[857] | 1 | //=======================================================================
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| 2 | // Copyright 2000 University of Notre Dame.
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| 3 | // Authors: Jeremy G. Siek, Andrew Lumsdaine, Lie-Quan Lee
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| 4 | //
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| 5 | // Distributed under the Boost Software License, Version 1.0. (See
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| 6 | // accompanying file LICENSE_1_0.txt or copy at
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| 7 | // http://www.boost.org/LICENSE_1_0.txt)
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| 8 | //=======================================================================
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| 9 |
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| 10 | #ifndef EDMUNDS_KARP_MAX_FLOW_HPP
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| 11 | #define EDMUNDS_KARP_MAX_FLOW_HPP
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| 12 |
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| 13 | #include <boost/config.hpp>
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| 14 | #include <vector>
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| 15 | #include <algorithm> // for std::min and std::max
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| 16 | #include <boost/config.hpp>
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| 17 | #include <boost/pending/queue.hpp>
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| 18 | #include <boost/property_map.hpp>
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| 19 | #include <boost/graph/graph_traits.hpp>
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| 20 | #include <boost/graph/properties.hpp>
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| 21 | #include <boost/graph/filtered_graph.hpp>
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| 22 | #include <boost/graph/breadth_first_search.hpp>
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| 23 |
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| 24 | namespace boost {
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| 25 |
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| 26 | // The "labeling" algorithm from "Network Flows" by Ahuja, Magnanti,
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| 27 | // Orlin. I think this is the same as or very similar to the original
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| 28 | // Edmunds-Karp algorithm. This solves the maximum flow problem.
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| 29 |
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| 30 | namespace detail {
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| 31 |
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| 32 | template <class Graph, class ResCapMap>
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| 33 | filtered_graph<Graph, is_residual_edge<ResCapMap> >
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| 34 | residual_graph(Graph& g, ResCapMap residual_capacity) {
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| 35 | return filtered_graph<Graph, is_residual_edge<ResCapMap> >
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| 36 | (g, is_residual_edge<ResCapMap>(residual_capacity));
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| 37 | }
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| 38 |
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| 39 | template <class Graph, class PredEdgeMap, class ResCapMap,
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| 40 | class RevEdgeMap>
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| 41 | inline void
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| 42 | augment(Graph& g,
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| 43 | typename graph_traits<Graph>::vertex_descriptor src,
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| 44 | typename graph_traits<Graph>::vertex_descriptor sink,
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| 45 | PredEdgeMap p,
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| 46 | ResCapMap residual_capacity,
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| 47 | RevEdgeMap reverse_edge)
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| 48 | {
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| 49 | typename graph_traits<Graph>::edge_descriptor e;
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| 50 | typename graph_traits<Graph>::vertex_descriptor u;
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| 51 | typedef typename property_traits<ResCapMap>::value_type FlowValue;
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| 52 |
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| 53 | // find minimum residual capacity along the augmenting path
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| 54 | FlowValue delta = (std::numeric_limits<FlowValue>::max)();
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| 55 | e = p[sink];
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| 56 | do {
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| 57 | BOOST_USING_STD_MIN();
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| 58 | delta = min BOOST_PREVENT_MACRO_SUBSTITUTION(delta, residual_capacity[e]);
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| 59 | u = source(e, g);
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| 60 | e = p[u];
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| 61 | } while (u != src);
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| 62 |
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| 63 | // push delta units of flow along the augmenting path
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| 64 | e = p[sink];
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| 65 | do {
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| 66 | residual_capacity[e] -= delta;
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| 67 | residual_capacity[reverse_edge[e]] += delta;
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| 68 | u = source(e, g);
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| 69 | e = p[u];
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| 70 | } while (u != src);
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| 71 | }
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| 72 |
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| 73 | } // namespace detail
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| 74 |
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| 75 | template <class Graph,
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| 76 | class CapacityEdgeMap, class ResidualCapacityEdgeMap,
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| 77 | class ReverseEdgeMap, class ColorMap, class PredEdgeMap>
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| 78 | typename property_traits<CapacityEdgeMap>::value_type
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| 79 | edmunds_karp_max_flow
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| 80 | (Graph& g,
