//  Copyright (c) 2006, Stephan Diederich
//
//  This code may be used under either of the following two licences:
//
//    Permission is hereby granted, free of charge, to any person
//    obtaining a copy of this software and associated documentation
//    files (the "Software"), to deal in the Software without
//    restriction, including without limitation the rights to use,
//    copy, modify, merge, publish, distribute, sublicense, and/or
//    sell copies of the Software, and to permit persons to whom the
//    Software is furnished to do so, subject to the following
//    conditions:
//
//    The above copyright notice and this permission notice shall be
//    included in all copies or substantial portions of the Software.
//
//    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
//    EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
//    OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
//    NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
//    HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
//    WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
//    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
//    OTHER DEALINGS IN THE SOFTWARE. OF SUCH DAMAGE.
//
//  Or:
//
//    Distributed under 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)

#include <vector>
#include <iterator>
#include <iostream>
#include <algorithm>
#include <fstream>

#include <boost/core/lightweight_test.hpp>
#include <boost/graph/boykov_kolmogorov_max_flow.hpp>

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/adjacency_matrix.hpp>
#include <boost/graph/random.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/random/linear_congruential.hpp>
#include <boost/lexical_cast.hpp>

using namespace boost;

template < typename Graph, typename CapacityMap, typename ReverseEdgeMap >
std::pair< typename graph_traits< Graph >::vertex_descriptor,
    typename graph_traits< Graph >::vertex_descriptor >
fill_random_max_flow_graph(Graph& g, CapacityMap cap, ReverseEdgeMap rev,
    typename graph_traits< Graph >::vertices_size_type n_verts,
    typename graph_traits< Graph >::edges_size_type n_edges, std::size_t seed)
{
    typedef typename graph_traits< Graph >::edge_descriptor edge_descriptor;
    typedef typename graph_traits< Graph >::vertex_descriptor vertex_descriptor;
    const int cap_low = 1;
    const int cap_high = 1000;

    // init random numer generator
    minstd_rand gen(seed);
    // generate graph
    generate_random_graph(g, n_verts, n_edges, gen);

    // init an uniform distribution int generator
    typedef variate_generator< minstd_rand, uniform_int< int > > tIntGen;
    tIntGen int_gen(gen, uniform_int< int >(cap_low, cap_high));
    // randomize edge-capacities
    // randomize_property<edge_capacity, Graph, tIntGen> (g,int_gen); //we
    // cannot use this, as we have no idea how properties are stored, right?
    typename graph_traits< Graph >::edge_iterator ei, e_end;
    for (boost::tie(ei, e_end) = edges(g); ei != e_end; ++ei)
        cap[*ei] = int_gen();

    // get source and sink node
    vertex_descriptor s = random_vertex(g, gen);
    vertex_descriptor t = graph_traits< Graph >::null_vertex();
    while (t == graph_traits< Graph >::null_vertex() || t == s)
        t = random_vertex(g, gen);

    // add reverse edges (ugly... how to do better?!)
    std::list< edge_descriptor > edges_copy;
    boost::tie(ei, e_end) = edges(g);
    std::copy(ei, e_end,
        std::back_insert_iterator< std::list< edge_descriptor > >(edges_copy));
    while (!edges_copy.empty())
    {
        edge_descriptor old_edge = edges_copy.front();
        edges_copy.pop_front();
        vertex_descriptor source_vertex = target(old_edge, g);
        vertex_descriptor target_vertex = source(old_edge, g);
        bool inserted;
        edge_descriptor new_edge;
        boost::tie(new_edge, inserted)
            = add_edge(source_vertex, target_vertex, g);
        assert(inserted);
        rev[old_edge] = new_edge;
        rev[new_edge] = old_edge;
        cap[new_edge] = 0;
    }
    return std::make_pair(s, t);
}

long test_adjacency_list_vecS(int n_verts, int n_edges, std::size_t seed)
{
    typedef adjacency_list_traits< vecS, vecS, directedS > tVectorTraits;
    typedef adjacency_list< vecS, vecS, directedS,
        property< vertex_index_t, long,
            property< vertex_predecessor_t, tVectorTraits::edge_descriptor,
                property< vertex_color_t, boost::default_color_type,
                    property< vertex_distance_t, long > > > >,
        property< edge_capacity_t, long,
            property< edge_residual_capacity_t, long,
                property< edge_reverse_t, tVectorTraits::edge_descriptor > > > >
        tVectorGraph;

