[765] | 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) 2003-2008 |
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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_KARP_H |
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| 20 | #define LEMON_KARP_H |
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| 21 | |
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[768] | 22 | /// \ingroup min_mean_cycle |
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[765] | 23 | /// |
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| 24 | /// \file |
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| 25 | /// \brief Karp's algorithm for finding a minimum mean cycle. |
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| 26 | |
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| 27 | #include <vector> |
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| 28 | #include <limits> |
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| 29 | #include <lemon/core.h> |
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| 30 | #include <lemon/path.h> |
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| 31 | #include <lemon/tolerance.h> |
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| 32 | #include <lemon/connectivity.h> |
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| 33 | |
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| 34 | namespace lemon { |
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| 35 | |
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| 36 | /// \brief Default traits class of Karp algorithm. |
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| 37 | /// |
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| 38 | /// Default traits class of Karp algorithm. |
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| 39 | /// \tparam GR The type of the digraph. |
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| 40 | /// \tparam LEN The type of the length map. |
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| 41 | /// It must conform to the \ref concepts::ReadMap "ReadMap" concept. |
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| 42 | #ifdef DOXYGEN |
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| 43 | template <typename GR, typename LEN> |
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| 44 | #else |
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| 45 | template <typename GR, typename LEN, |
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| 46 | bool integer = std::numeric_limits<typename LEN::Value>::is_integer> |
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| 47 | #endif |
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| 48 | struct KarpDefaultTraits |
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| 49 | { |
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| 50 | /// The type of the digraph |
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| 51 | typedef GR Digraph; |
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| 52 | /// The type of the length map |
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| 53 | typedef LEN LengthMap; |
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| 54 | /// The type of the arc lengths |
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| 55 | typedef typename LengthMap::Value Value; |
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| 56 | |
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| 57 | /// \brief The large value type used for internal computations |
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| 58 | /// |
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| 59 | /// The large value type used for internal computations. |
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| 60 | /// It is \c long \c long if the \c Value type is integer, |
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| 61 | /// otherwise it is \c double. |
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| 62 | /// \c Value must be convertible to \c LargeValue. |
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| 63 | typedef double LargeValue; |
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| 64 | |
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| 65 | /// The tolerance type used for internal computations |
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| 66 | typedef lemon::Tolerance<LargeValue> Tolerance; |
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| 67 | |
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| 68 | /// \brief The path type of the found cycles |
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| 69 | /// |
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| 70 | /// The path type of the found cycles. |
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| 71 | /// It must conform to the \ref lemon::concepts::Path "Path" concept |
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| 72 | /// and it must have an \c addBack() function. |
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| 73 | typedef lemon::Path<Digraph> Path; |
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| 74 | }; |
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| 75 | |
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| 76 | // Default traits class for integer value types |
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| 77 | template <typename GR, typename LEN> |
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| 78 | struct KarpDefaultTraits<GR, LEN, true> |
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| 79 | { |
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| 80 | typedef GR Digraph; |
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| 81 | typedef LEN LengthMap; |
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| 82 | typedef typename LengthMap::Value Value; |
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| 83 | #ifdef LEMON_HAVE_LONG_LONG |
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| 84 | typedef long long LargeValue; |
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| 85 | #else |
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| 86 | typedef long LargeValue; |
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| 87 | #endif |
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| 88 | typedef lemon::Tolerance<LargeValue> Tolerance; |
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| 89 | typedef lemon::Path<Digraph> Path; |
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| 90 | }; |
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| 91 | |
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| 92 | |
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[768] | 93 | /// \addtogroup min_mean_cycle |
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[765] | 94 | /// @{ |
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| 95 | |
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| 96 | /// \brief Implementation of Karp's algorithm for finding a minimum |
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| 97 | /// mean cycle. |
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| 98 | /// |
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| 99 | /// This class implements Karp's algorithm for finding a directed |
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[771] | 100 | /// cycle of minimum mean length (cost) in a digraph |
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| 101 | /// \ref amo93networkflows, \ref dasdan98minmeancycle. |
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[768] | 102 | /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e). |
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[765] | 103 | /// |
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| 104 | /// \tparam GR The type of the digraph the algorithm runs on. |
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| 105 | /// \tparam LEN The type of the length map. The default |
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| 106 | /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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| 107 | #ifdef DOXYGEN |
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| 108 | template <typename GR, typename LEN, typename TR> |