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| 81 | typename graph_traits<Graph>::vertex_descriptor src,
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| 82 | typename graph_traits<Graph>::vertex_descriptor sink,
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| 83 | CapacityEdgeMap cap,
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| 84 | ResidualCapacityEdgeMap res,
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| 85 | ReverseEdgeMap rev,
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| 86 | ColorMap color,
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| 87 | PredEdgeMap pred)
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| 88 | {
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| 89 | typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
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| 90 | typedef typename property_traits<ColorMap>::value_type ColorValue;
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| 91 | typedef color_traits<ColorValue> Color;
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| 92 |
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| 93 | typename graph_traits<Graph>::vertex_iterator u_iter, u_end;
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| 94 | typename graph_traits<Graph>::out_edge_iterator ei, e_end;
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| 95 | for (tie(u_iter, u_end) = vertices(g); u_iter != u_end; ++u_iter)
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| 96 | for (tie(ei, e_end) = out_edges(*u_iter, g); ei != e_end; ++ei)
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| 97 | res[*ei] = cap[*ei];
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| 98 |
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| 99 | color[sink] = Color::gray();
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| 100 | while (color[sink] != Color::white()) {
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| 101 | boost::queue<vertex_t> Q;
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| 102 | breadth_first_search
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| 103 | (detail::residual_graph(g, res), src, Q,
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| 104 | make_bfs_visitor(record_edge_predecessors(pred, on_tree_edge())),
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| 105 | color);
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| 106 | if (color[sink] != Color::white())
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| 107 | detail::augment(g, src, sink, pred, res, rev);
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| 108 | } // while
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| 109 |
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| 110 | typename property_traits<CapacityEdgeMap>::value_type flow = 0;
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| 111 | for (tie(ei, e_end) = out_edges(src, g); ei != e_end; ++ei)
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| 112 | flow += (cap[*ei] - res[*ei]);
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| 113 | return flow;
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| 114 | } // edmunds_karp_max_flow()
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| 115 |
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| 116 | namespace detail {
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| 117 | //-------------------------------------------------------------------------
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| 118 | // Handle default for color property map
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| 119 |
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| 120 | // use of class here is a VC++ workaround
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| 121 | template <class ColorMap>
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| 122 | struct edmunds_karp_dispatch2 {
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| 123 | template <class Graph, class PredMap, class P, class T, class R>
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| 124 | static typename edge_capacity_value<Graph, P, T, R>::type
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| 125 | apply
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| 126 | (Graph& g,
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| 127 | typename graph_traits<Graph>::vertex_descriptor src,
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| 128 | typename graph_traits<Graph>::vertex_descriptor sink,
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| 129 | PredMap pred,
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| 130 | const bgl_named_params<P, T, R>& params,
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| 131 | ColorMap color)
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| 132 | {
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| 133 | return edmunds_karp_max_flow
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| 134 | (g, src, sink,
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| 135 | choose_const_pmap(get_param(params, edge_capacity), g, edge_capacity),
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| 136 | choose_pmap(get_param(params, edge_residual_capacity),
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| 137 | g, edge_residual_capacity),
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| 138 | choose_const_pmap(get_param(params, edge_reverse), g, edge_reverse),
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| 139 | color, pred);
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| 140 | }
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| 141 | };
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| 142 | template<>
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| 143 | struct edmunds_karp_dispatch2<detail::error_property_not_found> {
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| 144 | template <class Graph, class PredMap, class P, class T, class R>
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| 145 | static typename edge_capacity_value<Graph, P, T, R>::type
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| 146 | apply
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| 147 | (Graph& g,
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| 148 | typename graph_traits<Graph>::vertex_descriptor src,
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| 149 | typename graph_traits<Graph>::vertex_descriptor sink,
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| 150 | PredMap pred,
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| 151 | const bgl_named_params<P, T, R>& params,
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| 152 | detail::error_property_not_found)
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| 153 | {
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| 154 | typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
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| 155 | typedef typename graph_traits<Graph>::vertices_size_type size_type;
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| 156 | size_type n = is_default_param(get_param(params, vertex_color)) ?
