[442] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[441] | 2 | * |
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[442] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[441] | 4 | * |
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[444] | 5 | * Copyright (C) 2003-2009 |
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[441] | 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 RADIX_SORT_H |
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| 20 | #define RADIX_SORT_H |
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| 21 | |
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| 22 | /// \ingroup auxalg |
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| 23 | /// \file |
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| 24 | /// \brief Radix sort |
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| 25 | /// |
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| 26 | /// Linear time sorting algorithms |
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| 27 | |
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| 28 | #include <vector> |
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| 29 | #include <limits> |
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| 30 | #include <iterator> |
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| 31 | #include <algorithm> |
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| 32 | |
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| 33 | namespace lemon { |
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| 34 | |
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| 35 | namespace _radix_sort_bits { |
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| 36 | |
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| 37 | template <typename Value> |
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| 38 | struct Identity { |
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| 39 | const Value& operator()(const Value& val) { |
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[442] | 40 | return val; |
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[441] | 41 | } |
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| 42 | }; |
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| 43 | |
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| 44 | |
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| 45 | template <typename Value, typename Iterator, typename Functor> |
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[442] | 46 | Iterator radixSortPartition(Iterator first, Iterator last, |
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| 47 | Functor functor, Value mask) { |
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[441] | 48 | while (first != last && !(functor(*first) & mask)) { |
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[442] | 49 | ++first; |
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[441] | 50 | } |
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| 51 | if (first == last) { |
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[442] | 52 | return first; |
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[441] | 53 | } |
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| 54 | --last; |
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| 55 | while (first != last && (functor(*last) & mask)) { |
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[442] | 56 | --last; |
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[441] | 57 | } |
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| 58 | if (first == last) { |
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[442] | 59 | return first; |
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[441] | 60 | } |
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| 61 | std::iter_swap(first, last); |
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| 62 | ++first; |
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| 63 | if (!(first < last)) { |
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[442] | 64 | return first; |
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[441] | 65 | } |
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| 66 | while (true) { |
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[442] | 67 | while (!(functor(*first) & mask)) { |
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| 68 | ++first; |
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| 69 | } |
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| 70 | --last; |
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| 71 | while (functor(*last) & mask) { |
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| 72 | --last; |
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| 73 | } |
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| 74 | if (!(first < last)) { |
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| 75 | return first; |
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| 76 | } |
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| 77 | std::iter_swap(first, last); |
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| 78 | ++first; |
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[441] | 79 | } |
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| 80 | } |
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| 81 | |
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| 82 | template <typename Iterator, typename Functor> |
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[442] | 83 | Iterator radixSortSignPartition(Iterator first, Iterator last, |
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| 84 | Functor functor) { |
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[441] | 85 | while (first != last && functor(*first) < 0) { |
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[442] | 86 | ++first; |
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[441] | 87 | } |
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| 88 | if (first == last) { |
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[442] | 89 | return first; |
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[441] | 90 | } |
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| 91 | --last; |
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| 92 | while (first != last && functor(*last) >= 0) { |
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[442] | 93 | --last; |
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[441] | 94 | } |
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| 95 | if (first == last) { |
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[442] | 96 | return first; |
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[441] | 97 | } |
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| 98 | std::iter_swap(first, last); |
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| 99 | ++first; |
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| 100 | if (!(first < last)) { |
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[442] | 101 | return first; |
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[441] | 102 | } |
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| 103 | while (true) { |
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[442] | 104 | while (functor(*first) < 0) { |
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| 105 | ++first; |
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| 106 | } |
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| 107 | --last; |
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| 108 | while (functor(*last) >= 0) { |
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| 109 | --last; |
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| 110 | } |
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| 111 | if (!(first < last)) { |
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| 112 | return first; |
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| 113 | } |
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| 114 | std::iter_swap(first, last); |
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| 115 | ++first; |
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[441] | 116 | } |
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| 117 | } |
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| 118 | |
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| 119 | template <typename Value, typename Iterator, typename Functor> |
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[442] | 120 | void radixIntroSort(Iterator first, Iterator last, |
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| 121 | Functor functor, Value mask) { |