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| 109 | #else |
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| 110 | template < typename GR, |
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| 111 | typename LEN = typename GR::template ArcMap<int>, |
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| 112 | typename TR = KarpDefaultTraits<GR, LEN> > |
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| 113 | #endif |
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| 114 | class Karp |
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| 115 | { |
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| 116 | public: |
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| 117 | |
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| 118 | /// The type of the digraph |
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| 119 | typedef typename TR::Digraph Digraph; |
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| 120 | /// The type of the length map |
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| 121 | typedef typename TR::LengthMap LengthMap; |
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| 122 | /// The type of the arc lengths |
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| 123 | typedef typename TR::Value Value; |
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| 124 | |
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| 125 | /// \brief The large value type |
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| 126 | /// |
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| 127 | /// The large value type used for internal computations. |
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| 128 | /// Using the \ref KarpDefaultTraits "default traits class", |
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| 129 | /// it is \c long \c long if the \c Value type is integer, |
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| 130 | /// otherwise it is \c double. |
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| 131 | typedef typename TR::LargeValue LargeValue; |
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| 132 | |
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| 133 | /// The tolerance type |
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| 134 | typedef typename TR::Tolerance Tolerance; |
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| 135 | |
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| 136 | /// \brief The path type of the found cycles |
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| 137 | /// |
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| 138 | /// The path type of the found cycles. |
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| 139 | /// Using the \ref KarpDefaultTraits "default traits class", |
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| 140 | /// it is \ref lemon::Path "Path<Digraph>". |
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| 141 | typedef typename TR::Path Path; |
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| 142 | |
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| 143 | /// The \ref KarpDefaultTraits "traits class" of the algorithm |
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| 144 | typedef TR Traits; |
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| 145 | |
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| 146 | private: |
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| 147 | |
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| 148 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 149 | |
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| 150 | // Data sturcture for path data |
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| 151 | struct PathData |
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| 152 | { |
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| 153 | LargeValue dist; |
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| 154 | Arc pred; |
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[767] | 155 | PathData(LargeValue d, Arc p = INVALID) : |
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| 156 | dist(d), pred(p) {} |
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[765] | 157 | }; |
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| 158 | |
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| 159 | typedef typename Digraph::template NodeMap<std::vector<PathData> > |
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| 160 | PathDataNodeMap; |
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| 161 | |
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| 162 | private: |
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| 163 | |
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| 164 | // The digraph the algorithm runs on |
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| 165 | const Digraph &_gr; |
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| 166 | // The length of the arcs |
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| 167 | const LengthMap &_length; |
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| 168 | |
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| 169 | // Data for storing the strongly connected components |
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| 170 | int _comp_num; |
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| 171 | typename Digraph::template NodeMap<int> _comp; |
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| 172 | std::vector<std::vector<Node> > _comp_nodes; |
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| 173 | std::vector<Node>* _nodes; |
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| 174 | typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs; |
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| 175 | |
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| 176 | // Data for the found cycle |
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| 177 | LargeValue _cycle_length; |
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| 178 | int _cycle_size; |
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| 179 | Node _cycle_node; |
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| 180 | |
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| 181 | Path *_cycle_path; |
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| 182 | bool _local_path; |
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| 183 | |
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| 184 | // Node map for storing path data |
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| 185 | PathDataNodeMap _data; |
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| 186 | // The processed nodes in the last round |
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| 187 | std::vector<Node> _process; |
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| 188 | |
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| 189 | Tolerance _tolerance; |
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[767] | 190 | |
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| 191 | // Infinite constant |
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| 192 | const LargeValue INF; |
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[765] | 193 | |
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| 194 | public: |
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| 195 | |
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| 196 | /// \name Named Template Parameters |
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| 197 | /// @{ |
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| 198 | |
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| 199 | template <typename T> |
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| 200 | struct SetLargeValueTraits : public Traits { |
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| 201 | typedef T LargeValue; |
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| 202 | typedef lemon::Tolerance<T> Tolerance; |
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| 203 | }; |
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| 204 | |
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| 205 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 206 | /// \c LargeValue type. |
