexIndexMap
>
void call_hawick_circuits(Graph const& graph,
                          Visitor /* by value */ visitor,
                          VertexIndexMap const& vertex_index_map) {
    typedef graph_traits<Graph> Traits;
    typedef typename Traits::vertex_descriptor Vertex;
    typedef typename Traits::vertices_size_type VerticesSize;
    typedef typename Traits::vertex_iterator VertexIterator;

    typedef std::vector<Vertex> Stack;
    typedef std::vector<std::vector<Vertex> > ClosedMatrix;

    typedef hawick_circuits_from<
                Graph, Visitor, VertexIndexMap, Stack, ClosedMatrix,
                GetAdjacentVertices
            > SubAlgorithm;

    VerticesSize const n_vertices = num_vertices(graph);
    Stack stack; stack.reserve(n_vertices);
    ClosedMatrix closed(n_vertices);

    VertexIterator start, last;
    for (boost::tie(start, last) = vertices(graph); start != last; ++start) {
        // Note1: The sub algorithm may NOT be reused once it has been called.

        // Note2: We reuse the Stack and the ClosedMatrix (after clearing them)
        // in each iteration to avoid redundant destruction and construction.
        // It would be strictly equivalent to have these as member variables
        // of the sub algorithm.
        SubAlgorithm sub_algo(graph, visitor, vertex_index_map,
                              stack, closed, n_vertices);
        sub_algo(*start);
        stack.clear();
        typename ClosedMatrix::iterator row, last_row = closed.end();
        for (row = closed.begin(); row != last_row; ++row)
            row->clear();
    }
}

template <typename GetAdjacentVertices, typename Graph, typename Visitor>
void call_hawick_circuits(Graph const& graph, BOOST_FWD_REF(Visitor) visitor) {
    call_hawick_circuits<GetAdjacentVertices>(
        graph, boost::forward<Visitor>(visitor), get(vertex_index, graph)
    );
}
} // end namespace hawick_circuits_detail

//! Enumerate all the elementary circuits in a directed multigraph.
template <typename Graph, typename Visitor, typename VertexIndexMap>
void hawick_circuits(BOOST_FWD_REF(Graph) graph,
                     BOOST_FWD_REF(Visitor) visitor,
                     BOOST_FWD_REF(VertexIndexMap) vertex_index_map) {
    hawick_circuits_detail::call_hawick_circuits<
        hawick_circuits_detail::get_all_adjacent_vertices
    >(
        boost::forward<Graph>(graph),
        boost::forward<Visitor>(visitor),
        boost::forward<VertexIndexMap>(vertex_index_map)
    );
}

template <typename Graph, typename Visitor>
void hawick_circuits(BOOST_FWD_REF(Graph) graph,
                     BOOST_FWD_REF(Visitor) visitor) {
    hawick_circuits_detail::call_hawick_circuits<
        hawick_circuits_detail::get_all_adjacent_vertices
    >(boost::forward<Graph>(graph), boost::forward<Visitor>(visitor));
}

/*!
 * Same as `boost::hawick_circuits`, but duplicate circuits caused by parallel
 * edges will not be considered. Each circuit will be considered only once.
 */
template <typename Graph, typename Visitor, typename VertexIndexMap>
void hawick_unique_circuits(BOOST_FWD_REF(Graph) graph,
                            BOOST_FWD_REF(Visitor) visitor,
                            BOOST_FWD_REF(VertexIndexMap) vertex_index_map) {
    hawick_circuits_detail::call_hawick_circuits<
        hawick_circuits_detail::get_unique_adjacent_vertices
    >(
        boost::forward<Graph>(graph),
        boost::forward<Visitor>(visitor),
        boost::forward<VertexIndexMap>(vertex_index_map)
    );
}

template <typename Graph, typename Visitor>
void hawick_unique_circuits(BOOST_FWD_REF(Graph) graph,
                            BOOST_FWD_REF(Visitor) visitor) {
    hawick_circuits_detail::call_hawick_circuits<
        hawick_circuits_detail::get_unique_adjacent_vertices
    >(boost::forward<Graph>(graph), boost::forward<Visitor>(visitor));
}
} // end namespace boost

#endif // !BOOST_GRAPH_HAWICK_CIRCUITS_HPP