[2440] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2007 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_CYCLE_CANCELING_H |
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| 20 | #define LEMON_CYCLE_CANCELING_H |
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| 21 | |
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| 22 | /// \ingroup min_cost_flow |
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| 23 | /// |
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| 24 | /// \file |
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[2457] | 25 | /// \brief A cycle-canceling algorithm for finding a minimum cost flow. |
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[2440] | 26 | |
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| 27 | #include <vector> |
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| 28 | #include <lemon/circulation.h> |
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| 29 | #include <lemon/graph_adaptor.h> |
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| 30 | |
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[2457] | 31 | /// \brief The used cycle-canceling method. |
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[2440] | 32 | #define LIMITED_CYCLE_CANCELING |
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| 33 | //#define MIN_MEAN_CYCLE_CANCELING |
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| 34 | |
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| 35 | #ifdef LIMITED_CYCLE_CANCELING |
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| 36 | #include <lemon/bellman_ford.h> |
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| 37 | /// \brief The maximum number of iterations for the first execution |
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| 38 | /// of the \ref lemon::BellmanFord "Bellman-Ford" algorithm. |
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[2457] | 39 | /// It should be at least 2. |
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[2440] | 40 | #define STARTING_LIMIT 2 |
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| 41 | /// \brief The iteration limit for the |
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| 42 | /// \ref lemon::BellmanFord "Bellman-Ford" algorithm is multiplied by |
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[2457] | 43 | /// <tt>ALPHA_MUL / ALPHA_DIV</tt> in every round. |
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| 44 | /// <tt>ALPHA_MUL / ALPHA_DIV</tt> must be greater than 1. |
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[2440] | 45 | #define ALPHA_MUL 3 |
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| 46 | /// \brief The iteration limit for the |
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| 47 | /// \ref lemon::BellmanFord "Bellman-Ford" algorithm is multiplied by |
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[2457] | 48 | /// <tt>ALPHA_MUL / ALPHA_DIV</tt> in every round. |
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| 49 | /// <tt>ALPHA_MUL / ALPHA_DIV</tt> must be greater than 1. |
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[2440] | 50 | #define ALPHA_DIV 2 |
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| 51 | |
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| 52 | //#define _ONLY_ONE_CYCLE_ |
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[2457] | 53 | //#define _NO_BACK_STEP_ |
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[2440] | 54 | //#define _DEBUG_ITER_ |
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| 55 | #endif |
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| 56 | |
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| 57 | #ifdef MIN_MEAN_CYCLE_CANCELING |
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| 58 | #include <lemon/min_mean_cycle.h> |
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| 59 | #include <lemon/path.h> |
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| 60 | #endif |
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| 61 | |
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| 62 | namespace lemon { |
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| 63 | |
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| 64 | /// \addtogroup min_cost_flow |
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| 65 | /// @{ |
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| 66 | |
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[2457] | 67 | /// \brief Implementation of a cycle-canceling algorithm for finding |
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[2440] | 68 | /// a minimum cost flow. |
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| 69 | /// |
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[2457] | 70 | /// \ref lemon::CycleCanceling "CycleCanceling" implements a |
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| 71 | /// cycle-canceling algorithm for finding a minimum cost flow. |
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[2440] | 72 | /// |
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| 73 | /// \param Graph The directed graph type the algorithm runs on. |
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| 74 | /// \param LowerMap The type of the lower bound map. |
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| 75 | /// \param CapacityMap The type of the capacity (upper bound) map. |
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| 76 | /// \param CostMap The type of the cost (length) map. |
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| 77 | /// \param SupplyMap The type of the supply map. |
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| 78 | /// |
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| 79 | /// \warning |
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| 80 | /// - Edge capacities and costs should be nonnegative integers. |
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| 81 | /// However \c CostMap::Value should be signed type. |
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| 82 | /// - Supply values should be integers. |
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| 83 | /// - \c LowerMap::Value must be convertible to |
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| 84 | /// \c CapacityMap::Value and \c CapacityMap::Value must be |
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| 85 | /// convertible to \c SupplyMap::Value. |
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| 86 | /// |
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| 87 | /// \author Peter Kovacs |
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| 88 | |
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| 89 | template < typename Graph, |
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| 90 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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| 91 | typename CapacityMap = LowerMap, |
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| 92 | typename CostMap = typename Graph::template EdgeMap<int>, |
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| 93 | typename SupplyMap = typename Graph::template NodeMap |