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[441] | 122 | while (mask != 0 && last - first > 1) { |
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[442] | 123 | Iterator cut = radixSortPartition(first, last, functor, mask); |
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| 124 | mask >>= 1; |
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| 125 | radixIntroSort(first, cut, functor, mask); |
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| 126 | first = cut; |
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[441] | 127 | } |
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| 128 | } |
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| 129 | |
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| 130 | template <typename Value, typename Iterator, typename Functor> |
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| 131 | void radixSignedSort(Iterator first, Iterator last, Functor functor) { |
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| 132 | |
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| 133 | Iterator cut = radixSortSignPartition(first, last, functor); |
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| 134 | |
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| 135 | Value mask; |
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| 136 | int max_digit; |
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| 137 | Iterator it; |
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| 138 | |
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| 139 | mask = ~0; max_digit = 0; |
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| 140 | for (it = first; it != cut; ++it) { |
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[442] | 141 | while ((mask & functor(*it)) != mask) { |
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| 142 | ++max_digit; |
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| 143 | mask <<= 1; |
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| 144 | } |
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[441] | 145 | } |
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| 146 | radixIntroSort(first, cut, functor, 1 << max_digit); |
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| 147 | |
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| 148 | mask = 0; max_digit = 0; |
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| 149 | for (it = cut; it != last; ++it) { |
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[442] | 150 | while ((mask | functor(*it)) != mask) { |
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| 151 | ++max_digit; |
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| 152 | mask <<= 1; mask |= 1; |
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| 153 | } |
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[441] | 154 | } |
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| 155 | radixIntroSort(cut, last, functor, 1 << max_digit); |
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| 156 | } |
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| 157 | |
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| 158 | template <typename Value, typename Iterator, typename Functor> |
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| 159 | void radixUnsignedSort(Iterator first, Iterator last, Functor functor) { |
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| 160 | |
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| 161 | Value mask = 0; |
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| 162 | int max_digit = 0; |
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| 163 | |
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| 164 | Iterator it; |
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| 165 | for (it = first; it != last; ++it) { |
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[442] | 166 | while ((mask | functor(*it)) != mask) { |
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| 167 | ++max_digit; |
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| 168 | mask <<= 1; mask |= 1; |
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| 169 | } |
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[441] | 170 | } |
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| 171 | radixIntroSort(first, last, functor, 1 << max_digit); |
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| 172 | } |
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| 173 | |
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| 174 | |
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[442] | 175 | template <typename Value, |
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| 176 | bool sign = std::numeric_limits<Value>::is_signed > |
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[441] | 177 | struct RadixSortSelector { |
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| 178 | template <typename Iterator, typename Functor> |
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| 179 | static void sort(Iterator first, Iterator last, Functor functor) { |
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[442] | 180 | radixSignedSort<Value>(first, last, functor); |
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[441] | 181 | } |
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| 182 | }; |
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| 183 | |
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| 184 | template <typename Value> |
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| 185 | struct RadixSortSelector<Value, false> { |
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| 186 | template <typename Iterator, typename Functor> |
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| 187 | static void sort(Iterator first, Iterator last, Functor functor) { |
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[442] | 188 | radixUnsignedSort<Value>(first, last, functor); |
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[441] | 189 | } |
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| 190 | }; |
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| 191 | |
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| 192 | } |
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| 193 | |
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| 194 | /// \ingroup auxalg |
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| 195 | /// |
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| 196 | /// \brief Sorts the STL compatible range into ascending order. |
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| 197 | /// |
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[442] | 198 | /// The \c radixSort sorts an STL compatible range into ascending |
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| 199 | /// order. The radix sort algorithm can sort items which are mapped |
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| 200 | /// to integers with an adaptable unary function \c functor and the |
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| 201 | /// order will be ascending according to these mapped values. |
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[441] | 202 | /// |
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[442] | 203 | /// It is also possible to use a normal function instead |
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| 204 | /// of the functor object. If the functor is not given it will use |
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| 205 | /// the identity function instead. |
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| 206 | /// |
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| 207 | /// This is a special quick sort algorithm where the pivot |
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[559] | 208 | /// values to split the items are choosen to be 2<sup>k</sup> |
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| 209 | /// for each \c k. |
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| 210 | /// Therefore, the time complexity of the algorithm is O(log(c)*n) and |
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| 211 | /// it uses O(log(c)) additional space, where \c c is the maximal value |
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| 212 | /// and \c n is the number of the items in the container. |
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[441] | 213 | /// |
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| 214 | /// \param first The begin of the given range. |
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| 215 | /// \param last The end of the given range. |
