| author | Christian Urban <christian.urban@kcl.ac.uk> | 
| Mon, 06 Nov 2023 21:49:55 +0000 | |
| changeset 477 | 2403c931a32f | 
| parent 464 | 1b1330cde075 | 
| child 492 | 17e6f46260bd | 
| permissions | -rw-r--r-- | 
| 268 | 1 | // Sudoku | 
| 2 | //======== | |
| 3 | ||
| 301 | 4 | // call parallel version with | 
| 5 | // | |
| 462 
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changeset | 6 | // scala -cp scala-parallel-collections_3-1.0.4.jar sudoku.scala | 
| 301 | 7 | // | 
| 462 
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changeset | 8 | // java -cp .:scala3-library_3-3.2.2.jar:scala-parallel-collections_3-1.0.4.jar Sudoku | 
| 301 | 9 | |
| 462 
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changeset | 10 | |
| 268 | 11 | |
| 12 | import scala.collection.parallel.CollectionConverters._ | |
| 13 | ||
| 14 | type Pos = (Int, Int) | |
| 15 | val emptyValue = '.' | |
| 16 | val maxValue = 9 | |
| 17 | ||
| 18 | val allValues = "123456789".toList | |
| 19 | val indexes = (0 to 8).toList | |
| 20 | ||
| 21 | ||
| 22 | def empty(game: String) = game.indexOf(emptyValue) | |
| 23 | def isDone(game: String) = empty(game) == -1 | |
| 384 | 24 | |
| 383 | 25 | //def emptyPosition(game: String) : Pos = | 
| 26 | // (empty(game) % maxValue, empty(game) / maxValue) | |
| 384 | 27 | |
| 383 | 28 | def emptyPosition(game: String) = {
 | 
| 29 | val e = empty(game) | |
| 30 | (e % maxValue, e / maxValue) | |
| 31 | } | |
| 268 | 32 | |
| 33 | ||
| 34 | def get_row(game: String, y: Int) = indexes.map(col => game(y * maxValue + col)) | |
| 35 | def get_col(game: String, x: Int) = indexes.map(row => game(x + row * maxValue)) | |
| 36 | ||
| 37 | def get_box(game: String, pos: Pos): List[Char] = {
 | |
| 38 | def base(p: Int): Int = (p / 3) * 3 | |
| 39 | val x0 = base(pos._1) | |
| 40 | val y0 = base(pos._2) | |
| 41 | for (x <- (x0 until x0 + 3).toList; | |
| 42 | y <- (y0 until y0 + 3).toList) yield game(x + y * maxValue) | |
| 43 | } | |
| 44 | ||
| 45 | ||
| 46 | def update(game: String, pos: Int, value: Char): String = | |
| 47 | game.updated(pos, value) | |
| 48 | ||
| 49 | def toAvoid(game: String, pos: Pos): List[Char] = | |
| 50 | (get_col(game, pos._1) ++ get_row(game, pos._2) ++ get_box(game, pos)) | |
| 51 | ||
| 52 | def candidates(game: String, pos: Pos): List[Char] = | |
| 53 | allValues.diff(toAvoid(game, pos)) | |
| 54 | ||
| 462 
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changeset | 55 | // search for all solutions | 
| 268 | 56 | def search(game: String): List[String] = {
 | 
| 57 | if (isDone(game)) List(game) | |
| 58 | else | |
| 464 | 59 | candidates(game, emptyPosition(game)).par. | 
| 268 | 60 | map(c => search(update(game, empty(game), c))).toList.flatten | 
| 61 | } | |
| 62 | ||
| 447 | 63 | |
| 462 
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changeset | 64 | // search for single solution | 
| 325 | 65 | def search1T(games: List[String]): Option[String] = games match {
 | 
| 66 | case Nil => None | |
| 67 |   case game::rest => {
 | |
| 68 | if (isDone(game)) Some(game) | |
| 69 |     else {
 | |
| 70 | val cs = candidates(game, emptyPosition(game)) | |
| 71 | search1T(cs.map(c => update(game, empty(game), c)) ::: rest) | |
| 72 | } | |
| 73 | } | |
| 74 | } | |
| 75 | ||
| 329 | 76 | def pretty(game: String): String = | 
| 383 | 77 |   "\n" + (game.grouped(maxValue).mkString(",\n"))
 | 
| 329 | 78 | |
| 79 | ||
| 301 | 80 | // a list of hard games according to Andrew Coles and Peter Norvig | 
