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1 // Sudoku |
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2 //======== |
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3 |
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4 object Sudoku extends App { |
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5 |
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6 import scala.collection.parallel.CollectionConverters._ |
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7 |
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8 type Pos = (Int, Int) |
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9 val emptyValue = '.' |
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10 val maxValue = 9 |
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11 |
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12 val allValues = "123456789".toList |
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13 val indexes = (0 to 8).toList |
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14 |
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15 |
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16 def empty(game: String) = game.indexOf(emptyValue) |
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17 def isDone(game: String) = empty(game) == -1 |
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18 def emptyPosition(game: String) : Pos = |
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19 (empty(game) % maxValue, empty(game) / maxValue) |
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20 |
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21 |
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22 def get_row(game: String, y: Int) = indexes.map(col => game(y * maxValue + col)) |
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23 def get_col(game: String, x: Int) = indexes.map(row => game(x + row * maxValue)) |
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24 |
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25 def get_box(game: String, pos: Pos): List[Char] = { |
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26 def base(p: Int): Int = (p / 3) * 3 |
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27 val x0 = base(pos._1) |
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28 val y0 = base(pos._2) |
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29 for (x <- (x0 until x0 + 3).toList; |
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30 y <- (y0 until y0 + 3).toList) yield game(x + y * maxValue) |
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31 } |
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32 |
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33 |
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34 //get_row(game0, 0) |
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35 //get_row(game0, 1) |
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36 //get_box(game0, (3,1)) |
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37 |
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38 def update(game: String, pos: Int, value: Char): String = |
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39 game.updated(pos, value) |
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40 |
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41 def toAvoid(game: String, pos: Pos): List[Char] = |
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42 (get_col(game, pos._1) ++ get_row(game, pos._2) ++ get_box(game, pos)) |
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43 |
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44 def candidates(game: String, pos: Pos): List[Char] = |
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45 allValues.diff(toAvoid(game, pos)) |
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46 |
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47 //candidates(game0, (0, 0)) |
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48 |
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49 //def pretty(game: String): String = |
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50 // "\n" ++ (game.sliding(maxValue, maxValue).mkString("\n")) |
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51 |
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52 def search(game: String): List[String] = { |
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53 if (isDone(game)) List(game) |
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54 else |
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55 candidates(game, emptyPosition(game)).par. |
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56 map(c => search(update(game, empty(game), c))).toList.flatten |
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57 } |
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58 |
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59 // two easy games |
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60 val game0 = """.14.6.3.. |
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61 |62...4..9 |
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62 |.8..5.6.. |
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63 |.6.2....3 |
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64 |.7..1..5. |
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65 |5....9.6. |
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66 |..6.2..3. |
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67 |1..5...92 |
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68 |..7.9.41.""".stripMargin.replaceAll("\\n", "") |
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69 |
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70 val game1 = """23.915... |
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71 |...2..54. |
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72 |6.7...... |
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73 |..1.....9 |
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74 |89.5.3.17 |
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75 |5.....6.. |
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76 |......9.5 |
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77 |.16..7... |
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78 |...329..1""".stripMargin.replaceAll("\\n", "") |
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79 |
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80 |