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| 216 | /// \param functor An adaptible unary function or a normal function |
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| 217 | /// which maps the items to any integer type which can be either |
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| 218 | /// signed or unsigned. |
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[442] | 219 | /// |
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[443] | 220 | /// \sa stableRadixSort() |
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[441] | 221 | template <typename Iterator, typename Functor> |
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| 222 | void radixSort(Iterator first, Iterator last, Functor functor) { |
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| 223 | using namespace _radix_sort_bits; |
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| 224 | typedef typename Functor::result_type Value; |
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| 225 | RadixSortSelector<Value>::sort(first, last, functor); |
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| 226 | } |
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| 227 | |
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| 228 | template <typename Iterator, typename Value, typename Key> |
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| 229 | void radixSort(Iterator first, Iterator last, Value (*functor)(Key)) { |
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| 230 | using namespace _radix_sort_bits; |
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| 231 | RadixSortSelector<Value>::sort(first, last, functor); |
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| 232 | } |
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| 233 | |
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| 234 | template <typename Iterator, typename Value, typename Key> |
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| 235 | void radixSort(Iterator first, Iterator last, Value& (*functor)(Key)) { |
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| 236 | using namespace _radix_sort_bits; |
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| 237 | RadixSortSelector<Value>::sort(first, last, functor); |
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| 238 | } |
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| 239 | |
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| 240 | template <typename Iterator, typename Value, typename Key> |
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| 241 | void radixSort(Iterator first, Iterator last, Value (*functor)(Key&)) { |
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| 242 | using namespace _radix_sort_bits; |
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| 243 | RadixSortSelector<Value>::sort(first, last, functor); |
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| 244 | } |
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| 245 | |
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| 246 | template <typename Iterator, typename Value, typename Key> |
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| 247 | void radixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) { |
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| 248 | using namespace _radix_sort_bits; |
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| 249 | RadixSortSelector<Value>::sort(first, last, functor); |
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| 250 | } |
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| 251 | |
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| 252 | template <typename Iterator> |
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| 253 | void radixSort(Iterator first, Iterator last) { |
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| 254 | using namespace _radix_sort_bits; |
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| 255 | typedef typename std::iterator_traits<Iterator>::value_type Value; |
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| 256 | RadixSortSelector<Value>::sort(first, last, Identity<Value>()); |
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| 257 | } |
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| 258 | |
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| 259 | namespace _radix_sort_bits { |
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| 260 | |
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| 261 | template <typename Value> |
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| 262 | unsigned char valueByte(Value value, int byte) { |
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| 263 | return value >> (std::numeric_limits<unsigned char>::digits * byte); |
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| 264 | } |
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| 265 | |
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| 266 | template <typename Functor, typename Key> |
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[443] | 267 | void stableRadixIntroSort(Key *first, Key *last, Key *target, |
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| 268 | int byte, Functor functor) { |
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[442] | 269 | const int size = |
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| 270 | unsigned(std::numeric_limits<unsigned char>::max()) + 1; |
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[441] | 271 | std::vector<int> counter(size); |
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| 272 | for (int i = 0; i < size; ++i) { |
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[442] | 273 | counter[i] = 0; |
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[441] | 274 | } |
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| 275 | Key *it = first; |
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| 276 | while (first != last) { |
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[442] | 277 | ++counter[valueByte(functor(*first), byte)]; |
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| 278 | ++first; |
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[441] | 279 | } |
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| 280 | int prev, num = 0; |
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| 281 | for (int i = 0; i < size; ++i) { |
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[442] | 282 | prev = num; |
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| 283 | num += counter[i]; |
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| 284 | counter[i] = prev; |
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[441] | 285 | } |
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| 286 | while (it != last) { |
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[442] | 287 | target[counter[valueByte(functor(*it), byte)]++] = *it; |
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| 288 | ++it; |
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[441] | 289 | } |
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| 290 | } |
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| 291 | |
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| 292 | template <typename Functor, typename Key> |
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[443] | 293 | void signedStableRadixIntroSort(Key *first, Key *last, Key *target, |
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| 294 | int byte, Functor functor) { |
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[442] | 295 | const int size = |
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| 296 | unsigned(std::numeric_limits<unsigned char>::max()) + 1; |
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[441] | 297 | std::vector<int> counter(size); |
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| 298 | for (int i = 0; i < size; ++i) { |
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[442] | 299 | counter[i] = 0; |
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[441] | 300 | } |
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| 301 | Key *it = first; |
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| 302 | while (first != last) { |
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[442] | 303 | counter[valueByte(functor(*first), byte)]++; |
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| 304 | ++first; |
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[441] | 305 | } |
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| 306 | int prev, num = 0; |
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| 307 | for (int i = size / 2; i < size; ++i) { |