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| 94 | <typename CapacityMap::Value> > |
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| 95 | class CycleCanceling |
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| 96 | { |
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| 97 | typedef typename Graph::Node Node; |
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| 98 | typedef typename Graph::NodeIt NodeIt; |
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| 99 | typedef typename Graph::Edge Edge; |
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| 100 | typedef typename Graph::EdgeIt EdgeIt; |
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| 101 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 102 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 103 | |
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| 104 | typedef typename LowerMap::Value Lower; |
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| 105 | typedef typename CapacityMap::Value Capacity; |
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| 106 | typedef typename CostMap::Value Cost; |
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| 107 | typedef typename SupplyMap::Value Supply; |
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| 108 | typedef typename Graph::template EdgeMap<Capacity> CapacityRefMap; |
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| 109 | typedef typename Graph::template NodeMap<Supply> SupplyRefMap; |
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| 110 | |
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| 111 | typedef ResGraphAdaptor< const Graph, Capacity, |
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| 112 | CapacityRefMap, CapacityRefMap > ResGraph; |
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| 113 | typedef typename ResGraph::Node ResNode; |
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| 114 | typedef typename ResGraph::NodeIt ResNodeIt; |
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| 115 | typedef typename ResGraph::Edge ResEdge; |
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| 116 | typedef typename ResGraph::EdgeIt ResEdgeIt; |
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| 117 | |
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| 118 | public: |
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| 119 | |
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| 120 | /// \brief The type of the flow map. |
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| 121 | typedef CapacityRefMap FlowMap; |
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| 122 | |
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| 123 | protected: |
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| 124 | |
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| 125 | /// \brief Map adaptor class for handling residual edge costs. |
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| 126 | class ResCostMap : public MapBase<ResEdge, Cost> |
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| 127 | { |
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| 128 | private: |
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| 129 | |
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| 130 | const CostMap &cost_map; |
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| 131 | |
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| 132 | public: |
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| 133 | |
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| 134 | typedef typename MapBase<ResEdge, Cost>::Value Value; |
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| 135 | typedef typename MapBase<ResEdge, Cost>::Key Key; |
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| 136 | |
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| 137 | ResCostMap(const CostMap &_cost) : cost_map(_cost) {} |
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| 138 | |
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| 139 | Value operator[](const Key &e) const { |
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| 140 | return ResGraph::forward(e) ? cost_map[e] : -cost_map[e]; |
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| 141 | } |
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| 142 | |
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| 143 | }; //class ResCostMap |
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| 144 | |
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| 145 | protected: |
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| 146 | |
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| 147 | /// \brief The directed graph the algorithm runs on. |
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| 148 | const Graph &graph; |
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| 149 | /// \brief The original lower bound map. |
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| 150 | const LowerMap *lower; |
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| 151 | /// \brief The modified capacity map. |
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| 152 | CapacityRefMap capacity; |
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| 153 | /// \brief The cost map. |
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| 154 | const CostMap &cost; |
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| 155 | /// \brief The modified supply map. |
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| 156 | SupplyRefMap supply; |
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| 157 | /// \brief The sum of supply values equals zero. |
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| 158 | bool valid_supply; |
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| 159 | |
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| 160 | /// \brief The current flow. |
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| 161 | FlowMap flow; |
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| 162 | /// \brief The residual graph. |
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| 163 | ResGraph res_graph; |
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| 164 | /// \brief The residual cost map. |
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| 165 | ResCostMap res_cost; |
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| 166 | |
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| 167 | public : |
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| 168 | |
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| 169 | /// \brief General constructor of the class (with lower bounds). |
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| 170 | /// |
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| 171 | /// General constructor of the class (with lower bounds). |
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| 172 | /// |
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| 173 | /// \param _graph The directed graph the algorithm runs on. |
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| 174 | /// \param _lower The lower bounds of the edges. |
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| 175 | /// \param _capacity The capacities (upper bounds) of the edges. |