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81 // a game that is in the sligtly harder category |
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82 val game2 = """8........ |
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83 |..36..... |
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84 |.7..9.2.. |
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85 |.5...7... |
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86 |....457.. |
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87 |...1...3. |
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88 |..1....68 |
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89 |..85...1. |
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90 |.9....4..""".stripMargin.replaceAll("\\n", "") |
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91 |
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92 // a game with multiple solutions |
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93 val game3 = """.8...9743 |
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94 |.5...8.1. |
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95 |.1....... |
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96 |8....5... |
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97 |...8.4... |
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98 |...3....6 |
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99 |.......7. |
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100 |.3.5...8. |
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101 |9724...5.""".stripMargin.replaceAll("\\n", "") |
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102 |
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103 val hard_games = |
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104 List("85...24..72......9..4.........1.7..23.5...9...4...........8..7..17..........36.4.", |
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105 "..53.....8......2..7..1.5..4....53...1..7...6..32...8..6.5....9..4....3......97..", |
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106 "12..4......5.69.1...9...5.........7.7...52.9..3......2.9.6...5.4..9..8.1..3...9.4", |
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107 "...57..3.1......2.7...234......8...4..7..4...49....6.5.42...3.....7..9....18.....", |
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108 "7..1523........92....3.....1....47.8.......6............9...5.6.4.9.7...8....6.1.", |
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109 "1....7.9..3..2...8..96..5....53..9...1..8...26....4...3......1..4......7..7...3..", |
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110 "1...34.8....8..5....4.6..21.18......3..1.2..6......81.52..7.9....6..9....9.64...2", |
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111 "...92......68.3...19..7...623..4.1....1...7....8.3..297...8..91...5.72......64...", |
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112 ".6.5.4.3.1...9...8.........9...5...6.4.6.2.7.7...4...5.........4...8...1.5.2.3.4.", |
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113 "7.....4...2..7..8...3..8.799..5..3...6..2..9...1.97..6...3..9...3..4..6...9..1.35", |
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114 "....7..2.8.......6.1.2.5...9.54....8.........3....85.1...3.2.8.4.......9.7..6....", |
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115 // "4.....8.5.3..........7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......", |
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116 "52...6.........7.13...........4..8..6......5...........418.........3..2...87.....", |
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117 "6.....8.3.4.7.................5.4.7.3..2.....1.6.......2.....5.....8.6......1....", |
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118 "48.3............71.2.......7.5....6....2..8.............1.76...3.....4......5....", |
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119 // "....14....3....2...7..........9...3.6.1.............8.2.....1.4....5.6.....7.8...", |
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120 "......52..8.4......3...9...5.1...6..2..7........3.....6...1..........7.4.......3.", |
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121 "6.2.5.........3.4..........43...8....1....2........7..5..27...........81...6.....", |
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122 ".524.........7.1..............8.2...3.....6...9.5.....1.6.3...........897........", |
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123 "6.2.5.........4.3..........43...8....1....2........7..5..27...........81...6.....", |
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124 ".923.........8.1...........1.7.4...........658.........6.5.2...4.....7.....9.....", |
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125 "6..3.2....5.....1..........7.26............543.........8.15........4.2........7..", |
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126 ".6.5.1.9.1...9..539....7....4.8...7.......5.8.817.5.3.....5.2............76..8...", |
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127 "..5...987.4..5...1..7......2...48....9.1.....6..2.....3..6..2.......9.7.......5..", |
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128 "3.6.7...........518.........1.4.5...7.....6.....2......2.....4.....8.3.....5.....", |
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129 "1.....3.8.7.4..............2.3.1...........958.........5.6...7.....8.2...4.......", |
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130 "6..3.2....4.....1..........7.26............543.........8.15........4.2........7..", |
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131 "....3..9....2....1.5.9..............1.2.8.4.6.8.5...2..75......4.1..6..3.....4.6.", |
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132 "45.....3....8.1....9...........5..9.2..7.....8.........1..4..........7.2...6..8..", |
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133 ".237....68...6.59.9.....7......4.97.3.7.96..2.........5..47.........2....8.......", |
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134 "..84...3....3.....9....157479...8........7..514.....2...9.6...2.5....4......9..56", |
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135 ".98.1....2......6.............3.2.5..84.........6.........4.8.93..5...........1..", |
