[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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[2553] | 5 | * Copyright (C) 2003-2008 |
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[2440] | 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_CAPACITY_SCALING_H |
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| 20 | #define LEMON_CAPACITY_SCALING_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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[2574] | 25 | /// \brief Capacity scaling algorithm for finding a minimum cost flow. |
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| 26 | |
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| 27 | #include <vector> |
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[2535] | 28 | #include <lemon/bin_heap.h> |
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[2457] | 29 | |
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[2440] | 30 | namespace lemon { |
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| 31 | |
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| 32 | /// \addtogroup min_cost_flow |
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| 33 | /// @{ |
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| 34 | |
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[2574] | 35 | /// \brief Implementation of the capacity scaling algorithm for |
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| 36 | /// finding a minimum cost flow. |
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[2440] | 37 | /// |
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[2535] | 38 | /// \ref CapacityScaling implements the capacity scaling version |
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| 39 | /// of the successive shortest path algorithm for finding a minimum |
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| 40 | /// cost flow. |
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[2440] | 41 | /// |
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[2574] | 42 | /// \tparam Graph The directed graph type the algorithm runs on. |
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| 43 | /// \tparam LowerMap The type of the lower bound map. |
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| 44 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
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| 45 | /// \tparam CostMap The type of the cost (length) map. |
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| 46 | /// \tparam SupplyMap The type of the supply map. |
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[2440] | 47 | /// |
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| 48 | /// \warning |
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[2574] | 49 | /// - Edge capacities and costs should be \e non-negative \e integers. |
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| 50 | /// - Supply values should be \e signed \e integers. |
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[2581] | 51 | /// - The value types of the maps should be convertible to each other. |
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| 52 | /// - \c CostMap::Value must be signed type. |
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[2440] | 53 | /// |
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| 54 | /// \author Peter Kovacs |
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[2533] | 55 | template < typename Graph, |
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[2535] | 56 | typename LowerMap = typename Graph::template EdgeMap<int>, |
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[2574] | 57 | typename CapacityMap = typename Graph::template EdgeMap<int>, |
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[2535] | 58 | typename CostMap = typename Graph::template EdgeMap<int>, |
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[2574] | 59 | typename SupplyMap = typename Graph::template NodeMap<int> > |
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[2440] | 60 | class CapacityScaling |
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| 61 | { |
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[2556] | 62 | GRAPH_TYPEDEFS(typename Graph); |
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[2440] | 63 | |
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| 64 | typedef typename CapacityMap::Value Capacity; |
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| 65 | typedef typename CostMap::Value Cost; |
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| 66 | typedef typename SupplyMap::Value Supply; |
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[2556] | 67 | typedef typename Graph::template EdgeMap<Capacity> CapacityEdgeMap; |
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| 68 | typedef typename Graph::template NodeMap<Supply> SupplyNodeMap; |
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[2535] | 69 | typedef typename Graph::template NodeMap<Edge> PredMap; |
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[2440] | 70 | |
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| 71 | public: |
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| 72 | |
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[2556] | 73 | /// The type of the flow map. |
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| 74 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
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| 75 | /// The type of the potential map. |
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[2440] | 76 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
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| 77 | |
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[2574] | 78 | private: |
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[2440] | 79 | |
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[2535] | 80 | /// \brief Special implementation of the \ref Dijkstra algorithm |
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[2574] | 81 | /// for finding shortest paths in the residual network. |
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| 82 | /// |
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| 83 | /// \ref ResidualDijkstra is a special implementation of the |
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| 84 | /// \ref Dijkstra algorithm for finding shortest paths in the |
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| 85 | /// residual network of the graph with respect to the reduced edge |
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| 86 | /// costs and modifying the node potentials according to the |
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| 87 | /// distance of the nodes. |
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[2535] | 88 | class ResidualDijkstra |
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[2440] | 89 | { |
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[2535] | 90 | typedef typename Graph::template NodeMap<int> HeapCrossRef; |
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| 91 | typedef BinHeap<Cost, HeapCrossRef> Heap; |
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| 92 | |
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[2574] | 93 | private: |
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[2535] | 94 | |
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[2574] | 95 | // The directed graph the algorithm runs on |
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| 96 | const Graph &_graph; |
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[2535] | 97 | |
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[2574] | 98 | // The main maps |