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[442] | 308 | prev = num; |
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| 309 | num += counter[i]; |
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| 310 | counter[i] = prev; |
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[441] | 311 | } |
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| 312 | for (int i = 0; i < size / 2; ++i) { |
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[442] | 313 | prev = num; |
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| 314 | num += counter[i]; |
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| 315 | counter[i] = prev; |
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[441] | 316 | } |
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| 317 | while (it != last) { |
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[442] | 318 | target[counter[valueByte(functor(*it), byte)]++] = *it; |
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| 319 | ++it; |
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[441] | 320 | } |
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| 321 | } |
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| 322 | |
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[442] | 323 | |
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[441] | 324 | template <typename Value, typename Iterator, typename Functor> |
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[443] | 325 | void stableRadixSignedSort(Iterator first, Iterator last, Functor functor) { |
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[441] | 326 | if (first == last) return; |
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| 327 | typedef typename std::iterator_traits<Iterator>::value_type Key; |
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| 328 | typedef std::allocator<Key> Allocator; |
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| 329 | Allocator allocator; |
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| 330 | |
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| 331 | int length = std::distance(first, last); |
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| 332 | Key* buffer = allocator.allocate(2 * length); |
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| 333 | try { |
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[442] | 334 | bool dir = true; |
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| 335 | std::copy(first, last, buffer); |
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| 336 | for (int i = 0; i < int(sizeof(Value)) - 1; ++i) { |
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| 337 | if (dir) { |
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[443] | 338 | stableRadixIntroSort(buffer, buffer + length, buffer + length, |
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| 339 | i, functor); |
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[442] | 340 | } else { |
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[443] | 341 | stableRadixIntroSort(buffer + length, buffer + 2 * length, buffer, |
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| 342 | i, functor); |
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[442] | 343 | } |
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| 344 | dir = !dir; |
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| 345 | } |
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| 346 | if (dir) { |
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[443] | 347 | signedStableRadixIntroSort(buffer, buffer + length, buffer + length, |
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| 348 | sizeof(Value) - 1, functor); |
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[442] | 349 | std::copy(buffer + length, buffer + 2 * length, first); |
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| 350 | } else { |
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[444] | 351 | signedStableRadixIntroSort(buffer + length, buffer + 2 * length, |
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[443] | 352 | buffer, sizeof(Value) - 1, functor); |
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[442] | 353 | std::copy(buffer, buffer + length, first); |
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| 354 | } |
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[441] | 355 | } catch (...) { |
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[442] | 356 | allocator.deallocate(buffer, 2 * length); |
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| 357 | throw; |
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[441] | 358 | } |
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| 359 | allocator.deallocate(buffer, 2 * length); |
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| 360 | } |
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| 361 | |
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| 362 | template <typename Value, typename Iterator, typename Functor> |
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[444] | 363 | void stableRadixUnsignedSort(Iterator first, Iterator last, |
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[443] | 364 | Functor functor) { |
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[441] | 365 | if (first == last) return; |
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| 366 | typedef typename std::iterator_traits<Iterator>::value_type Key; |
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| 367 | typedef std::allocator<Key> Allocator; |
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| 368 | Allocator allocator; |
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| 369 | |
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| 370 | int length = std::distance(first, last); |
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| 371 | Key *buffer = allocator.allocate(2 * length); |
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| 372 | try { |
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[442] | 373 | bool dir = true; |
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| 374 | std::copy(first, last, buffer); |
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| 375 | for (int i = 0; i < int(sizeof(Value)); ++i) { |
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| 376 | if (dir) { |
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[443] | 377 | stableRadixIntroSort(buffer, buffer + length, |
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| 378 | buffer + length, i, functor); |
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[442] | 379 | } else { |
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[443] | 380 | stableRadixIntroSort(buffer + length, buffer + 2 * length, |
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| 381 | buffer, i, functor); |
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[442] | 382 | } |
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| 383 | dir = !dir; |
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| 384 | } |
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| 385 | if (dir) { |
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| 386 | std::copy(buffer, buffer + length, first); |
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| 387 | } else { |
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| 388 | std::copy(buffer + length, buffer + 2 * length, first); |
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| 389 | } |
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[441] | 390 | } catch (...) { |
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[442] | 391 | allocator.deallocate(buffer, 2 * length); |
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| 392 | throw; |
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[441] | 393 | } |
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| 394 | allocator.deallocate(buffer, 2 * length); |
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| 395 | } |
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| 396 | |
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| 397 | |
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| 398 | |
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[442] | 399 | template <typename Value, |
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| 400 | bool sign = std::numeric_limits<Value>::is_signed > |
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[443] | 401 | struct StableRadixSortSelector { |
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[441] | 402 | template <typename Iterator, typename Functor> |