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136 "..247..58..............1.4.....2...9528.9.4....9...1.........3.3....75..685..2...", |
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137 // "4.....8.5.3..........7......2.....6.....5.4......1.......6.3.7.5..2.....1.9......", |
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138 ".2.3......63.....58.......15....9.3....7........1....8.879..26......6.7...6..7..4", |
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139 "1.....7.9.4...72..8.........7..1..6.3.......5.6..4..2.........8..53...7.7.2....46", |
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140 "4.....3.....8.2......7........1...8734.......6........5...6........1.4...82......", |
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141 ".......71.2.8........4.3...7...6..5....2..3..9........6...7.....8....4......5....", |
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142 "6..3.2....4.....8..........7.26............543.........8.15........8.2........7..", |
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143 ".47.8...1............6..7..6....357......5....1..6....28..4.....9.1...4.....2.69.", |
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144 "......8.17..2........5.6......7...5..1....3...8.......5......2..4..8....6...3....", |
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145 "38.6.......9.......2..3.51......5....3..1..6....4......17.5..8.......9.......7.32", |
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146 "...5...........5.697.....2...48.2...25.1...3..8..3.........4.7..13.5..9..2...31..", |
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147 ".2.......3.5.62..9.68...3...5..........64.8.2..47..9....3.....1.....6...17.43....", |
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148 ".8..4....3......1........2...5...4.69..1..8..2...........3.9....6....5.....2.....", |
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149 "..8.9.1...6.5...2......6....3.1.7.5.........9..4...3...5....2...7...3.8.2..7....4", |
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150 // "4.....5.8.3..........7......2.....6.....5.8......1.......6.3.7.5..2.....1.8......", |
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151 "1.....3.8.6.4..............2.3.1...........958.........5.6...7.....8.2...4.......", |
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152 "1....6.8..64..........4...7....9.6...7.4..5..5...7.1...5....32.3....8...4........", |
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153 "249.6...3.3....2..8.......5.....6......2......1..4.82..9.5..7....4.....1.7...3...", |
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154 "...8....9.873...4.6..7.......85..97...........43..75.......3....3...145.4....2..1", |
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155 // "...5.1....9....8...6.......4.1..........7..9........3.8.....1.5...2..4.....36....", |
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156 "......8.16..2........7.5......6...2..1....3...8.......2......7..3..8....5...4....", |
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157 ".476...5.8.3.....2.....9......8.5..6...1.....6.24......78...51...6....4..9...4..7", |
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158 ".....7.95.....1...86..2.....2..73..85......6...3..49..3.5...41724................", |
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159 ".4.5.....8...9..3..76.2.....146..........9..7.....36....1..4.5..6......3..71..2..", |
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160 ".834.........7..5...........4.1.8..........27...3.....2.6.5....5.....8........1..", |
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161 "..9.....3.....9...7.....5.6..65..4.....3......28......3..75.6..6...........12.3.8", |
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162 ".26.39......6....19.....7.......4..9.5....2....85.....3..2..9..4....762.........4", |
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163 "2.3.8....8..7...........1...6.5.7...4......3....1............82.5....6...1.......", |
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164 "6..3.2....1.....5..........7.26............843.........8.15........8.2........7..", |
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165 "1.....9...64..1.7..7..4.......3.....3.89..5....7....2.....6.7.9.....4.1....129.3.", |
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166 ".........9......84.623...5....6...453...1...6...9...7....1.....4.5..2....3.8....9", |
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167 ".2....5938..5..46.94..6...8..2.3.....6..8.73.7..2.........4.38..7....6..........5", |
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168 "9.4..5...25.6..1..31......8.7...9...4..26......147....7.......2...3..8.6.4.....9.", |
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169 "...52.....9...3..4......7...1.....4..8..453..6...1...87.2........8....32.4..8..1.", |
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170 "53..2.9...24.3..5...9..........1.827...7.........981.............64....91.2.5.43.", |
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171 "1....786...7..8.1.8..2....9........24...1......9..5...6.8..........5.9.......93.4", |
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172 "....5...11......7..6.....8......4.....9.1.3.....596.2..8..62..7..7......3.5.7.2..", |
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173 ".47.2....8....1....3....9.2.....5...6..81..5.....4.....7....3.4...9...1.4..27.8..", |
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174 "......94.....9...53....5.7..8.4..1..463...........7.8.8..7.....7......28.5.26....", |
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175 ".2......6....41.....78....1......7....37.....6..412....1..74..5..8.5..7......39..", |
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176 "1.....3.8.6.4..............2.3.1...........758.........7.5...6.....8.2...4.......", |
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177 "2....1.9..1..3.7..9..8...2.......85..6.4.........7...3.2.3...6....5.....1.9...2.5", |
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178 "..7..8.....6.2.3...3......9.1..5..6.....1.....7.9....2........4.83..4...26....51.", |
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179 "...36....85.......9.4..8........68.........17..9..45...1.5...6.4....9..2.....3...", |
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180 "34.6.......7.......2..8.57......5....7..1..2....4......36.2..1.......9.......7.82", |