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| 99 | const FlowMap &_flow; |
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| 100 | const CapacityEdgeMap &_res_cap; |
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| 101 | const CostMap &_cost; |
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| 102 | const SupplyNodeMap &_excess; |
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| 103 | PotentialMap &_potential; |
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[2535] | 104 | |
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[2574] | 105 | // The distance map |
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[2588] | 106 | PotentialMap _dist; |
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[2574] | 107 | // The pred edge map |
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| 108 | PredMap &_pred; |
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| 109 | // The processed (i.e. permanently labeled) nodes |
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| 110 | std::vector<Node> _proc_nodes; |
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[2440] | 111 | |
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| 112 | public: |
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| 113 | |
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[2581] | 114 | /// Constructor. |
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[2574] | 115 | ResidualDijkstra( const Graph &graph, |
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| 116 | const FlowMap &flow, |
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| 117 | const CapacityEdgeMap &res_cap, |
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| 118 | const CostMap &cost, |
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| 119 | const SupplyMap &excess, |
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| 120 | PotentialMap &potential, |
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| 121 | PredMap &pred ) : |
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| 122 | _graph(graph), _flow(flow), _res_cap(res_cap), _cost(cost), |
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| 123 | _excess(excess), _potential(potential), _dist(graph), |
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| 124 | _pred(pred) |
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[2535] | 125 | {} |
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[2440] | 126 | |
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[2620] | 127 | /// Run the algorithm from the given source node. |
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[2588] | 128 | Node run(Node s, Capacity delta = 1) { |
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[2574] | 129 | HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP); |
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[2535] | 130 | Heap heap(heap_cross_ref); |
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| 131 | heap.push(s, 0); |
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[2574] | 132 | _pred[s] = INVALID; |
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| 133 | _proc_nodes.clear(); |
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[2535] | 134 | |
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| 135 | // Processing nodes |
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[2574] | 136 | while (!heap.empty() && _excess[heap.top()] > -delta) { |
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[2535] | 137 | Node u = heap.top(), v; |
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[2574] | 138 | Cost d = heap.prio() + _potential[u], nd; |
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| 139 | _dist[u] = heap.prio(); |
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[2535] | 140 | heap.pop(); |
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[2574] | 141 | _proc_nodes.push_back(u); |
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[2535] | 142 | |
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| 143 | // Traversing outgoing edges |
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[2574] | 144 | for (OutEdgeIt e(_graph, u); e != INVALID; ++e) { |
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| 145 | if (_res_cap[e] >= delta) { |
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| 146 | v = _graph.target(e); |
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[2535] | 147 | switch(heap.state(v)) { |
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| 148 | case Heap::PRE_HEAP: |
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[2574] | 149 | heap.push(v, d + _cost[e] - _potential[v]); |
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| 150 | _pred[v] = e; |
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[2535] | 151 | break; |
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| 152 | case Heap::IN_HEAP: |
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[2574] | 153 | nd = d + _cost[e] - _potential[v]; |
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[2535] | 154 | if (nd < heap[v]) { |
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| 155 | heap.decrease(v, nd); |
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[2574] | 156 | _pred[v] = e; |
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[2535] | 157 | } |
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| 158 | break; |
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| 159 | case Heap::POST_HEAP: |
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| 160 | break; |
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| 161 | } |
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| 162 | } |
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| 163 | } |
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| 164 | |
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| 165 | // Traversing incoming edges |
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[2574] | 166 | for (InEdgeIt e(_graph, u); e != INVALID; ++e) { |
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| 167 | if (_flow[e] >= delta) { |
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| 168 | v = _graph.source(e); |
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[2535] | 169 | switch(heap.state(v)) { |
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| 170 | case Heap::PRE_HEAP: |
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[2574] | 171 | heap.push(v, d - _cost[e] - _potential[v]); |
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| 172 | _pred[v] = e; |
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[2535] | 173 | break; |
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| 174 | case Heap::IN_HEAP: |
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[2574] | 175 | nd = d - _cost[e] - _potential[v]; |
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[2535] | 176 | if (nd < heap[v]) { |
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| 177 | heap.decrease(v, nd); |
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[2574] | 178 | _pred[v] = e; |
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[2535] | 179 | } |
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| 180 | break; |
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| 181 | case Heap::POST_HEAP: |
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| 182 | break; |
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| 183 | } |
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| 184 | } |
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| 185 | } |
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| 186 | } |
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| 187 | if (heap.empty()) return INVALID; |
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| 188 | |
