1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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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 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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40 | return val; |
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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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46 | Iterator radixSortPartition(Iterator first, Iterator last, |
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47 | Functor functor, Value mask) { |
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48 | while (first != last && !(functor(*first) & mask)) { |
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49 | ++first; |
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50 | } |
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51 | if (first == last) { |
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52 | return first; |
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53 | } |
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54 | --last; |
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55 | while (first != last && (functor(*last) & mask)) { |
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56 | --last; |
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57 | } |
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58 | if (first == last) { |
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59 | return first; |
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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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64 | return first; |
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65 | } |
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66 | while (true) { |
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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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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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83 | Iterator radixSortSignPartition(Iterator first, Iterator last, |
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84 | Functor functor) { |
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85 | while (first != last && functor(*first) < 0) { |
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86 | ++first; |
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87 | } |
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88 | if (first == last) { |
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89 | return first; |
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90 | } |
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91 | --last; |
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92 | while (first != last && functor(*last) >= 0) { |
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93 | --last; |
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94 | } |
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95 | if (first == last) { |
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96 | return first; |
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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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101 | return first; |
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102 | } |
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103 | while (true) { |
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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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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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120 | void radixIntroSort(Iterator first, Iterator last, |
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121 | Functor functor, Value mask) { |
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122 | while (mask != 0 && last - first > 1) { |
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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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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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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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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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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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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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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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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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175 | template <typename Value, |
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176 | bool sign = std::numeric_limits<Value>::is_signed > |
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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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180 | radixSignedSort<Value>(first, last, functor); |
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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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188 | radixUnsignedSort<Value>(first, last, functor); |
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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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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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202 | /// |
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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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208 | /// values to split the items are choosen to be \f$ 2^k \f$ for each \c k. |
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209 | /// Therefore, the time complexity of the |
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210 | /// algorithm is \f$ O(\log(c)n) \f$ and it uses \f$ O(\log(c)) \f$, |
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211 | /// additional space, where \c c is the maximal value and \c n is the |
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212 | /// number of the items in the container. |
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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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219 | /// |
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220 | /// \sa stableRadixSort() |
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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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267 | void stableRadixIntroSort(Key *first, Key *last, Key *target, |
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268 | int byte, Functor functor) { |
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269 | const int size = |
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270 | unsigned(std::numeric_limits<unsigned char>::max()) + 1; |
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271 | std::vector<int> counter(size); |
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272 | for (int i = 0; i < size; ++i) { |
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273 | counter[i] = 0; |
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274 | } |
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275 | Key *it = first; |
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276 | while (first != last) { |
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277 | ++counter[valueByte(functor(*first), byte)]; |
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278 | ++first; |
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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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282 | prev = num; |
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283 | num += counter[i]; |
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284 | counter[i] = prev; |
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285 | } |
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286 | while (it != last) { |
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287 | target[counter[valueByte(functor(*it), byte)]++] = *it; |
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288 | ++it; |
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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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293 | void signedStableRadixIntroSort(Key *first, Key *last, Key *target, |
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294 | int byte, Functor functor) { |
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295 | const int size = |
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296 | unsigned(std::numeric_limits<unsigned char>::max()) + 1; |
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297 | std::vector<int> counter(size); |
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298 | for (int i = 0; i < size; ++i) { |
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299 | counter[i] = 0; |
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300 | } |
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301 | Key *it = first; |
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302 | while (first != last) { |
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303 | counter[valueByte(functor(*first), byte)]++; |
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304 | ++first; |
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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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308 | prev = num; |
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309 | num += counter[i]; |
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310 | counter[i] = prev; |
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311 | } |
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312 | for (int i = 0; i < size / 2; ++i) { |
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313 | prev = num; |
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314 | num += counter[i]; |
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315 | counter[i] = prev; |
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316 | } |
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317 | while (it != last) { |
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318 | target[counter[valueByte(functor(*it), byte)]++] = *it; |
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319 | ++it; |
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320 | } |
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321 | } |
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322 | |
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323 | |