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| 157 | num_vertices(g) : 1;
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| 158 | std::vector<default_color_type> color_vec(n);
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| 159 | return edmunds_karp_max_flow
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| 160 | (g, src, sink,
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| 161 | choose_const_pmap(get_param(params, edge_capacity), g, edge_capacity),
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| 162 | choose_pmap(get_param(params, edge_residual_capacity),
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| 163 | g, edge_residual_capacity),
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| 164 | choose_const_pmap(get_param(params, edge_reverse), g, edge_reverse),
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| 165 | make_iterator_property_map(color_vec.begin(), choose_const_pmap
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| 166 | (get_param(params, vertex_index),
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| 167 | g, vertex_index), color_vec[0]),
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| 168 | pred);
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| 169 | }
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| 170 | };
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| 171 |
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| 172 | //-------------------------------------------------------------------------
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| 173 | // Handle default for predecessor property map
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| 174 |
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| 175 | // use of class here is a VC++ workaround
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| 176 | template <class PredMap>
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| 177 | struct edmunds_karp_dispatch1 {
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| 178 | template <class Graph, class P, class T, class R>
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| 179 | static typename edge_capacity_value<Graph, P, T, R>::type
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| 180 | apply(Graph& g,
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| 181 | typename graph_traits<Graph>::vertex_descriptor src,
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| 182 | typename graph_traits<Graph>::vertex_descriptor sink,
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| 183 | const bgl_named_params<P, T, R>& params,
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| 184 | PredMap pred)
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| 185 | {
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| 186 | typedef typename property_value< bgl_named_params<P,T,R>, vertex_color_t>::type C;
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| 187 | return edmunds_karp_dispatch2<C>::apply
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| 188 | (g, src, sink, pred, params, get_param(params, vertex_color));
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| 189 | }
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| 190 | };
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| 191 | template<>
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| 192 | struct edmunds_karp_dispatch1<detail::error_property_not_found> {
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| 193 |
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| 194 | template <class Graph, class P, class T, class R>
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| 195 | static typename edge_capacity_value<Graph, P, T, R>::type
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| 196 | apply
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| 197 | (Graph& g,
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| 198 | typename graph_traits<Graph>::vertex_descriptor src,
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| 199 | typename graph_traits<Graph>::vertex_descriptor sink,
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| 200 | const bgl_named_params<P, T, R>& params,
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| 201 | detail::error_property_not_found)
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| 202 | {
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| 203 | typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
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| 204 | typedef typename graph_traits<Graph>::vertices_size_type size_type;
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| 205 | size_type n = is_default_param(get_param(params, vertex_predecessor)) ?
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| 206 | num_vertices(g) : 1;
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| 207 | std::vector<edge_descriptor> pred_vec(n);
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| 208 |
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| 209 | typedef typename property_value< bgl_named_params<P,T,R>, vertex_color_t>::type C;
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| 210 | return edmunds_karp_dispatch2<C>::apply
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| 211 | (g, src, sink,
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| 212 | make_iterator_property_map(pred_vec.begin(), choose_const_pmap
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| 213 | (get_param(params, vertex_index),
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| 214 | g, vertex_index), pred_vec[0]),
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| 215 | params,
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| 216 | get_param(params, vertex_color));
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| 217 | }
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| 218 | };
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| 219 |
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| 220 | } // namespace detail
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| 221 |
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| 222 | template <class Graph, class P, class T, class R>
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| 223 | typename detail::edge_capacity_value<Graph, P, T, R>::type
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| 224 | edmunds_karp_max_flow
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| 225 | (Graph& g,
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| 226 | typename graph_traits<Graph>::vertex_descriptor src,
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| 227 | typename graph_traits<Graph>::vertex_descriptor sink,
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| 228 | const bgl_named_params<P, T, R>& params)
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| 229 | {
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| 230 | typedef typename property_value< bgl_named_params<P,T,R>, vertex_predecessor_t>::type Pred;
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| 231 | return detail::edmunds_karp_dispatch1<Pred>::apply
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| 232 | (g, src, sink, params, get_param(params, vertex_predecessor));
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| 233 | }
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| 234 |
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| 235 | template <class Graph>
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| 236 | typename property_traits<
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| 237 | typename property_map<Graph, edge_capacity_t>::const_type
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| 238 | >::value_type
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| 239 | edmunds_karp_max_flow
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| 240 | (Graph& g,
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| 241 | typename graph_traits<Graph>::vertex_descriptor src,
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| 242 | typename graph_traits<Graph>::vertex_descriptor sink)
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| 243 | {
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| 244 | bgl_named_params<int, buffer_param_t> params(0);
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| 245 | return edmunds_karp_max_flow(g, src, sink, params);
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| 246 | }
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| 247 |
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| 248 | } // namespace boost
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| 249 |
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| 250 | #endif // EDMUNDS_KARP_MAX_FLOW_HPP
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