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| 189 | // Updating potentials of processed nodes |
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| 190 | Node t = heap.top(); |
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[2574] | 191 | Cost t_dist = heap.prio(); |
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| 192 | for (int i = 0; i < int(_proc_nodes.size()); ++i) |
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| 193 | _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist; |
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[2535] | 194 | |
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| 195 | return t; |
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[2440] | 196 | } |
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| 197 | |
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[2535] | 198 | }; //class ResidualDijkstra |
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[2440] | 199 | |
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[2574] | 200 | private: |
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[2440] | 201 | |
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[2574] | 202 | // The directed graph the algorithm runs on |
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| 203 | const Graph &_graph; |
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| 204 | // The original lower bound map |
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| 205 | const LowerMap *_lower; |
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| 206 | // The modified capacity map |
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| 207 | CapacityEdgeMap _capacity; |
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| 208 | // The original cost map |
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| 209 | const CostMap &_cost; |
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| 210 | // The modified supply map |
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| 211 | SupplyNodeMap _supply; |
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| 212 | bool _valid_supply; |
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[2440] | 213 | |
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[2574] | 214 | // Edge map of the current flow |
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[2581] | 215 | FlowMap *_flow; |
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| 216 | bool _local_flow; |
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[2574] | 217 | // Node map of the current potentials |
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[2581] | 218 | PotentialMap *_potential; |
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| 219 | bool _local_potential; |
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[2440] | 220 | |
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[2574] | 221 | // The residual capacity map |
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| 222 | CapacityEdgeMap _res_cap; |
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| 223 | // The excess map |
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| 224 | SupplyNodeMap _excess; |
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| 225 | // The excess nodes (i.e. nodes with positive excess) |
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| 226 | std::vector<Node> _excess_nodes; |
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| 227 | // The deficit nodes (i.e. nodes with negative excess) |
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| 228 | std::vector<Node> _deficit_nodes; |
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[2440] | 229 | |
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[2574] | 230 | // The delta parameter used for capacity scaling |
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| 231 | Capacity _delta; |
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| 232 | // The maximum number of phases |
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| 233 | int _phase_num; |
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[2440] | 234 | |
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[2574] | 235 | // The pred edge map |
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| 236 | PredMap _pred; |
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| 237 | // Implementation of the Dijkstra algorithm for finding augmenting |
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| 238 | // shortest paths in the residual network |
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[2581] | 239 | ResidualDijkstra *_dijkstra; |
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[2440] | 240 | |
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[2581] | 241 | public: |
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[2440] | 242 | |
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[2581] | 243 | /// \brief General constructor (with lower bounds). |
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[2440] | 244 | /// |
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[2581] | 245 | /// General constructor (with lower bounds). |
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[2440] | 246 | /// |
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[2574] | 247 | /// \param graph The directed graph the algorithm runs on. |
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| 248 | /// \param lower The lower bounds of the edges. |
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| 249 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 250 | /// \param cost The cost (length) values of the edges. |
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| 251 | /// \param supply The supply values of the nodes (signed). |
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| 252 | CapacityScaling( const Graph &graph, |
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| 253 | const LowerMap &lower, |
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| 254 | const CapacityMap &capacity, |
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| 255 | const CostMap &cost, |
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| 256 | const SupplyMap &supply ) : |
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| 257 | _graph(graph), _lower(&lower), _capacity(graph), _cost(cost), |
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[2581] | 258 | _supply(graph), _flow(0), _local_flow(false), |
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| 259 | _potential(0), _local_potential(false), |
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| 260 | _res_cap(graph), _excess(graph), _pred(graph) |
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[2440] | 261 | { |
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[2556] | 262 | // Removing non-zero lower bounds |
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[2574] | 263 | _capacity = subMap(capacity, lower); |
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| 264 | _res_cap = _capacity; |
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[2440] | 265 | Supply sum = 0; |
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[2574] | 266 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 267 | Supply s = supply[n]; |
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| 268 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 269 | s += lower[e]; |
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| 270 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 271 | s -= lower[e]; |
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| 272 | _supply[n] = s; |
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[2535] | 273 | sum += s; |