    tVectorGraph g;

    graph_traits< tVectorGraph >::vertex_descriptor src, sink;
    boost::tie(src, sink) = fill_random_max_flow_graph(
        g, get(edge_capacity, g), get(edge_reverse, g), n_verts, n_edges, seed);

    return boykov_kolmogorov_max_flow(g, get(edge_capacity, g),
        get(edge_residual_capacity, g), get(edge_reverse, g),
        get(vertex_predecessor, g), get(vertex_color, g),
        get(vertex_distance, g), get(vertex_index, g), src, sink);
}

long test_adjacency_list_listS(int n_verts, int n_edges, std::size_t seed)
{
    typedef adjacency_list_traits< listS, listS, directedS > tListTraits;
    typedef adjacency_list< listS, listS, directedS,
        property< vertex_index_t, long,
            property< vertex_predecessor_t, tListTraits::edge_descriptor,
                property< vertex_color_t, boost::default_color_type,
                    property< vertex_distance_t, long > > > >,
        property< edge_capacity_t, long,
            property< edge_residual_capacity_t, long,
                property< edge_reverse_t, tListTraits::edge_descriptor > > > >
        tListGraph;

    tListGraph g;

    graph_traits< tListGraph >::vertex_descriptor src, sink;
    boost::tie(src, sink) = fill_random_max_flow_graph(
        g, get(edge_capacity, g), get(edge_reverse, g), n_verts, n_edges, seed);

    // initialize vertex indices
    graph_traits< tListGraph >::vertex_iterator vi, v_end;
    graph_traits< tListGraph >::vertices_size_type index = 0;
    for (boost::tie(vi, v_end) = vertices(g); vi != v_end; ++vi)
    {
        put(vertex_index, g, *vi, index++);
    }
    return boykov_kolmogorov_max_flow(g, get(edge_capacity, g),
        get(edge_residual_capacity, g), get(edge_reverse, g),
        get(vertex_predecessor, g), get(vertex_color, g),
        get(vertex_distance, g), get(vertex_index, g), src, sink);
}

template < typename EdgeDescriptor > struct Node
{
    boost::default_color_type vertex_color;
    long vertex_distance;
    EdgeDescriptor vertex_predecessor;
};

template < typename EdgeDescriptor > struct Link
{
    long edge_capacity;
    long edge_residual_capacity;
    EdgeDescriptor edge_reverse;
};

long test_bundled_properties(int n_verts, int n_edges, std::size_t seed)
{
    typedef adjacency_list_traits< vecS, vecS, directedS > tTraits;
    typedef Node< tTraits::edge_descriptor > tVertex;
    typedef Link< tTraits::edge_descriptor > tEdge;
    typedef adjacency_list< vecS, vecS, directedS, tVertex, tEdge >
        tBundleGraph;

    tBundleGraph g;

    graph_traits< tBundleGraph >::vertex_descriptor src, sink;
    boost::tie(src, sink)
        = fill_random_max_flow_graph(g, get(&tEdge::edge_capacity, g),
            get(&tEdge::edge_reverse, g), n_verts, n_edges, seed);
    return boykov_kolmogorov_max_flow(g, get(&tEdge::edge_capacity, g),
        get(&tEdge::edge_residual_capacity, g), get(&tEdge::edge_reverse, g),
        get(&tVertex::vertex_predecessor, g), get(&tVertex::vertex_color, g),
        get(&tVertex::vertex_distance, g), get(vertex_index, g), src, sink);
}

long test_overloads(int n_verts, int n_edges, std::size_t seed)
{
    typedef adjacency_list_traits< vecS, vecS, directedS > tTraits;
    typedef property< edge_capacity_t, long,
        property< edge_residual_capacity_t, long,
            property< edge_reverse_t, tTraits::edge_descriptor > > >
        tEdgeProperty;
    typedef adjacency_list< vecS, vecS, directedS, no_property, tEdgeProperty >
        tGraph;