| 268 | 81 | |
| 82 | val hard_games = | |
| 321 | 83 |   List("52...6.........7.13...........4..8..6......5...........418.........3..2...87.....",
 | 
| 301 | 84 | "6.....8.3.4.7.................5.4.7.3..2.....1.6.......2.....5.....8.6......1....", | 
| 85 | "48.3............71.2.......7.5....6....2..8.............1.76...3.....4......5....", | |
| 86 | "......52..8.4......3...9...5.1...6..2..7........3.....6...1..........7.4.......3.", | |
| 87 | "6.2.5.........3.4..........43...8....1....2........7..5..27...........81...6.....", | |
| 88 | ".524.........7.1..............8.2...3.....6...9.5.....1.6.3...........897........", | |
| 89 | "6.2.5.........4.3..........43...8....1....2........7..5..27...........81...6.....", | |
| 384 | 90 | ".923.........8.1...........1.7.4...........658.........6.5.2...4.....7.....9.....", | 
| 301 | 91 | "85...24..72......9..4.........1.7..23.5...9...4...........8..7..17..........36.4.", | 
| 268 | 92 | "..53.....8......2..7..1.5..4....53...1..7...6..32...8..6.5....9..4....3......97..", | 
| 93 | "12..4......5.69.1...9...5.........7.7...52.9..3......2.9.6...5.4..9..8.1..3...9.4", | |
| 94 | "...57..3.1......2.7...234......8...4..7..4...49....6.5.42...3.....7..9....18.....", | |
| 95 | "7..1523........92....3.....1....47.8.......6............9...5.6.4.9.7...8....6.1.", | |
| 96 | "1....7.9..3..2...8..96..5....53..9...1..8...26....4...3......1..4......7..7...3..", | |
| 97 | "1...34.8....8..5....4.6..21.18......3..1.2..6......81.52..7.9....6..9....9.64...2", | |
| 98 | "...92......68.3...19..7...623..4.1....1...7....8.3..297...8..91...5.72......64...", | |
| 99 | ".6.5.4.3.1...9...8.........9...5...6.4.6.2.7.7...4...5.........4...8...1.5.2.3.4.", | |
| 100 | "7.....4...2..7..8...3..8.799..5..3...6..2..9...1.97..6...3..9...3..4..6...9..1.35", | |
| 101 | "....7..2.8.......6.1.2.5...9.54....8.........3....85.1...3.2.8.4.......9.7..6....", | |
| 102 | "52...6.........7.13...........4..8..6......5...........418.........3..2...87.....", | |
| 103 | "6.....8.3.4.7.................5.4.7.3..2.....1.6.......2.....5.....8.6......1....", | |
| 104 | "48.3............71.2.......7.5....6....2..8.............1.76...3.....4......5....", | |
| 105 | "......52..8.4......3...9...5.1...6..2..7........3.....6...1..........7.4.......3.", | |
| 106 | "6.2.5.........3.4..........43...8....1....2........7..5..27...........81...6.....", | |
| 107 | ".524.........7.1..............8.2...3.....6...9.5.....1.6.3...........897........", | |
| 108 | "6.2.5.........4.3..........43...8....1....2........7..5..27...........81...6.....", | |
| 109 | ".923.........8.1...........1.7.4...........658.........6.5.2...4.....7.....9.....", | |
| 110 | "6..3.2....5.....1..........7.26............543.........8.15........4.2........7..", | |
| 111 | ".6.5.1.9.1...9..539....7....4.8...7.......5.8.817.5.3.....5.2............76..8...", | |
| 112 | "..5...987.4..5...1..7......2...48....9.1.....6..2.....3..6..2.......9.7.......5..", | |
| 113 | "3.6.7...........518.........1.4.5...7.....6.....2......2.....4.....8.3.....5.....", | |
| 114 | "1.....3.8.7.4..............2.3.1...........958.........5.6...7.....8.2...4.......", | |
| 115 | "6..3.2....4.....1..........7.26............543.........8.15........4.2........7..", | |
| 116 | "....3..9....2....1.5.9..............1.2.8.4.6.8.5...2..75......4.1..6..3.....4.6.", | |
| 117 | "45.....3....8.1....9...........5..9.2..7.....8.........1..4..........7.2...6..8..", | |