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181 "......4.18..2........6.7......8...6..4....3...1.......6......2..5..1....7...3....", |
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182 ".4..5..67...1...4....2.....1..8..3........2...6...........4..5.3.....8..2........", |
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183 ".......4...2..4..1.7..5..9...3..7....4..6....6..1..8...2....1..85.9...6.....8...3", |
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184 "8..7....4.5....6............3.97...8....43..5....2.9....6......2...6...7.71..83.2", |
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185 ".8...4.5....7..3............1..85...6.....2......4....3.26............417........", |
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186 "....7..8...6...5...2...3.61.1...7..2..8..534.2..9.......2......58...6.3.4...1....", |
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187 "......8.16..2........7.5......6...2..1....3...8.......2......7..4..8....5...3....", |
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188 ".2..........6....3.74.8.........3..2.8..4..1.6..5.........1.78.5....9..........4.", |
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189 ".52..68.......7.2.......6....48..9..2..41......1.....8..61..38.....9...63..6..1.9", |
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190 "....1.78.5....9..........4..2..........6....3.74.8.........3..2.8..4..1.6..5.....", |
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191 "1.......3.6.3..7...7...5..121.7...9...7........8.1..2....8.64....9.2..6....4.....", |
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192 "4...7.1....19.46.5.....1......7....2..2.3....847..6....14...8.6.2....3..6...9....", |
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193 "......8.17..2........5.6......7...5..1....3...8.......5......2..3..8....6...4....", |
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194 "963......1....8......2.5....4.8......1....7......3..257......3...9.2.4.7......9..", |
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195 "15.3......7..4.2....4.72.....8.........9..1.8.1..8.79......38...........6....7423", |
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196 "..........5724...98....947...9..3...5..9..12...3.1.9...6....25....56.....7......6", |
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197 "....75....1..2.....4...3...5.....3.2...8...1.......6.....1..48.2........7........", |
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198 "6.....7.3.4.8.................5.4.8.7..2.....1.3.......2.....5.....7.9......1....", |
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199 "....6...4..6.3....1..4..5.77.....8.5...8.....6.8....9...2.9....4....32....97..1..", |
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200 ".32.....58..3.....9.428...1...4...39...6...5.....1.....2...67.8.....4....95....6.", |
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201 "...5.3.......6.7..5.8....1636..2.......4.1.......3...567....2.8..4.7.......2..5..", |
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202 ".5.3.7.4.1.........3.......5.8.3.61....8..5.9.6..1........4...6...6927....2...9..", |
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203 "..5..8..18......9.......78....4.....64....9......53..2.6.........138..5....9.714.", |
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204 "..........72.6.1....51...82.8...13..4.........37.9..1.....238..5.4..9.........79.", |
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205 "...658.....4......12............96.7...3..5....2.8...3..19..8..3.6.....4....473..", |
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206 ".2.3.......6..8.9.83.5........2...8.7.9..5........6..4.......1...1...4.22..7..8.9", |
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207 ".5..9....1.....6.....3.8.....8.4...9514.......3....2..........4.8...6..77..15..6.", |
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208 ".....2.......7...17..3...9.8..7......2.89.6...13..6....9..5.824.....891..........", |
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209 "3...8.......7....51..............36...2..4....7...........6.13..452...........8..") |
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210 |
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211 |
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212 |
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213 //search(game0).map(pretty) |
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214 //search(game1).map(pretty) |
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215 |
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216 // for measuring time |
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217 def time_needed[T](i: Int, code: => T) = { |
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218 val start = System.nanoTime() |
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219 for (j <- 1 to i) code |
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220 val end = System.nanoTime() |
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221 s"${(end - start) / i / 1.0e9} secs" |
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222 } |
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223 |
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224 //search(game2).map(pretty) |
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225 //search(game3).distinct.length |
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226 println(time_needed(10, search(game0))) |
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227 println(time_needed(10, search(game1))) |
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228 println(time_needed(4, search(game2))) |
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229 println(time_needed(8, search(game3))) |
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230 |
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231 for (i <- 0 until hard_games.length) { |
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232 println(" " ++ hard_games(i)) |
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233 println(s"$i: ${time_needed(1, search(hard_games(i)))}") |
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234 } |
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235 |
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236 } |