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| 403 | static void sort(Iterator first, Iterator last, Functor functor) { |
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[443] | 404 | stableRadixSignedSort<Value>(first, last, functor); |
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[441] | 405 | } |
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| 406 | }; |
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| 407 | |
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| 408 | template <typename Value> |
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[443] | 409 | struct StableRadixSortSelector<Value, false> { |
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[441] | 410 | template <typename Iterator, typename Functor> |
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| 411 | static void sort(Iterator first, Iterator last, Functor functor) { |
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[443] | 412 | stableRadixUnsignedSort<Value>(first, last, functor); |
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[441] | 413 | } |
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| 414 | }; |
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| 415 | |
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| 416 | } |
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| 417 | |
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| 418 | /// \ingroup auxalg |
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| 419 | /// |
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[442] | 420 | /// \brief Sorts the STL compatible range into ascending order in a stable |
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| 421 | /// way. |
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[441] | 422 | /// |
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[442] | 423 | /// This function sorts an STL compatible range into ascending |
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| 424 | /// order according to an integer mapping in the same as radixSort() does. |
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[441] | 425 | /// |
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[442] | 426 | /// This sorting algorithm is stable, i.e. the order of two equal |
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[443] | 427 | /// elements remains the same after the sorting. |
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[442] | 428 | /// |
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| 429 | /// This sort algorithm use a radix forward sort on the |
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[441] | 430 | /// bytes of the integer number. The algorithm sorts the items |
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[442] | 431 | /// byte-by-byte. First, it counts how many times a byte value occurs |
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| 432 | /// in the container, then it copies the corresponding items to |
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[559] | 433 | /// another container in asceding order in O(n) time. |
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[441] | 434 | /// |
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[559] | 435 | /// The time complexity of the algorithm is O(log(c)*n) and |
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| 436 | /// it uses O(n) additional space, where \c c is the |
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[442] | 437 | /// maximal value and \c n is the number of the items in the |
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| 438 | /// container. |
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[441] | 439 | /// |
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[442] | 440 | |
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[441] | 441 | /// \param first The begin of the given range. |
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| 442 | /// \param last The end of the given range. |
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| 443 | /// \param functor An adaptible unary function or a normal function |
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| 444 | /// which maps the items to any integer type which can be either |
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| 445 | /// signed or unsigned. |
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[442] | 446 | /// \sa radixSort() |
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[441] | 447 | template <typename Iterator, typename Functor> |
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[443] | 448 | void stableRadixSort(Iterator first, Iterator last, Functor functor) { |
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[441] | 449 | using namespace _radix_sort_bits; |
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| 450 | typedef typename Functor::result_type Value; |
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[443] | 451 | StableRadixSortSelector<Value>::sort(first, last, functor); |
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[441] | 452 | } |
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| 453 | |
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| 454 | template <typename Iterator, typename Value, typename Key> |
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[443] | 455 | void stableRadixSort(Iterator first, Iterator last, Value (*functor)(Key)) { |
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[441] | 456 | using namespace _radix_sort_bits; |
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[443] | 457 | StableRadixSortSelector<Value>::sort(first, last, functor); |
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[441] | 458 | } |
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| 459 | |
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| 460 | template <typename Iterator, typename Value, typename Key> |
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[443] | 461 | void stableRadixSort(Iterator first, Iterator last, Value& (*functor)(Key)) { |
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[441] | 462 | using namespace _radix_sort_bits; |
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[443] | 463 | StableRadixSortSelector<Value>::sort(first, last, functor); |
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[441] | 464 | } |
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| 465 | |
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| 466 | template <typename Iterator, typename Value, typename Key> |
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[443] | 467 | void stableRadixSort(Iterator first, Iterator last, Value (*functor)(Key&)) { |
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[441] | 468 | using namespace _radix_sort_bits; |
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[443] | 469 | StableRadixSortSelector<Value>::sort(first, last, functor); |
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[441] | 470 | } |
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| 471 | |
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| 472 | template <typename Iterator, typename Value, typename Key> |
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[443] | 473 | void stableRadixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) { |
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[441] | 474 | using namespace _radix_sort_bits; |
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[443] | 475 | StableRadixSortSelector<Value>::sort(first, last, functor); |
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[441] | 476 | } |
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| 477 | |
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| 478 | template <typename Iterator> |
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[443] | 479 | void stableRadixSort(Iterator first, Iterator last) { |
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[441] | 480 | using namespace _radix_sort_bits; |
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| 481 | typedef typename std::iterator_traits<Iterator>::value_type Value; |
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[443] | 482 | StableRadixSortSelector<Value>::sort(first, last, Identity<Value>()); |
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[441] | 483 | } |
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| 484 | |
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| 485 | } |
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| 486 | |
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| 487 | #endif |
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