| 118 | ".237....68...6.59.9.....7......4.97.3.7.96..2.........5..47.........2....8.......", | |
| 119 | "..84...3....3.....9....157479...8........7..514.....2...9.6...2.5....4......9..56", | |
| 120 | ".98.1....2......6.............3.2.5..84.........6.........4.8.93..5...........1..", | |
| 121 | "..247..58..............1.4.....2...9528.9.4....9...1.........3.3....75..685..2...", | |
| 122 | ".2.3......63.....58.......15....9.3....7........1....8.879..26......6.7...6..7..4", | |
| 123 | "1.....7.9.4...72..8.........7..1..6.3.......5.6..4..2.........8..53...7.7.2....46", | |
| 124 | "4.....3.....8.2......7........1...8734.......6........5...6........1.4...82......", | |
| 125 | ".......71.2.8........4.3...7...6..5....2..3..9........6...7.....8....4......5....", | |
| 126 | "6..3.2....4.....8..........7.26............543.........8.15........8.2........7..", | |
| 127 | ".47.8...1............6..7..6....357......5....1..6....28..4.....9.1...4.....2.69.", | |
| 128 | "......8.17..2........5.6......7...5..1....3...8.......5......2..4..8....6...3....", | |
| 129 | "38.6.......9.......2..3.51......5....3..1..6....4......17.5..8.......9.......7.32", | |
| 130 | "...5...........5.697.....2...48.2...25.1...3..8..3.........4.7..13.5..9..2...31..", | |
| 131 | ".2.......3.5.62..9.68...3...5..........64.8.2..47..9....3.....1.....6...17.43....", | |
| 132 | ".8..4....3......1........2...5...4.69..1..8..2...........3.9....6....5.....2.....", | |
| 133 | "..8.9.1...6.5...2......6....3.1.7.5.........9..4...3...5....2...7...3.8.2..7....4", | |
| 134 | "1.....3.8.6.4..............2.3.1...........958.........5.6...7.....8.2...4.......", | |
| 135 | "1....6.8..64..........4...7....9.6...7.4..5..5...7.1...5....32.3....8...4........", | |
| 136 | "249.6...3.3....2..8.......5.....6......2......1..4.82..9.5..7....4.....1.7...3...", | |
| 137 | "...8....9.873...4.6..7.......85..97...........43..75.......3....3...145.4....2..1", | |
| 138 | "......8.16..2........7.5......6...2..1....3...8.......2......7..3..8....5...4....", | |
| 139 | ".476...5.8.3.....2.....9......8.5..6...1.....6.24......78...51...6....4..9...4..7", | |
| 140 | ".....7.95.....1...86..2.....2..73..85......6...3..49..3.5...41724................", | |
| 141 | ".4.5.....8...9..3..76.2.....146..........9..7.....36....1..4.5..6......3..71..2..", | |
| 142 | ".834.........7..5...........4.1.8..........27...3.....2.6.5....5.....8........1..", | |
| 143 | "..9.....3.....9...7.....5.6..65..4.....3......28......3..75.6..6...........12.3.8", | |
| 144 | ".26.39......6....19.....7.......4..9.5....2....85.....3..2..9..4....762.........4", | |
| 145 | "2.3.8....8..7...........1...6.5.7...4......3....1............82.5....6...1.......", | |
| 146 | "6..3.2....1.....5..........7.26............843.........8.15........8.2........7..", | |
| 147 | "1.....9...64..1.7..7..4.......3.....3.89..5....7....2.....6.7.9.....4.1....129.3.", | |
| 148 | ".........9......84.623...5....6...453...1...6...9...7....1.....4.5..2....3.8....9", | |
| 149 | ".2....5938..5..46.94..6...8..2.3.....6..8.73.7..2.........4.38..7....6..........5", | |
| 150 | "9.4..5...25.6..1..31......8.7...9...4..26......147....7.......2...3..8.6.4.....9.", | |
| 151 | "...52.....9...3..4......7...1.....4..8..453..6...1...87.2........8....32.4..8..1.", | |
| 152 | "53..2.9...24.3..5...9..........1.827...7.........981.............64....91.2.5.43.", | |
| 153 | "1....786...7..8.1.8..2....9........24...1......9..5...6.8..........5.9.......93.4", | |