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[2440] | 274 | } |
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[2574] | 275 | _valid_supply = sum == 0; |
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[2440] | 276 | } |
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| 277 | |
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[2581] | 278 | /// \brief General constructor (without lower bounds). |
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[2440] | 279 | /// |
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[2581] | 280 | /// General constructor (without lower bounds). |
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[2440] | 281 | /// |
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[2574] | 282 | /// \param graph The directed graph the algorithm runs on. |
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| 283 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 284 | /// \param cost The cost (length) values of the edges. |
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| 285 | /// \param supply The supply values of the nodes (signed). |
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| 286 | CapacityScaling( const Graph &graph, |
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| 287 | const CapacityMap &capacity, |
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| 288 | const CostMap &cost, |
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| 289 | const SupplyMap &supply ) : |
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| 290 | _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost), |
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[2581] | 291 | _supply(supply), _flow(0), _local_flow(false), |
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| 292 | _potential(0), _local_potential(false), |
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| 293 | _res_cap(capacity), _excess(graph), _pred(graph) |
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[2440] | 294 | { |
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| 295 | // Checking the sum of supply values |
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| 296 | Supply sum = 0; |
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[2574] | 297 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
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| 298 | _valid_supply = sum == 0; |
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[2440] | 299 | } |
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| 300 | |
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[2581] | 301 | /// \brief Simple constructor (with lower bounds). |
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[2440] | 302 | /// |
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[2581] | 303 | /// Simple constructor (with lower bounds). |
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[2440] | 304 | /// |
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[2574] | 305 | /// \param graph The directed graph the algorithm runs on. |
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| 306 | /// \param lower The lower bounds of the edges. |
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| 307 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 308 | /// \param cost The cost (length) values of the edges. |
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| 309 | /// \param s The source node. |
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| 310 | /// \param t The target node. |
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| 311 | /// \param flow_value The required amount of flow from node \c s |
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| 312 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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| 313 | CapacityScaling( const Graph &graph, |
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| 314 | const LowerMap &lower, |
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| 315 | const CapacityMap &capacity, |
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| 316 | const CostMap &cost, |
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| 317 | Node s, Node t, |
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| 318 | Supply flow_value ) : |
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| 319 | _graph(graph), _lower(&lower), _capacity(graph), _cost(cost), |
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[2581] | 320 | _supply(graph), _flow(0), _local_flow(false), |
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| 321 | _potential(0), _local_potential(false), |
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| 322 | _res_cap(graph), _excess(graph), _pred(graph) |
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[2440] | 323 | { |
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[2556] | 324 | // Removing non-zero lower bounds |
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[2574] | 325 | _capacity = subMap(capacity, lower); |
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| 326 | _res_cap = _capacity; |
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| 327 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 328 | Supply sum = 0; |
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| 329 | if (n == s) sum = flow_value; |
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| 330 | if (n == t) sum = -flow_value; |
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| 331 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 332 | sum += lower[e]; |
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| 333 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) |
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| 334 | sum -= lower[e]; |
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| 335 | _supply[n] = sum; |
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[2440] | 336 | } |
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[2574] | 337 | _valid_supply = true; |
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[2440] | 338 | } |
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| 339 | |
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[2581] | 340 | /// \brief Simple constructor (without lower bounds). |
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[2440] | 341 | /// |
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[2581] | 342 | /// Simple constructor (without lower bounds). |
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[2440] | 343 | /// |
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[2574] | 344 | /// \param graph The directed graph the algorithm runs on. |
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| 345 | /// \param capacity The capacities (upper bounds) of the edges. |
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| 346 | /// \param cost The cost (length) values of the edges. |
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| 347 | /// \param s The source node. |
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| 348 | /// \param t The target node. |
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| 349 | /// \param flow_value The required amount of flow from node \c s |
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| 350 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
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| 351 | CapacityScaling( const Graph &graph, |
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| 352 | const CapacityMap &capacity, |
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| 353 | const CostMap &cost, |
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| 354 | Node s, Node t, |
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| 355 | Supply flow_value ) : |