    tGraph g;

    graph_traits< tGraph >::vertex_descriptor src, sink;
    boost::tie(src, sink) = fill_random_max_flow_graph(
        g, get(edge_capacity, g), get(edge_reverse, g), n_verts, n_edges, seed);

    std::vector< graph_traits< tGraph >::edge_descriptor > predecessor_vec(
        n_verts);
    std::vector< default_color_type > color_vec(n_verts);
    std::vector< graph_traits< tGraph >::vertices_size_type > distance_vec(
        n_verts);

    long flow_overload_1 = boykov_kolmogorov_max_flow(g, get(edge_capacity, g),
        get(edge_residual_capacity, g), get(edge_reverse, g),
        get(vertex_index, g), src, sink);

    long flow_overload_2 = boykov_kolmogorov_max_flow(g, get(edge_capacity, g),
        get(edge_residual_capacity, g), get(edge_reverse, g),
        boost::make_iterator_property_map(
            color_vec.begin(), get(vertex_index, g)),
        get(vertex_index, g), src, sink);

    BOOST_TEST(flow_overload_1 == flow_overload_2);
    return flow_overload_1;
}

template < class Graph, class EdgeCapacityMap, class ResidualCapacityEdgeMap,
    class ReverseEdgeMap, class PredecessorMap, class ColorMap,
    class DistanceMap, class IndexMap >
class boykov_kolmogorov_test
: public detail::bk_max_flow< Graph, EdgeCapacityMap, ResidualCapacityEdgeMap,
      ReverseEdgeMap, PredecessorMap, ColorMap, DistanceMap, IndexMap >
{

    typedef typename graph_traits< Graph >::edge_descriptor tEdge;
    typedef typename graph_traits< Graph >::vertex_descriptor tVertex;
    typedef typename property_traits< typename property_map< Graph,
        edge_capacity_t >::const_type >::value_type tEdgeVal;
    typedef typename graph_traits< Graph >::vertex_iterator tVertexIterator;
    typedef typename graph_traits< Graph >::out_edge_iterator tOutEdgeIterator;
    typedef typename property_traits< ColorMap >::value_type tColorValue;
    typedef color_traits< tColorValue > tColorTraits;
    typedef typename property_traits< DistanceMap >::value_type tDistanceVal;
    typedef typename detail::bk_max_flow< Graph, EdgeCapacityMap,
        ResidualCapacityEdgeMap, ReverseEdgeMap, PredecessorMap, ColorMap,
        DistanceMap, IndexMap >
        tSuper;

public:
    boykov_kolmogorov_test(Graph& g,
        typename graph_traits< Graph >::vertex_descriptor src,
        typename graph_traits< Graph >::vertex_descriptor sink)
    : tSuper(g, get(edge_capacity, g), get(edge_residual_capacity, g),
        get(edge_reverse, g), get(vertex_predecessor, g), get(vertex_color, g),
        get(vertex_distance, g), get(vertex_index, g), src, sink)
    {
    }

    void invariant_four(tVertex v) const
    {
        // passive nodes in S or T
        if (v == tSuper::m_source || v == tSuper::m_sink)
            return;
        typename std::list< tVertex >::const_iterator it
            = find(tSuper::m_orphans.begin(), tSuper::m_orphans.end(), v);
        // a node is active, if its in the active_list AND (is has_a_parent, or
        // its already in the orphans_list or its the sink, or its the source)
        bool is_active = (tSuper::m_in_active_list_map[v]
            && (tSuper::has_parent(v) || it != tSuper::m_orphans.end()));
        if (this->get_tree(v) != tColorTraits::gray() && !is_active)
        {
            typename graph_traits< Graph >::out_edge_iterator ei, e_end;
            for (boost::tie(ei, e_end) = out_edges(v, tSuper::m_g); ei != e_end;
                 ++ei)
            {
                const tVertex& other_node = target(*ei, tSuper::m_g);
                if (this->get_tree(other_node) != this->get_tree(v))
                {
                    if (this->get_tree(v) == tColorTraits::black())
                        BOOST_TEST(tSuper::m_res_cap_map[*ei] == 0);
                    else
                        BOOST_TEST(
                            tSuper::m_res_cap_map[tSuper::m_rev_edge_map[*ei]]
                            == 0);
                }
            }
        }
    }

