[2360] | 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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[2391] | 5 | * Copyright (C) 2003-2007 |
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[2360] | 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_CSP_H |
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| 20 | #define LEMON_CSP_H |
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| 21 | |
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[2376] | 22 | ///\ingroup approx |
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[2360] | 23 | ///\file |
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| 24 | ///\brief Algorithm for the Resource Constrained Shortest Path problem. |
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| 25 | /// |
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| 26 | /// |
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| 27 | ///\todo dijkstraZero() solution should be revised. |
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| 28 | |
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| 29 | #include <lemon/list_graph.h> |
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| 30 | #include <lemon/graph_utils.h> |
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| 31 | #include <lemon/error.h> |
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| 32 | #include <lemon/maps.h> |
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| 33 | #include <lemon/tolerance.h> |
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| 34 | #include <lemon/dijkstra.h> |
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| 35 | #include <lemon/path.h> |
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| 36 | #include <lemon/counter.h> |
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| 37 | namespace lemon { |
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[2377] | 38 | |
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| 39 | ///\ingroup approx |
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[2360] | 40 | |
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| 41 | ///Algorithms for the Resource Constrained Shortest Path Problem |
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| 42 | |
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[2373] | 43 | ///The Resource Constrained Shortest (Least Cost) Path problem is the |
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| 44 | ///following. We are given a directed graph with two additive weightings |
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| 45 | ///on the edges, referred as \e cost and \e delay. In addition, |
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| 46 | ///a source and a destination node \e s and \e t and a delay |
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| 47 | ///constraint \e D is given. A path \e p is called \e feasible |
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| 48 | ///if <em>delay(p)\<=D</em>. Then, the task is to find the least cost |
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| 49 | ///feasible path. |
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[2360] | 50 | /// |
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| 51 | template<class Graph, |
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| 52 | class CM=typename Graph:: template EdgeMap<double>, |
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| 53 | class DM=CM> |
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| 54 | class ConstrainedShortestPath |
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| 55 | { |
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| 56 | public: |
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| 57 | |
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| 58 | GRAPH_TYPEDEFS(typename Graph); |
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| 59 | |
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| 60 | typedef SimplePath<Graph> Path; |
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| 61 | |
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[2401] | 62 | private: |
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| 63 | |
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| 64 | const Graph &_g; |
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[2360] | 65 | Tolerance<double> tol; |
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| 66 | |
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[2401] | 67 | const CM &_cost; |
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| 68 | const DM &_delay; |
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[2360] | 69 | |
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| 70 | class CoMap |
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| 71 | { |
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[2401] | 72 | const CM &_cost; |
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| 73 | const DM &_delay; |
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[2360] | 74 | double _lambda; |
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| 75 | public: |
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| 76 | typedef typename CM::Key Key; |
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| 77 | typedef double Value; |
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[2401] | 78 | CoMap(const CM &c, const DM &d) :_cost(c), _delay(d), _lambda(0) {} |
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[2360] | 79 | double lambda() const { return _lambda; } |
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| 80 | void lambda(double l) { _lambda=l; } |
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| 81 | Value operator[](Key &e) const |
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| 82 | { |
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| 83 | return _cost[e]+_lambda*_delay[e]; |
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| 84 | } |
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[2401] | 85 | }; |
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| 86 | |
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| 87 | CoMap _co_map; |
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[2360] | 88 | |
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| 89 | |
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| 90 | Dijkstra<Graph, CoMap> _dij; |
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[2401] | 91 | |
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| 92 | public: |
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| 93 | |
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[2360] | 94 | ///\e |
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| 95 | |
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| 96 | ///\e |
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| 97 | /// |
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[2401] | 98 | ConstrainedShortestPath(const Graph &g, const CM &ct, const DM &dl) |
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[2386] | 99 | : _g(g), _cost(ct), _delay(dl), |
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[2401] | 100 | _co_map(ct, dl), _dij(_g,_co_map) {} |
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[2360] | 101 | |
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| 102 | |
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| 103 | ///Compute the cost of a path |
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[2401] | 104 | double cost(const Path &p) const |
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[2360] | 105 | { |
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| 106 | double s=0; |
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| 107 | // Path r; |
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| 108 | for(typename Path::EdgeIt e(p);e!=INVALID;++e) s+=_cost[e]; |
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| 109 | return s; |
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| 110 | } |
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| 111 | |
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| 112 | ///Compute the delay of a path |
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[2401] | 113 | double delay(const Path &p) const |
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[2360] | 114 | { |
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| 115 | double s=0; |
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| 116 | for(typename Path::EdgeIt e(p);e!=INVALID;++e) s+=_delay[e]; |
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| 117 | return s; |
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| 118 | } |
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| 119 | |
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| 120 | ///Runs the LARAC algorithm |
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| 121 | |
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| 122 | ///This function runs a Lagrange relaxation based heuristic to find |
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| 123 | ///a delay constrained least cost path. |
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| 124 | ///\param s source node |
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| 125 | ///\param t target node |
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| 126 | ///\retval lo_bo a lower bound on the optimal solution |
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| 127 | ///\return the found path or an empty |
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| 128 | Path larac(Node s, Node t, double delta, double &lo_bo) |
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| 129 | { |
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| 130 | NoCounter cnt("LARAC iterations: "); |
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| 131 | double lambda=0; |
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| 132 | double cp,cq,dp,dq,cr,dr; |
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| 133 | Path p; |
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| 134 | Path q; |
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| 135 | Path r; |
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| 136 | { |
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| 137 | Dijkstra<Graph,CM> dij(_g,_cost); |
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| 138 | dij.run(s,t); |
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| 139 | cnt++; |
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| 140 | if(!dij.reached(t)) return Path(); |
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| 141 | p=dij.path(t); |
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| 142 | cp=cost(p); |
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| 143 | dp=delay(p); |
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| 144 | } |
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| 145 | if(delay(p)<=delta) return p; |
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| 146 | { |
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| 147 | Dijkstra<Graph,DM> dij(_g,_delay); |
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| 148 | dij.run(s,t); |
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| 149 | cnt++; |
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| 150 | q=dij.path(t); |
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| 151 | cq=cost(q); |
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| 152 | dq=delay(q); |
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| 153 | } |
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| 154 | if(delay(q)>delta) return Path(); |
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| 155 | while (true) { |
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| 156 | lambda=(cp-cq)/(dq-dp); |
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| 157 | _co_map.lambda(lambda); |
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| 158 | _dij.run(s,t); |
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| 159 | cnt++; |
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| 160 | r=_dij.path(t); |
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| 161 | cr=cost(r); |
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| 162 | dr=delay(r); |
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| 163 | if(!tol.less(cr+lambda*dr,cp+lambda*dp)) { |
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| 164 | lo_bo=cq+lambda*(dq-delta); |
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| 165 | return q; |
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| 166 | } |
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| 167 | else if(tol.less(dr,delta)) |
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| 168 | { |
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| 169 | q=r; |
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| 170 | cq=cr; |
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| 171 | dq=dr; |
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| 172 | } |
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| 173 | else if(tol.less(delta,dr)) |
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| 174 | { |
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| 175 | p=r; |
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| 176 | cp=cr; |
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| 177 | dp=dr; |
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| 178 | } |
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| 179 | else return r; |
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| 180 | } |
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| 181 | } |
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| 182 | }; |
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| 183 | |
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| 184 | |
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| 185 | } //END OF NAMESPACE LEMON |
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| 186 | |
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| 187 | #endif |
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