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| 176 | /// \param _cost The cost (length) values of the edges. |
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| 177 | /// \param _supply The supply values of the nodes (signed). |
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| 178 | CycleCanceling( const Graph &_graph, |
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| 179 | const LowerMap &_lower, |
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| 180 | const CapacityMap &_capacity, |
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| 181 | const CostMap &_cost, |
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| 182 | const SupplyMap &_supply ) : |
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| 183 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
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[2457] | 184 | supply(_graph), flow(_graph, 0), |
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[2440] | 185 | res_graph(_graph, capacity, flow), res_cost(cost) |
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| 186 | { |
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| 187 | // Removing nonzero lower bounds |
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| 188 | capacity = subMap(_capacity, _lower); |
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| 189 | Supply sum = 0; |
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| 190 | for (NodeIt n(graph); n != INVALID; ++n) { |
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| 191 | Supply s = _supply[n]; |
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| 192 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
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| 193 | s += _lower[e]; |
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| 194 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
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| 195 | s -= _lower[e]; |
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| 196 | sum += (supply[n] = s); |
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| 197 | } |
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| 198 | valid_supply = sum == 0; |
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| 199 | } |
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| 200 | |
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| 201 | /// \brief General constructor of the class (without lower bounds). |
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| 202 | /// |
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| 203 | /// General constructor of the class (without lower bounds). |
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| 204 | /// |
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| 205 | /// \param _graph The directed graph the algorithm runs on. |
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| 206 | /// \param _capacity The capacities (upper bounds) of the edges. |
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| 207 | /// \param _cost The cost (length) values of the edges. |
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| 208 | /// \param _supply The supply values of the nodes (signed). |
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| 209 | CycleCanceling( const Graph &_graph, |
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| 210 | const CapacityMap &_capacity, |
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| 211 | const CostMap &_cost, |
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| 212 | const SupplyMap &_supply ) : |
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| 213 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
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[2457] | 214 | supply(_supply), flow(_graph, 0), |
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[2440] | 215 | res_graph(_graph, capacity, flow), res_cost(cost) |
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| 216 | { |
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| 217 | // Checking the sum of supply values |
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| 218 | Supply sum = 0; |
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| 219 | for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n]; |
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| 220 | valid_supply = sum == 0; |
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| 221 | } |
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| 222 | |
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| 223 | |
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| 224 | /// \brief Simple constructor of the class (with lower bounds). |
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| 225 | /// |
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| 226 | /// Simple constructor of the class (with lower bounds). |
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| 227 | /// |
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| 228 | /// \param _graph The directed graph the algorithm runs on. |
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| 229 | /// \param _lower The lower bounds of the edges. |
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| 230 | /// \param _capacity The capacities (upper bounds) of the edges. |
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| 231 | /// \param _cost The cost (length) values of the edges. |
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| 232 | /// \param _s The source node. |
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| 233 | /// \param _t The target node. |
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| 234 | /// \param _flow_value The required amount of flow from node \c _s |
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| 235 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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| 236 | /// \c _t). |
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| 237 | CycleCanceling( const Graph &_graph, |
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| 238 | const LowerMap &_lower, |
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| 239 | const CapacityMap &_capacity, |
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| 240 | const CostMap &_cost, |
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| 241 | Node _s, Node _t, |
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| 242 | Supply _flow_value ) : |
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| 243 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
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[2457] | 244 | supply(_graph), flow(_graph, 0), |
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[2440] | 245 | res_graph(_graph, capacity, flow), res_cost(cost) |
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| 246 | { |
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| 247 | // Removing nonzero lower bounds |
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| 248 | capacity = subMap(_capacity, _lower); |
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| 249 | for (NodeIt n(graph); n != INVALID; ++n) { |