    void invariant_five(const tVertex& v) const
    {
        BOOST_TEST(this->get_tree(v) != tColorTraits::gray()
            || tSuper::m_time_map[v] <= tSuper::m_time);
    }

    void invariant_six(const tVertex& v) const
    {
        if (this->get_tree(v) == tColorTraits::gray()
            || tSuper::m_time_map[v] != tSuper::m_time)
            return;
        else
        {
            tVertex current_node = v;
            tDistanceVal distance = 0;
            tColorValue color = this->get_tree(v);
            tVertex terminal = (color == tColorTraits::black())
                ? tSuper::m_source
                : tSuper::m_sink;
            while (current_node != terminal)
            {
                BOOST_TEST(tSuper::has_parent(current_node));
                tEdge e = this->get_edge_to_parent(current_node);
                ++distance;
                current_node = (color == tColorTraits::black())
                    ? source(e, tSuper::m_g)
                    : target(e, tSuper::m_g);
                if (distance > tSuper::m_dist_map[v])
                    break;
            }
            BOOST_TEST(distance == tSuper::m_dist_map[v]);
        }
    }

    void invariant_seven(const tVertex& v) const
    {
        if (this->get_tree(v) == tColorTraits::gray())
            return;
        else
        {
            tColorValue color = this->get_tree(v);
            long time = tSuper::m_time_map[v];
            tVertex current_node = v;
            while (tSuper::has_parent(current_node))
            {
                tEdge e = this->get_edge_to_parent(current_node);
                current_node = (color == tColorTraits::black())
                    ? source(e, tSuper::m_g)
                    : target(e, tSuper::m_g);
                BOOST_TEST(tSuper::m_time_map[current_node] >= time);
            }
        }
    } // invariant_seven

    void invariant_eight(const tVertex& v) const
    {
        if (this->get_tree(v) == tColorTraits::gray())
            return;
        else
        {
            tColorValue color = this->get_tree(v);
            long time = tSuper::m_time_map[v];
            tDistanceVal distance = tSuper::m_dist_map[v];
            tVertex current_node = v;
            while (tSuper::has_parent(current_node))
            {
                tEdge e = this->get_edge_to_parent(current_node);
                current_node = (color == tColorTraits::black())
                    ? source(e, tSuper::m_g)
                    : target(e, tSuper::m_g);
                if (tSuper::m_time_map[current_node] == time)
                    BOOST_TEST(tSuper::m_dist_map[current_node] < distance);
            }
        }
    } // invariant_eight

    void check_invariants()
    {
        tVertexIterator vi, v_end;
        for (boost::tie(vi, v_end) = vertices(tSuper::m_g); vi != v_end; ++vi)
        {
            invariant_four(*vi);
            invariant_five(*vi);
            invariant_six(*vi);
            invariant_seven(*vi);
            invariant_eight(*vi);
        }
    }

    tEdgeVal test()
    {
        this->add_active_node(this->m_sink);
        this->augment_direct_paths();
        check_invariants();
        // start the main-loop
        while (true)
        {
            bool path_found;
            tEdge connecting_edge;
            boost::tie(connecting_edge, path_found)
                = this->grow(); // find a path from source to sink
            if (!path_found)
            {
                // we're finished, no more paths were found
                break;
            }
            check_invariants();
            this->m_time++;
            this->augment(connecting_edge); // augment that path
            check_invariants();
            this->adopt(); // rebuild search tree structure
            check_invariants();
        }