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| 207 | /// |
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| 208 | /// \ref named-templ-param "Named parameter" for setting \c LargeValue |
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| 209 | /// type. It is used for internal computations in the algorithm. |
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| 210 | template <typename T> |
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| 211 | struct SetLargeValue |
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| 212 | : public Karp<GR, LEN, SetLargeValueTraits<T> > { |
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| 213 | typedef Karp<GR, LEN, SetLargeValueTraits<T> > Create; |
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| 214 | }; |
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| 215 | |
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| 216 | template <typename T> |
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| 217 | struct SetPathTraits : public Traits { |
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| 218 | typedef T Path; |
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| 219 | }; |
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| 220 | |
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| 221 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 222 | /// \c %Path type. |
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| 223 | /// |
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| 224 | /// \ref named-templ-param "Named parameter" for setting the \c %Path |
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| 225 | /// type of the found cycles. |
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| 226 | /// It must conform to the \ref lemon::concepts::Path "Path" concept |
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| 227 | /// and it must have an \c addFront() function. |
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| 228 | template <typename T> |
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| 229 | struct SetPath |
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| 230 | : public Karp<GR, LEN, SetPathTraits<T> > { |
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| 231 | typedef Karp<GR, LEN, SetPathTraits<T> > Create; |
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| 232 | }; |
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| 233 | |
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| 234 | /// @} |
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| 235 | |
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| 236 | public: |
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| 237 | |
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| 238 | /// \brief Constructor. |
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| 239 | /// |
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| 240 | /// The constructor of the class. |
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| 241 | /// |
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| 242 | /// \param digraph The digraph the algorithm runs on. |
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| 243 | /// \param length The lengths (costs) of the arcs. |
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| 244 | Karp( const Digraph &digraph, |
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| 245 | const LengthMap &length ) : |
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| 246 | _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph), |
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| 247 | _cycle_length(0), _cycle_size(1), _cycle_node(INVALID), |
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[767] | 248 | _cycle_path(NULL), _local_path(false), _data(digraph), |
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| 249 | INF(std::numeric_limits<LargeValue>::has_infinity ? |
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| 250 | std::numeric_limits<LargeValue>::infinity() : |
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| 251 | std::numeric_limits<LargeValue>::max()) |
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[765] | 252 | {} |
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| 253 | |
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| 254 | /// Destructor. |
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| 255 | ~Karp() { |
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| 256 | if (_local_path) delete _cycle_path; |
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| 257 | } |
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| 258 | |
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| 259 | /// \brief Set the path structure for storing the found cycle. |
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| 260 | /// |
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| 261 | /// This function sets an external path structure for storing the |
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| 262 | /// found cycle. |
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| 263 | /// |
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| 264 | /// If you don't call this function before calling \ref run() or |
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| 265 | /// \ref findMinMean(), it will allocate a local \ref Path "path" |
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| 266 | /// structure. The destuctor deallocates this automatically |
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| 267 | /// allocated object, of course. |
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| 268 | /// |
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| 269 | /// \note The algorithm calls only the \ref lemon::Path::addFront() |
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| 270 | /// "addFront()" function of the given path structure. |
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| 271 | /// |
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| 272 | /// \return <tt>(*this)</tt> |
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| 273 | Karp& cycle(Path &path) { |
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| 274 | if (_local_path) { |
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| 275 | delete _cycle_path; |
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| 276 | _local_path = false; |
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| 277 | } |
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| 278 | _cycle_path = &path; |
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| 279 | return *this; |
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| 280 | } |
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| 281 | |
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[769] | 282 | /// \brief Set the tolerance used by the algorithm. |
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| 283 | /// |
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| 284 | /// This function sets the tolerance object used by the algorithm. |
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| 285 | /// |
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| 286 | /// \return <tt>(*this)</tt> |
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| 287 | Karp& tolerance(const Tolerance& tolerance) { |
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| 288 | _tolerance = tolerance; |
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| 289 | return *this; |
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| 290 | } |
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| 291 | |
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| 292 | /// \brief Return a const reference to the tolerance. |
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| 293 | /// |
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| 294 | /// This function returns a const reference to the tolerance object |
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| 295 | /// used by the algorithm. |
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| 296 | const Tolerance& tolerance() const { |
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| 297 | return _tolerance; |