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| 250 | Supply s = 0; |
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| 251 | if (n == _s) s = _flow_value; |
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| 252 | if (n == _t) s = -_flow_value; |
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| 253 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
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| 254 | s += _lower[e]; |
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| 255 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
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| 256 | s -= _lower[e]; |
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| 257 | supply[n] = s; |
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| 258 | } |
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| 259 | valid_supply = true; |
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| 260 | } |
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| 261 | |
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| 262 | /// \brief Simple constructor of the class (without lower bounds). |
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| 263 | /// |
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| 264 | /// Simple constructor of the class (without lower bounds). |
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| 265 | /// |
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| 266 | /// \param _graph The directed graph the algorithm runs on. |
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| 267 | /// \param _capacity The capacities (upper bounds) of the edges. |
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| 268 | /// \param _cost The cost (length) values of the edges. |
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| 269 | /// \param _s The source node. |
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| 270 | /// \param _t The target node. |
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| 271 | /// \param _flow_value The required amount of flow from node \c _s |
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| 272 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
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| 273 | /// \c _t). |
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| 274 | CycleCanceling( const Graph &_graph, |
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| 275 | const CapacityMap &_capacity, |
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| 276 | const CostMap &_cost, |
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| 277 | Node _s, Node _t, |
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| 278 | Supply _flow_value ) : |
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| 279 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
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[2457] | 280 | supply(_graph, 0), flow(_graph, 0), |
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[2440] | 281 | res_graph(_graph, capacity, flow), res_cost(cost) |
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| 282 | { |
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| 283 | supply[_s] = _flow_value; |
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| 284 | supply[_t] = -_flow_value; |
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| 285 | valid_supply = true; |
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| 286 | } |
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| 287 | |
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| 288 | /// \brief Returns a const reference to the flow map. |
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| 289 | /// |
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| 290 | /// Returns a const reference to the flow map. |
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| 291 | /// |
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| 292 | /// \pre \ref run() must be called before using this function. |
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| 293 | const FlowMap& flowMap() const { |
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| 294 | return flow; |
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| 295 | } |
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| 296 | |
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| 297 | /// \brief Returns the total cost of the found flow. |
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| 298 | /// |
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| 299 | /// Returns the total cost of the found flow. The complexity of the |
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| 300 | /// function is \f$ O(e) \f$. |
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| 301 | /// |
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| 302 | /// \pre \ref run() must be called before using this function. |
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| 303 | Cost totalCost() const { |
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| 304 | Cost c = 0; |
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| 305 | for (EdgeIt e(graph); e != INVALID; ++e) |
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| 306 | c += flow[e] * cost[e]; |
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| 307 | return c; |
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| 308 | } |
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| 309 | |
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| 310 | /// \brief Runs the algorithm. |
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| 311 | /// |
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| 312 | /// Runs the algorithm. |
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| 313 | /// |
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| 314 | /// \return \c true if a feasible flow can be found. |
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| 315 | bool run() { |
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| 316 | return init() && start(); |
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| 317 | } |
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| 318 | |
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| 319 | protected: |
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| 320 | |
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| 321 | /// \brief Initializes the algorithm. |
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| 322 | bool init() { |
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| 323 | // Checking the sum of supply values |
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| 324 | Supply sum = 0; |
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| 325 | for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n]; |
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| 326 | if (sum != 0) return false; |
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| 327 | |
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| 328 | // Finding a feasible flow |
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| 329 | Circulation< Graph, Capacity, FlowMap, ConstMap<Edge, Capacity>, |
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[2457] | 330 | CapacityRefMap, SupplyMap > |