        // check if flow is the sum of outgoing edges of src
        tOutEdgeIterator ei, e_end;
        tEdgeVal src_sum = 0;
        for (boost::tie(ei, e_end) = out_edges(this->m_source, this->m_g);
             ei != e_end; ++ei)
        {
            src_sum += this->m_cap_map[*ei] - this->m_res_cap_map[*ei];
        }
        BOOST_TEST(this->m_flow == src_sum);
        // check if flow is the sum of ingoing edges of sink
        tEdgeVal sink_sum = 0;
        for (boost::tie(ei, e_end) = out_edges(this->m_sink, this->m_g);
             ei != e_end; ++ei)
        {
            tEdge in_edge = this->m_rev_edge_map[*ei];
            sink_sum += this->m_cap_map[in_edge] - this->m_res_cap_map[in_edge];
        }
        BOOST_TEST(this->m_flow == sink_sum);
        return this->m_flow;
    }
};

long test_algorithms_invariant(int n_verts, int n_edges, std::size_t seed)
{
    typedef adjacency_list_traits< vecS, vecS, directedS > tVectorTraits;
    typedef adjacency_list< vecS, vecS, directedS,
        property< vertex_index_t, long,
            property< vertex_predecessor_t, tVectorTraits::edge_descriptor,
                property< vertex_color_t, default_color_type,
                    property< vertex_distance_t, long > > > >,
        property< edge_capacity_t, long,
            property< edge_residual_capacity_t, long,
                property< edge_reverse_t, tVectorTraits::edge_descriptor > > > >
        tVectorGraph;

    tVectorGraph g;

    graph_traits< tVectorGraph >::vertex_descriptor src, sink;
    boost::tie(src, sink) = fill_random_max_flow_graph(
        g, get(edge_capacity, g), get(edge_reverse, g), n_verts, n_edges, seed);

    typedef property_map< tVectorGraph, edge_capacity_t >::type tEdgeCapMap;
    typedef property_map< tVectorGraph, edge_residual_capacity_t >::type
        tEdgeResCapMap;
    typedef property_map< tVectorGraph, edge_reverse_t >::type tRevEdgeMap;
    typedef property_map< tVectorGraph, vertex_predecessor_t >::type
        tVertexPredMap;
    typedef property_map< tVectorGraph, vertex_color_t >::type tVertexColorMap;
    typedef property_map< tVectorGraph, vertex_distance_t >::type tDistanceMap;
    typedef property_map< tVectorGraph, vertex_index_t >::type tIndexMap;
    typedef boykov_kolmogorov_test< tVectorGraph, tEdgeCapMap, tEdgeResCapMap,
        tRevEdgeMap, tVertexPredMap, tVertexColorMap, tDistanceMap, tIndexMap >
        tKolmo;
    tKolmo instance(g, src, sink);
    return instance.test();
}

int main(int argc, char* argv[])
{
    int n_verts = 10;
    int n_edges = 500;
    std::size_t seed = 1;

    if (argc > 1)
        n_verts = lexical_cast< int >(argv[1]);
    if (argc > 2)
        n_edges = lexical_cast< int >(argv[2]);
    if (argc > 3)
        seed = lexical_cast< std::size_t >(argv[3]);

    // we need at least 2 vertices to create src and sink in random graphs
    // this case is also caught in boykov_kolmogorov_max_flow
    if (n_verts < 2)
        n_verts = 2;

    // below are checks for different calls to boykov_kolmogorov_max_flow and
    // different graph-types

    // checks support of vecS storage
    long flow_vecS = test_adjacency_list_vecS(n_verts, n_edges, seed);
    std::cout << "vecS flow: " << flow_vecS << std::endl;
    // checks support of listS storage (especially problems with vertex indices)
    long flow_listS = test_adjacency_list_listS(n_verts, n_edges, seed);
    std::cout << "listS flow: " << flow_listS << std::endl;
    BOOST_TEST(flow_vecS == flow_listS);
    // checks bundled properties
    long flow_bundles = test_bundled_properties(n_verts, n_edges, seed);
    std::cout << "bundles flow: " << flow_bundles << std::endl;
    BOOST_TEST(flow_listS == flow_bundles);
    // checks overloads
    long flow_overloads = test_overloads(n_verts, n_edges, seed);
    std::cout << "overloads flow: " << flow_overloads << std::endl;
    BOOST_TEST(flow_bundles == flow_overloads);

    // excessive test version where Boykov-Kolmogorov's algorithm invariants are
    // checked
    long flow_invariants = test_algorithms_invariant(n_verts, n_edges, seed);
    std::cout << "invariants flow: " << flow_invariants << std::endl;
    BOOST_TEST(flow_overloads == flow_invariants);
    return boost::report_errors();
}