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| 298 | } |
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| 299 | |
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[765] | 300 | /// \name Execution control |
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| 301 | /// The simplest way to execute the algorithm is to call the \ref run() |
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| 302 | /// function.\n |
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| 303 | /// If you only need the minimum mean length, you may call |
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| 304 | /// \ref findMinMean(). |
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| 305 | |
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| 306 | /// @{ |
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| 307 | |
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| 308 | /// \brief Run the algorithm. |
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| 309 | /// |
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| 310 | /// This function runs the algorithm. |
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| 311 | /// It can be called more than once (e.g. if the underlying digraph |
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| 312 | /// and/or the arc lengths have been modified). |
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| 313 | /// |
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| 314 | /// \return \c true if a directed cycle exists in the digraph. |
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| 315 | /// |
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| 316 | /// \note <tt>mmc.run()</tt> is just a shortcut of the following code. |
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| 317 | /// \code |
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| 318 | /// return mmc.findMinMean() && mmc.findCycle(); |
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| 319 | /// \endcode |
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| 320 | bool run() { |
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| 321 | return findMinMean() && findCycle(); |
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| 322 | } |
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| 323 | |
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| 324 | /// \brief Find the minimum cycle mean. |
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| 325 | /// |
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| 326 | /// This function finds the minimum mean length of the directed |
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| 327 | /// cycles in the digraph. |
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| 328 | /// |
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| 329 | /// \return \c true if a directed cycle exists in the digraph. |
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| 330 | bool findMinMean() { |
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| 331 | // Initialization and find strongly connected components |
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| 332 | init(); |
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| 333 | findComponents(); |
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| 334 | |
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| 335 | // Find the minimum cycle mean in the components |
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| 336 | for (int comp = 0; comp < _comp_num; ++comp) { |
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| 337 | if (!initComponent(comp)) continue; |
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| 338 | processRounds(); |
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| 339 | updateMinMean(); |
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| 340 | } |
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| 341 | return (_cycle_node != INVALID); |
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| 342 | } |
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| 343 | |
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| 344 | /// \brief Find a minimum mean directed cycle. |
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| 345 | /// |
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| 346 | /// This function finds a directed cycle of minimum mean length |
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| 347 | /// in the digraph using the data computed by findMinMean(). |
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| 348 | /// |
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| 349 | /// \return \c true if a directed cycle exists in the digraph. |
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| 350 | /// |
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| 351 | /// \pre \ref findMinMean() must be called before using this function. |
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| 352 | bool findCycle() { |
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| 353 | if (_cycle_node == INVALID) return false; |
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| 354 | IntNodeMap reached(_gr, -1); |
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| 355 | int r = _data[_cycle_node].size(); |
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| 356 | Node u = _cycle_node; |
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| 357 | while (reached[u] < 0) { |
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| 358 | reached[u] = --r; |
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| 359 | u = _gr.source(_data[u][r].pred); |
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| 360 | } |
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| 361 | r = reached[u]; |
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| 362 | Arc e = _data[u][r].pred; |
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| 363 | _cycle_path->addFront(e); |
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| 364 | _cycle_length = _length[e]; |
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| 365 | _cycle_size = 1; |
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| 366 | Node v; |
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| 367 | while ((v = _gr.source(e)) != u) { |
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| 368 | e = _data[v][--r].pred; |
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| 369 | _cycle_path->addFront(e); |
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| 370 | _cycle_length += _length[e]; |
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| 371 | ++_cycle_size; |
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| 372 | } |
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| 373 | return true; |
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| 374 | } |
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| 375 | |
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| 376 | /// @} |
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| 377 | |
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| 378 | /// \name Query Functions |
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| 379 | /// The results of the algorithm can be obtained using these |
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| 380 | /// functions.\n |
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| 381 | /// The algorithm should be executed before using them. |
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| 382 | |
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| 383 | /// @{ |
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| 384 | |
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| 385 | /// \brief Return the total length of the found cycle. |
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| 386 | /// |
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| 387 | /// This function returns the total length of the found cycle. |
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| 388 | /// |
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| 389 | /// \pre \ref run() or \ref findMinMean() must be called before |
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| 390 | /// using this function. |
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| 391 | LargeValue cycleLength() const { |