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324 | template <typename Value, typename Iterator, typename Functor> |
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325 | void stableRadixSignedSort(Iterator first, Iterator last, Functor functor) { |
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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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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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338 | stableRadixIntroSort(buffer, buffer + length, buffer + length, |
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339 | i, functor); |
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340 | } else { |
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341 | stableRadixIntroSort(buffer + length, buffer + 2 * length, buffer, |
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342 | i, functor); |
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343 | } |
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344 | dir = !dir; |
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345 | } |
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346 | if (dir) { |
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347 | signedStableRadixIntroSort(buffer, buffer + length, buffer + length, |
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348 | sizeof(Value) - 1, functor); |
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349 | std::copy(buffer + length, buffer + 2 * length, first); |
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350 | } else { |
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351 | signedStableRadixIntroSort(buffer + length, buffer + 2 * length, |
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352 | buffer, sizeof(Value) - 1, functor); |
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353 | std::copy(buffer, buffer + length, first); |
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354 | } |
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355 | } catch (...) { |
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356 | allocator.deallocate(buffer, 2 * length); |
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357 | throw; |
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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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363 | void stableRadixUnsignedSort(Iterator first, Iterator last, |
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364 | Functor functor) { |
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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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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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377 | stableRadixIntroSort(buffer, buffer + length, |
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378 | buffer + length, i, functor); |
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379 | } else { |
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380 | stableRadixIntroSort(buffer + length, buffer + 2 * length, |
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381 | buffer, i, functor); |
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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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390 | } catch (...) { |
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391 | allocator.deallocate(buffer, 2 * length); |
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392 | throw; |
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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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399 | template <typename Value, |
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400 | bool sign = std::numeric_limits<Value>::is_signed > |
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401 | struct StableRadixSortSelector { |
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402 | template <typename Iterator, typename Functor> |
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403 | static void sort(Iterator first, Iterator last, Functor functor) { |
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404 | stableRadixSignedSort<Value>(first, last, functor); |
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405 | } |
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406 | }; |
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407 | |
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408 | template <typename Value> |
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409 | struct StableRadixSortSelector<Value, false> { |
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410 | template <typename Iterator, typename Functor> |
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411 | static void sort(Iterator first, Iterator last, Functor functor) { |
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412 | stableRadixUnsignedSort<Value>(first, last, functor); |
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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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420 | /// \brief Sorts the STL compatible range into ascending order in a stable |
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421 | /// way. |
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422 | /// |
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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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425 | /// |
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426 | /// This sorting algorithm is stable, i.e. the order of two equal |
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427 | /// elements remains the same after the sorting. |
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428 | /// |
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429 | /// This sort algorithm use a radix forward sort on the |
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430 | /// bytes of the integer number. The algorithm sorts the items |
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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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433 | /// another container in asceding order in \c O(n) time. |
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434 | /// |
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435 | /// The time complexity of the algorithm is \f$ O(\log(c)n) \f$ and |
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436 | /// it uses \f$ O(n) \f$, additional space, where \c c is the |
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437 | /// maximal value and \c n is the number of the items in the |
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438 | /// container. |
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439 | /// |
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440 | |
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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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446 | /// \sa radixSort() |
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447 | template <typename Iterator, typename Functor> |
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448 | void stableRadixSort(Iterator first, Iterator last, Functor functor) { |
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449 | using namespace _radix_sort_bits; |
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450 | typedef typename Functor::result_type Value; |
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451 | StableRadixSortSelector<Value>::sort(first, last, functor); |
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452 | } |
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453 | |
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454 | template <typename Iterator, typename Value, typename Key> |
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455 | void stableRadixSort(Iterator first, Iterator last, Value (*functor)(Key)) { |
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456 | using namespace _radix_sort_bits; |
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457 | StableRadixSortSelector<Value>::sort(first, last, functor); |
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458 | } |
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459 | |
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460 | template <typename Iterator, typename Value, typename Key> |
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461 | void stableRadixSort(Iterator first, Iterator last, Value& (*functor)(Key)) { |
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462 | using namespace _radix_sort_bits; |
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463 | StableRadixSortSelector<Value>::sort(first, last, functor); |
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464 | } |
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465 | |
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466 | template <typename Iterator, typename Value, typename Key> |
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467 | void stableRadixSort(Iterator first, Iterator last, Value (*functor)(Key&)) { |
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468 | using namespace _radix_sort_bits; |
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469 | StableRadixSortSelector<Value>::sort(first, last, functor); |
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470 | } |
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471 | |
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472 | template <typename Iterator, typename Value, typename Key> |
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473 | void stableRadixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) { |
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474 | using namespace _radix_sort_bits; |
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475 | StableRadixSortSelector<Value>::sort(first, last, functor); |
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476 | } |
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477 | |
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478 | template <typename Iterator> |
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479 | void stableRadixSort(Iterator first, Iterator last) { |
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480 | using namespace _radix_sort_bits; |
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481 | typedef typename std::iterator_traits<Iterator>::value_type Value; |
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482 | StableRadixSortSelector<Value>::sort(first, last, Identity<Value>()); |
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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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