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| 356 | _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost), |
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[2581] | 357 | _supply(graph, 0), _flow(0), _local_flow(false), |
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| 358 | _potential(0), _local_potential(false), |
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| 359 | _res_cap(capacity), _excess(graph), _pred(graph) |
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[2440] | 360 | { |
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[2574] | 361 | _supply[s] = flow_value; |
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| 362 | _supply[t] = -flow_value; |
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| 363 | _valid_supply = true; |
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[2440] | 364 | } |
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| 365 | |
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[2581] | 366 | /// Destructor. |
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| 367 | ~CapacityScaling() { |
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| 368 | if (_local_flow) delete _flow; |
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| 369 | if (_local_potential) delete _potential; |
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| 370 | delete _dijkstra; |
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| 371 | } |
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| 372 | |
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[2620] | 373 | /// \brief Set the flow map. |
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[2581] | 374 | /// |
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[2620] | 375 | /// Set the flow map. |
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[2581] | 376 | /// |
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| 377 | /// \return \c (*this) |
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| 378 | CapacityScaling& flowMap(FlowMap &map) { |
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| 379 | if (_local_flow) { |
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| 380 | delete _flow; |
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| 381 | _local_flow = false; |
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| 382 | } |
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| 383 | _flow = ↦ |
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| 384 | return *this; |
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| 385 | } |
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| 386 | |
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[2620] | 387 | /// \brief Set the potential map. |
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[2581] | 388 | /// |
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[2620] | 389 | /// Set the potential map. |
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[2581] | 390 | /// |
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| 391 | /// \return \c (*this) |
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| 392 | CapacityScaling& potentialMap(PotentialMap &map) { |
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| 393 | if (_local_potential) { |
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| 394 | delete _potential; |
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| 395 | _local_potential = false; |
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| 396 | } |
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| 397 | _potential = ↦ |
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| 398 | return *this; |
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| 399 | } |
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| 400 | |
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| 401 | /// \name Execution control |
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| 402 | |
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| 403 | /// @{ |
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| 404 | |
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[2620] | 405 | /// \brief Run the algorithm. |
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[2556] | 406 | /// |
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[2620] | 407 | /// This function runs the algorithm. |
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[2556] | 408 | /// |
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[2574] | 409 | /// \param scaling Enable or disable capacity scaling. |
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[2556] | 410 | /// If the maximum edge capacity and/or the amount of total supply |
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[2574] | 411 | /// is rather small, the algorithm could be slightly faster without |
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[2556] | 412 | /// scaling. |
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| 413 | /// |
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| 414 | /// \return \c true if a feasible flow can be found. |
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[2574] | 415 | bool run(bool scaling = true) { |
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| 416 | return init(scaling) && start(); |
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[2556] | 417 | } |
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| 418 | |
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[2581] | 419 | /// @} |
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| 420 | |
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| 421 | /// \name Query Functions |
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[2620] | 422 | /// The results of the algorithm can be obtained using these |
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| 423 | /// functions.\n |
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| 424 | /// \ref lemon::CapacityScaling::run() "run()" must be called before |
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| 425 | /// using them. |
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[2581] | 426 | |
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| 427 | /// @{ |
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| 428 | |
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[2620] | 429 | /// \brief Return a const reference to the edge map storing the |
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[2574] | 430 | /// found flow. |
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[2440] | 431 | /// |
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[2620] | 432 | /// Return a const reference to the edge map storing the found flow. |
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[2440] | 433 | /// |
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| 434 | /// \pre \ref run() must be called before using this function. |
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| 435 | const FlowMap& flowMap() const { |
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[2581] | 436 | return *_flow; |
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[2440] | 437 | } |
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| 438 | |
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[2620] | 439 | /// \brief Return a const reference to the node map storing the |
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[2574] | 440 | /// found potentials (the dual solution). |
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[2440] | 441 | /// |
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[2620] | 442 | /// Return a const reference to the node map storing the found |