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[2440] | 331 | circulation( graph, constMap<Edge>((Capacity)0), |
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[2457] | 332 | capacity, supply, flow ); |
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[2440] | 333 | return circulation.run() == -1; |
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| 334 | } |
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| 335 | |
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| 336 | #ifdef LIMITED_CYCLE_CANCELING |
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[2457] | 337 | /// \brief Executes a cycle-canceling algorithm using |
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[2440] | 338 | /// \ref lemon::BellmanFord "Bellman-Ford" algorithm with limited |
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| 339 | /// iteration count. |
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| 340 | bool start() { |
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| 341 | typename BellmanFord<ResGraph, ResCostMap>::PredMap pred(res_graph); |
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| 342 | typename ResGraph::template NodeMap<int> visited(res_graph); |
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| 343 | std::vector<ResEdge> cycle; |
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| 344 | int node_num = countNodes(graph); |
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| 345 | |
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| 346 | #ifdef _DEBUG_ITER_ |
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| 347 | int cycle_num = 0; |
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| 348 | #endif |
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| 349 | int length_bound = STARTING_LIMIT; |
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| 350 | bool optimal = false; |
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| 351 | while (!optimal) { |
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| 352 | BellmanFord<ResGraph, ResCostMap> bf(res_graph, res_cost); |
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| 353 | bf.predMap(pred); |
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| 354 | bf.init(0); |
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| 355 | int iter_num = 0; |
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| 356 | bool cycle_found = false; |
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| 357 | while (!cycle_found) { |
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[2457] | 358 | #ifdef _NO_BACK_STEP_ |
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| 359 | int curr_iter_num = length_bound <= node_num ? |
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| 360 | length_bound - iter_num : node_num - iter_num; |
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| 361 | #else |
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[2440] | 362 | int curr_iter_num = iter_num + length_bound <= node_num ? |
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| 363 | length_bound : node_num - iter_num; |
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[2457] | 364 | #endif |
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[2440] | 365 | iter_num += curr_iter_num; |
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| 366 | int real_iter_num = curr_iter_num; |
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| 367 | for (int i = 0; i < curr_iter_num; ++i) { |
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| 368 | if (bf.processNextWeakRound()) { |
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| 369 | real_iter_num = i; |
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| 370 | break; |
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| 371 | } |
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| 372 | } |
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| 373 | if (real_iter_num < curr_iter_num) { |
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| 374 | optimal = true; |
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| 375 | break; |
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| 376 | } else { |
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| 377 | // Searching for node disjoint negative cycles |
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| 378 | for (ResNodeIt n(res_graph); n != INVALID; ++n) |
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| 379 | visited[n] = 0; |
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| 380 | int id = 0; |
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| 381 | for (ResNodeIt n(res_graph); n != INVALID; ++n) { |
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| 382 | if (visited[n] > 0) continue; |
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| 383 | visited[n] = ++id; |
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| 384 | ResNode u = pred[n] == INVALID ? |
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| 385 | INVALID : res_graph.source(pred[n]); |
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| 386 | while (u != INVALID && visited[u] == 0) { |
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| 387 | visited[u] = id; |
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| 388 | u = pred[u] == INVALID ? |
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| 389 | INVALID : res_graph.source(pred[u]); |
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| 390 | } |
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| 391 | if (u != INVALID && visited[u] == id) { |
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| 392 | // Finding the negative cycle |
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| 393 | cycle_found = true; |
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| 394 | cycle.clear(); |
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| 395 | ResEdge e = pred[u]; |
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| 396 | cycle.push_back(e); |
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| 397 | Capacity d = res_graph.rescap(e); |
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| 398 | while (res_graph.source(e) != u) { |
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| 399 | cycle.push_back(e = pred[res_graph.source(e)]); |
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| 400 | if (res_graph.rescap(e) < d) |
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| 401 | d = res_graph.rescap(e); |
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| 402 | } |
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| 403 | #ifdef _DEBUG_ITER_ |
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| 404 | ++cycle_num; |
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| 405 | #endif |
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| 406 | // Augmenting along the cycle |
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| 407 | for (int i = 0; i < cycle.size(); ++i) |
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| 408 | res_graph.augment(cycle[i], d); |
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| 409 | #ifdef _ONLY_ONE_CYCLE_ |
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| 410 | break; |