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| 392 | return _cycle_length; |
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| 393 | } |
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| 394 | |
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| 395 | /// \brief Return the number of arcs on the found cycle. |
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| 396 | /// |
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| 397 | /// This function returns the number of arcs on the found cycle. |
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| 398 | /// |
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| 399 | /// \pre \ref run() or \ref findMinMean() must be called before |
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| 400 | /// using this function. |
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| 401 | int cycleArcNum() const { |
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| 402 | return _cycle_size; |
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| 403 | } |
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| 404 | |
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| 405 | /// \brief Return the mean length of the found cycle. |
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| 406 | /// |
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| 407 | /// This function returns the mean length of the found cycle. |
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| 408 | /// |
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| 409 | /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the |
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| 410 | /// following code. |
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| 411 | /// \code |
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| 412 | /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum(); |
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| 413 | /// \endcode |
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| 414 | /// |
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| 415 | /// \pre \ref run() or \ref findMinMean() must be called before |
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| 416 | /// using this function. |
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| 417 | double cycleMean() const { |
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| 418 | return static_cast<double>(_cycle_length) / _cycle_size; |
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| 419 | } |
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| 420 | |
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| 421 | /// \brief Return the found cycle. |
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| 422 | /// |
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| 423 | /// This function returns a const reference to the path structure |
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| 424 | /// storing the found cycle. |
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| 425 | /// |
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| 426 | /// \pre \ref run() or \ref findCycle() must be called before using |
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| 427 | /// this function. |
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| 428 | const Path& cycle() const { |
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| 429 | return *_cycle_path; |
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| 430 | } |
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| 431 | |
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| 432 | ///@} |
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| 433 | |
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| 434 | private: |
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| 435 | |
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| 436 | // Initialization |
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| 437 | void init() { |
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| 438 | if (!_cycle_path) { |
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| 439 | _local_path = true; |
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| 440 | _cycle_path = new Path; |
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| 441 | } |
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| 442 | _cycle_path->clear(); |
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| 443 | _cycle_length = 0; |
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| 444 | _cycle_size = 1; |
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| 445 | _cycle_node = INVALID; |
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| 446 | for (NodeIt u(_gr); u != INVALID; ++u) |
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| 447 | _data[u].clear(); |
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| 448 | } |
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| 449 | |
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| 450 | // Find strongly connected components and initialize _comp_nodes |
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| 451 | // and _out_arcs |
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| 452 | void findComponents() { |
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| 453 | _comp_num = stronglyConnectedComponents(_gr, _comp); |
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| 454 | _comp_nodes.resize(_comp_num); |
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| 455 | if (_comp_num == 1) { |
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| 456 | _comp_nodes[0].clear(); |
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| 457 | for (NodeIt n(_gr); n != INVALID; ++n) { |
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| 458 | _comp_nodes[0].push_back(n); |
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| 459 | _out_arcs[n].clear(); |
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| 460 | for (OutArcIt a(_gr, n); a != INVALID; ++a) { |
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| 461 | _out_arcs[n].push_back(a); |
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| 462 | } |
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| 463 | } |
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| 464 | } else { |
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| 465 | for (int i = 0; i < _comp_num; ++i) |
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| 466 | _comp_nodes[i].clear(); |
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| 467 | for (NodeIt n(_gr); n != INVALID; ++n) { |
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| 468 | int k = _comp[n]; |
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| 469 | _comp_nodes[k].push_back(n); |
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| 470 | _out_arcs[n].clear(); |
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| 471 | for (OutArcIt a(_gr, n); a != INVALID; ++a) { |
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| 472 | if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a); |
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| 473 | } |
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| 474 | } |
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| 475 | } |
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| 476 | } |
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| 477 | |
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| 478 | // Initialize path data for the current component |
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| 479 | bool initComponent(int comp) { |
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| 480 | _nodes = &(_comp_nodes[comp]); |
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| 481 | int n = _nodes->size(); |
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| 482 | if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) { |
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| 483 | return false; |
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| 484 | } |
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| 485 | for (int i = 0; i < n; ++i) { |
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[767] | 486 | _data[(*_nodes)[i]].resize(n + 1, PathData(INF)); |