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[2574] | 443 | /// potentials (the dual solution). |
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[2440] | 444 | /// |
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| 445 | /// \pre \ref run() must be called before using this function. |
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| 446 | const PotentialMap& potentialMap() const { |
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[2581] | 447 | return *_potential; |
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| 448 | } |
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| 449 | |
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[2620] | 450 | /// \brief Return the flow on the given edge. |
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[2581] | 451 | /// |
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[2620] | 452 | /// Return the flow on the given edge. |
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[2581] | 453 | /// |
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| 454 | /// \pre \ref run() must be called before using this function. |
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| 455 | Capacity flow(const Edge& edge) const { |
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| 456 | return (*_flow)[edge]; |
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| 457 | } |
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| 458 | |
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[2620] | 459 | /// \brief Return the potential of the given node. |
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[2581] | 460 | /// |
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[2620] | 461 | /// Return the potential of the given node. |
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[2581] | 462 | /// |
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| 463 | /// \pre \ref run() must be called before using this function. |
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| 464 | Cost potential(const Node& node) const { |
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| 465 | return (*_potential)[node]; |
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[2440] | 466 | } |
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| 467 | |
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[2620] | 468 | /// \brief Return the total cost of the found flow. |
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[2440] | 469 | /// |
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[2620] | 470 | /// Return the total cost of the found flow. The complexity of the |
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[2440] | 471 | /// function is \f$ O(e) \f$. |
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| 472 | /// |
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| 473 | /// \pre \ref run() must be called before using this function. |
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| 474 | Cost totalCost() const { |
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| 475 | Cost c = 0; |
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[2574] | 476 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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[2581] | 477 | c += (*_flow)[e] * _cost[e]; |
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[2440] | 478 | return c; |
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| 479 | } |
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| 480 | |
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[2581] | 481 | /// @} |
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| 482 | |
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[2574] | 483 | private: |
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[2440] | 484 | |
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[2620] | 485 | /// Initialize the algorithm. |
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[2574] | 486 | bool init(bool scaling) { |
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| 487 | if (!_valid_supply) return false; |
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[2581] | 488 | |
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| 489 | // Initializing maps |
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| 490 | if (!_flow) { |
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| 491 | _flow = new FlowMap(_graph); |
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| 492 | _local_flow = true; |
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| 493 | } |
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| 494 | if (!_potential) { |
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| 495 | _potential = new PotentialMap(_graph); |
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| 496 | _local_potential = true; |
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| 497 | } |
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| 498 | for (EdgeIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0; |
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| 499 | for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0; |
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[2574] | 500 | _excess = _supply; |
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[2440] | 501 | |
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[2581] | 502 | _dijkstra = new ResidualDijkstra( _graph, *_flow, _res_cap, _cost, |
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| 503 | _excess, *_potential, _pred ); |
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| 504 | |
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| 505 | // Initializing delta value |
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[2574] | 506 | if (scaling) { |
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[2535] | 507 | // With scaling |
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| 508 | Supply max_sup = 0, max_dem = 0; |
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[2574] | 509 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 510 | if ( _supply[n] > max_sup) max_sup = _supply[n]; |
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| 511 | if (-_supply[n] > max_dem) max_dem = -_supply[n]; |
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[2535] | 512 | } |
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[2588] | 513 | Capacity max_cap = 0; |
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| 514 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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| 515 | if (_capacity[e] > max_cap) max_cap = _capacity[e]; |
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| 516 | } |
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| 517 | max_sup = std::min(std::min(max_sup, max_dem), max_cap); |
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[2574] | 518 | _phase_num = 0; |
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| 519 | for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) |
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| 520 | ++_phase_num; |
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[2535] | 521 | } else { |
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| 522 | // Without scaling |
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[2574] | 523 | _delta = 1; |
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[2440] | 524 | } |
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[2581] | 525 | |
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[2440] | 526 | return true; |
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| 527 | } |
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| 528 | |
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[2535] | 529 | bool start() { |