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| 411 | #endif |
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| 412 | } |
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| 413 | } |
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| 414 | } |
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| 415 | |
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| 416 | if (!cycle_found) |
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| 417 | length_bound = length_bound * ALPHA_MUL / ALPHA_DIV; |
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| 418 | } |
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| 419 | } |
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| 420 | |
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| 421 | #ifdef _DEBUG_ITER_ |
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[2457] | 422 | std::cout << "Limited cycle-canceling algorithm finished. " |
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[2440] | 423 | << "Found " << cycle_num << " negative cycles." |
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| 424 | << std::endl; |
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| 425 | #endif |
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| 426 | |
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| 427 | // Handling nonzero lower bounds |
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| 428 | if (lower) { |
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| 429 | for (EdgeIt e(graph); e != INVALID; ++e) |
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| 430 | flow[e] += (*lower)[e]; |
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| 431 | } |
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| 432 | return true; |
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| 433 | } |
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| 434 | #endif |
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| 435 | |
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| 436 | #ifdef MIN_MEAN_CYCLE_CANCELING |
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[2457] | 437 | /// \brief Executes the minimum mean cycle-canceling algorithm |
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[2440] | 438 | /// using \ref lemon::MinMeanCycle "MinMeanCycle" class. |
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| 439 | bool start() { |
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| 440 | typedef Path<ResGraph> ResPath; |
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| 441 | MinMeanCycle<ResGraph, ResCostMap> mmc(res_graph, res_cost); |
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| 442 | ResPath cycle; |
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| 443 | |
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| 444 | #ifdef _DEBUG_ITER_ |
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| 445 | int cycle_num = 0; |
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| 446 | #endif |
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| 447 | mmc.cyclePath(cycle).init(); |
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| 448 | if (mmc.findMinMean()) { |
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| 449 | while (mmc.cycleLength() < 0) { |
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| 450 | #ifdef _DEBUG_ITER_ |
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| 451 | ++iter; |
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| 452 | #endif |
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| 453 | // Finding the cycle |
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| 454 | mmc.findCycle(); |
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| 455 | |
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| 456 | // Finding the largest flow amount that can be augmented |
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| 457 | // along the cycle |
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| 458 | Capacity delta = 0; |
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| 459 | for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) { |
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| 460 | if (delta == 0 || res_graph.rescap(e) < delta) |
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| 461 | delta = res_graph.rescap(e); |
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| 462 | } |
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| 463 | |
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| 464 | // Augmenting along the cycle |
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| 465 | for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) |
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| 466 | res_graph.augment(e, delta); |
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| 467 | |
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| 468 | // Finding the minimum cycle mean for the modified residual |
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| 469 | // graph |
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| 470 | mmc.reset(); |
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| 471 | if (!mmc.findMinMean()) break; |
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| 472 | } |
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| 473 | } |
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| 474 | |
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| 475 | #ifdef _DEBUG_ITER_ |
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[2457] | 476 | std::cout << "Minimum mean cycle-canceling algorithm finished. " |
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[2440] | 477 | << "Found " << cycle_num << " negative cycles." |
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| 478 | << std::endl; |
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| 479 | #endif |
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| 480 | |
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| 481 | // Handling nonzero lower bounds |
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| 482 | if (lower) { |
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| 483 | for (EdgeIt e(graph); e != INVALID; ++e) |
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| 484 | flow[e] += (*lower)[e]; |
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| 485 | } |
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| 486 | return true; |
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| 487 | } |
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| 488 | #endif |
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| 489 | |
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| 490 | }; //class CycleCanceling |
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| 491 | |
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| 492 | ///@} |
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| 493 | |
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| 494 | } //namespace lemon |
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| 495 | |
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| 496 | #endif //LEMON_CYCLE_CANCELING_H |
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