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[765] | 487 | } |
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| 488 | return true; |
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| 489 | } |
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| 490 | |
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| 491 | // Process all rounds of computing path data for the current component. |
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| 492 | // _data[v][k] is the length of a shortest directed walk from the root |
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| 493 | // node to node v containing exactly k arcs. |
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| 494 | void processRounds() { |
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| 495 | Node start = (*_nodes)[0]; |
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[767] | 496 | _data[start][0] = PathData(0); |
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[765] | 497 | _process.clear(); |
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| 498 | _process.push_back(start); |
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| 499 | |
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| 500 | int k, n = _nodes->size(); |
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| 501 | for (k = 1; k <= n && int(_process.size()) < n; ++k) { |
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| 502 | processNextBuildRound(k); |
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| 503 | } |
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| 504 | for ( ; k <= n; ++k) { |
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| 505 | processNextFullRound(k); |
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| 506 | } |
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| 507 | } |
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| 508 | |
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| 509 | // Process one round and rebuild _process |
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| 510 | void processNextBuildRound(int k) { |
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| 511 | std::vector<Node> next; |
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| 512 | Node u, v; |
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| 513 | Arc e; |
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| 514 | LargeValue d; |
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| 515 | for (int i = 0; i < int(_process.size()); ++i) { |
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| 516 | u = _process[i]; |
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| 517 | for (int j = 0; j < int(_out_arcs[u].size()); ++j) { |
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| 518 | e = _out_arcs[u][j]; |
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| 519 | v = _gr.target(e); |
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| 520 | d = _data[u][k-1].dist + _length[e]; |
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[767] | 521 | if (_tolerance.less(d, _data[v][k].dist)) { |
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| 522 | if (_data[v][k].dist == INF) next.push_back(v); |
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| 523 | _data[v][k] = PathData(d, e); |
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[765] | 524 | } |
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| 525 | } |
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| 526 | } |
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| 527 | _process.swap(next); |
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| 528 | } |
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| 529 | |
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| 530 | // Process one round using _nodes instead of _process |
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| 531 | void processNextFullRound(int k) { |
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| 532 | Node u, v; |
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| 533 | Arc e; |
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| 534 | LargeValue d; |
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| 535 | for (int i = 0; i < int(_nodes->size()); ++i) { |
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| 536 | u = (*_nodes)[i]; |
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| 537 | for (int j = 0; j < int(_out_arcs[u].size()); ++j) { |
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| 538 | e = _out_arcs[u][j]; |
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| 539 | v = _gr.target(e); |
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| 540 | d = _data[u][k-1].dist + _length[e]; |
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[767] | 541 | if (_tolerance.less(d, _data[v][k].dist)) { |
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| 542 | _data[v][k] = PathData(d, e); |
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[765] | 543 | } |
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| 544 | } |
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| 545 | } |
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| 546 | } |
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| 547 | |
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| 548 | // Update the minimum cycle mean |
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| 549 | void updateMinMean() { |
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| 550 | int n = _nodes->size(); |
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| 551 | for (int i = 0; i < n; ++i) { |
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| 552 | Node u = (*_nodes)[i]; |
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[767] | 553 | if (_data[u][n].dist == INF) continue; |
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[765] | 554 | LargeValue length, max_length = 0; |
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| 555 | int size, max_size = 1; |
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| 556 | bool found_curr = false; |
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| 557 | for (int k = 0; k < n; ++k) { |
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[767] | 558 | if (_data[u][k].dist == INF) continue; |
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[765] | 559 | length = _data[u][n].dist - _data[u][k].dist; |
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| 560 | size = n - k; |
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| 561 | if (!found_curr || length * max_size > max_length * size) { |
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| 562 | found_curr = true; |
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| 563 | max_length = length; |
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| 564 | max_size = size; |
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| 565 | } |
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| 566 | } |
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| 567 | if ( found_curr && (_cycle_node == INVALID || |
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| 568 | max_length * _cycle_size < _cycle_length * max_size) ) { |
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| 569 | _cycle_length = max_length; |
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| 570 | _cycle_size = max_size; |
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| 571 | _cycle_node = u; |
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| 572 | } |
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| 573 | } |
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| 574 | } |
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| 575 | |
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| 576 | }; //class Karp |
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| 577 | |
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| 578 | ///@} |
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| 579 | |
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| 580 | } //namespace lemon |
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| 581 | |
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| 582 | #endif //LEMON_KARP_H |
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