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[2574] | 530 | if (_delta > 1) |
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[2535] | 531 | return startWithScaling(); |
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| 532 | else |
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| 533 | return startWithoutScaling(); |
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| 534 | } |
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| 535 | |
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[2620] | 536 | /// Execute the capacity scaling algorithm. |
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[2535] | 537 | bool startWithScaling() { |
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| 538 | // Processing capacity scaling phases |
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| 539 | Node s, t; |
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| 540 | int phase_cnt = 0; |
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| 541 | int factor = 4; |
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| 542 | while (true) { |
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| 543 | // Saturating all edges not satisfying the optimality condition |
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[2574] | 544 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
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| 545 | Node u = _graph.source(e), v = _graph.target(e); |
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[2581] | 546 | Cost c = _cost[e] + (*_potential)[u] - (*_potential)[v]; |
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[2574] | 547 | if (c < 0 && _res_cap[e] >= _delta) { |
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| 548 | _excess[u] -= _res_cap[e]; |
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| 549 | _excess[v] += _res_cap[e]; |
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[2581] | 550 | (*_flow)[e] = _capacity[e]; |
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[2574] | 551 | _res_cap[e] = 0; |
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[2535] | 552 | } |
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[2581] | 553 | else if (c > 0 && (*_flow)[e] >= _delta) { |
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| 554 | _excess[u] += (*_flow)[e]; |
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| 555 | _excess[v] -= (*_flow)[e]; |
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| 556 | (*_flow)[e] = 0; |
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[2574] | 557 | _res_cap[e] = _capacity[e]; |
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[2535] | 558 | } |
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| 559 | } |
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| 560 | |
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| 561 | // Finding excess nodes and deficit nodes |
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[2574] | 562 | _excess_nodes.clear(); |
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| 563 | _deficit_nodes.clear(); |
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| 564 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 565 | if (_excess[n] >= _delta) _excess_nodes.push_back(n); |
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| 566 | if (_excess[n] <= -_delta) _deficit_nodes.push_back(n); |
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[2535] | 567 | } |
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[2620] | 568 | int next_node = 0, next_def_node = 0; |
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[2535] | 569 | |
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| 570 | // Finding augmenting shortest paths |
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[2574] | 571 | while (next_node < int(_excess_nodes.size())) { |
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[2535] | 572 | // Checking deficit nodes |
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[2574] | 573 | if (_delta > 1) { |
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[2535] | 574 | bool delta_deficit = false; |
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[2620] | 575 | for ( ; next_def_node < int(_deficit_nodes.size()); |
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| 576 | ++next_def_node ) { |
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| 577 | if (_excess[_deficit_nodes[next_def_node]] <= -_delta) { |
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[2535] | 578 | delta_deficit = true; |
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| 579 | break; |
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| 580 | } |
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| 581 | } |
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| 582 | if (!delta_deficit) break; |
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| 583 | } |
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| 584 | |
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| 585 | // Running Dijkstra |
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[2574] | 586 | s = _excess_nodes[next_node]; |
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[2581] | 587 | if ((t = _dijkstra->run(s, _delta)) == INVALID) { |
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[2574] | 588 | if (_delta > 1) { |
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[2535] | 589 | ++next_node; |
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| 590 | continue; |
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| 591 | } |
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| 592 | return false; |
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| 593 | } |
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| 594 | |
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| 595 | // Augmenting along a shortest path from s to t. |
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[2588] | 596 | Capacity d = std::min(_excess[s], -_excess[t]); |
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[2535] | 597 | Node u = t; |
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| 598 | Edge e; |
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[2574] | 599 | if (d > _delta) { |
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| 600 | while ((e = _pred[u]) != INVALID) { |
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[2535] | 601 | Capacity rc; |
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[2574] | 602 | if (u == _graph.target(e)) { |
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| 603 | rc = _res_cap[e]; |
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| 604 | u = _graph.source(e); |
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[2535] | 605 | } else { |
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[2581] | 606 | rc = (*_flow)[e]; |
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[2574] | 607 | u = _graph.target(e); |
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[2535] | 608 | } |
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| 609 | if (rc < d) d = rc; |
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| 610 | } |
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| 611 | } |
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| 612 | u = t; |
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[2574] | 613 | while ((e = _pred[u]) != INVALID) { |
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| 614 | if (u == _graph.target(e)) { |
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[2581] | 615 | (*_flow)[e] += d; |
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[2574] | 616 | _res_cap[e] -= d; |
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| 617 | u = _graph.source(e); |
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[2535] | 618 | } else { |
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[2581] | 619 | (*_flow)[e] -= d; |
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[2574] | 620 | _res_cap[e] += d; |
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| 621 | u = _graph.target(e); |
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[2535] | 622 | } |
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| 623 | } |
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[2574] | 624 | _excess[s] -= d; |
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| 625 | _excess[t] += d; |
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[2535] | 626 | |
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[2574] | 627 | if (_excess[s] < _delta) ++next_node; |
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[2535] | 628 | } |
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| 629 | |
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[2574] | 630 | if (_delta == 1) break; |
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| 631 | if (++phase_cnt > _phase_num / 4) factor = 2; |
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| 632 | _delta = _delta <= factor ? 1 : _delta / factor; |
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[2535] | 633 | } |
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| 634 | |
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[2556] | 635 | // Handling non-zero lower bounds |
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[2574] | 636 | if (_lower) { |
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| 637 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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[2581] | 638 | (*_flow)[e] += (*_lower)[e]; |
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[2535] | 639 | } |
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| 640 | return true; |
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| 641 | } |
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| 642 | |
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[2620] | 643 | /// Execute the successive shortest path algorithm. |
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[2535] | 644 | bool startWithoutScaling() { |
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[2440] | 645 | // Finding excess nodes |
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[2574] | 646 | for (NodeIt n(_graph); n != INVALID; ++n) |
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| 647 | if (_excess[n] > 0) _excess_nodes.push_back(n); |
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| 648 | if (_excess_nodes.size() == 0) return true; |
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[2556] | 649 | int next_node = 0; |
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[2440] | 650 | |
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[2457] | 651 | // Finding shortest paths |
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[2535] | 652 | Node s, t; |
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[2574] | 653 | while ( _excess[_excess_nodes[next_node]] > 0 || |
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| 654 | ++next_node < int(_excess_nodes.size()) ) |
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[2440] | 655 | { |
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[2535] | 656 | // Running Dijkstra |
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[2574] | 657 | s = _excess_nodes[next_node]; |
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[2589] | 658 | if ((t = _dijkstra->run(s)) == INVALID) return false; |
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[2440] | 659 | |
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[2535] | 660 | // Augmenting along a shortest path from s to t |
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[2588] | 661 | Capacity d = std::min(_excess[s], -_excess[t]); |
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[2535] | 662 | Node u = t; |
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| 663 | Edge e; |
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[2588] | 664 | if (d > 1) { |
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| 665 | while ((e = _pred[u]) != INVALID) { |
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| 666 | Capacity rc; |
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| 667 | if (u == _graph.target(e)) { |
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| 668 | rc = _res_cap[e]; |
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| 669 | u = _graph.source(e); |
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| 670 | } else { |
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| 671 | rc = (*_flow)[e]; |
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| 672 | u = _graph.target(e); |
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| 673 | } |
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| 674 | if (rc < d) d = rc; |
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[2535] | 675 | } |
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| 676 | } |
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| 677 | u = t; |
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[2574] | 678 | while ((e = _pred[u]) != INVALID) { |
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| 679 | if (u == _graph.target(e)) { |
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[2581] | 680 | (*_flow)[e] += d; |
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[2574] | 681 | _res_cap[e] -= d; |
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| 682 | u = _graph.source(e); |
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[2535] | 683 | } else { |
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[2581] | 684 | (*_flow)[e] -= d; |
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[2574] | 685 | _res_cap[e] += d; |
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| 686 | u = _graph.target(e); |
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[2535] | 687 | } |
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| 688 | } |
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[2574] | 689 | _excess[s] -= d; |
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| 690 | _excess[t] += d; |
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[2440] | 691 | } |
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| 692 | |
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[2556] | 693 | // Handling non-zero lower bounds |
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[2574] | 694 | if (_lower) { |
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| 695 | for (EdgeIt e(_graph); e != INVALID; ++e) |
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[2581] | 696 | (*_flow)[e] += (*_lower)[e]; |
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[2440] | 697 | } |
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| 698 | return true; |
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| 699 | } |
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| 700 | |
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| 701 | }; //class CapacityScaling |
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| 702 | |
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| 703 | ///@} |
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| 704 | |
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| 705 | } //namespace lemon |
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| 706 | |
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| 707 | #endif //LEMON_CAPACITY_SCALING_H |
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