| 154 | "....5...11......7..6.....8......4.....9.1.3.....596.2..8..62..7..7......3.5.7.2..", | |
| 155 | ".47.2....8....1....3....9.2.....5...6..81..5.....4.....7....3.4...9...1.4..27.8..", | |
| 156 | "......94.....9...53....5.7..8.4..1..463...........7.8.8..7.....7......28.5.26....", | |
| 157 | ".2......6....41.....78....1......7....37.....6..412....1..74..5..8.5..7......39..", | |
| 158 | "1.....3.8.6.4..............2.3.1...........758.........7.5...6.....8.2...4.......", | |
| 159 | "2....1.9..1..3.7..9..8...2.......85..6.4.........7...3.2.3...6....5.....1.9...2.5", | |
| 160 | "..7..8.....6.2.3...3......9.1..5..6.....1.....7.9....2........4.83..4...26....51.", | |
| 161 | "...36....85.......9.4..8........68.........17..9..45...1.5...6.4....9..2.....3...", | |
| 162 | "34.6.......7.......2..8.57......5....7..1..2....4......36.2..1.......9.......7.82", | |
| 163 | "......4.18..2........6.7......8...6..4....3...1.......6......2..5..1....7...3....", | |
| 164 | ".4..5..67...1...4....2.....1..8..3........2...6...........4..5.3.....8..2........", | |
| 165 | ".......4...2..4..1.7..5..9...3..7....4..6....6..1..8...2....1..85.9...6.....8...3", | |
| 166 | "8..7....4.5....6............3.97...8....43..5....2.9....6......2...6...7.71..83.2", | |
| 167 | ".8...4.5....7..3............1..85...6.....2......4....3.26............417........", | |
| 168 | "....7..8...6...5...2...3.61.1...7..2..8..534.2..9.......2......58...6.3.4...1....", | |
| 169 | "......8.16..2........7.5......6...2..1....3...8.......2......7..4..8....5...3....", | |
| 170 | ".2..........6....3.74.8.........3..2.8..4..1.6..5.........1.78.5....9..........4.", | |
| 171 | ".52..68.......7.2.......6....48..9..2..41......1.....8..61..38.....9...63..6..1.9", | |
| 172 | "....1.78.5....9..........4..2..........6....3.74.8.........3..2.8..4..1.6..5.....", | |
| 173 | "1.......3.6.3..7...7...5..121.7...9...7........8.1..2....8.64....9.2..6....4.....", | |
| 174 | "4...7.1....19.46.5.....1......7....2..2.3....847..6....14...8.6.2....3..6...9....", | |
| 175 | "......8.17..2........5.6......7...5..1....3...8.......5......2..3..8....6...4....", | |
| 176 | "963......1....8......2.5....4.8......1....7......3..257......3...9.2.4.7......9..", | |
| 177 | "15.3......7..4.2....4.72.....8.........9..1.8.1..8.79......38...........6....7423", | |
| 178 | "..........5724...98....947...9..3...5..9..12...3.1.9...6....25....56.....7......6", | |
| 179 | "....75....1..2.....4...3...5.....3.2...8...1.......6.....1..48.2........7........", | |
| 180 | "6.....7.3.4.8.................5.4.8.7..2.....1.3.......2.....5.....7.9......1....", | |
| 181 | "....6...4..6.3....1..4..5.77.....8.5...8.....6.8....9...2.9....4....32....97..1..", | |
| 182 | ".32.....58..3.....9.428...1...4...39...6...5.....1.....2...67.8.....4....95....6.", | |
| 183 | "...5.3.......6.7..5.8....1636..2.......4.1.......3...567....2.8..4.7.......2..5..", | |
| 184 | ".5.3.7.4.1.........3.......5.8.3.61....8..5.9.6..1........4...6...6927....2...9..", | |
| 185 | "..5..8..18......9.......78....4.....64....9......53..2.6.........138..5....9.714.", | |
| 186 | "..........72.6.1....51...82.8...13..4.........37.9..1.....238..5.4..9.........79.", | |
| 187 | "...658.....4......12............96.7...3..5....2.8...3..19..8..3.6.....4....473..", | |
| 188 | ".2.3.......6..8.9.83.5........2...8.7.9..5........6..4.......1...1...4.22..7..8.9", | |
| 189 | ".5..9....1.....6.....3.8.....8.4...9514.......3....2..........4.8...6..77..15..6.", | |
| 190 | ".....2.......7...17..3...9.8..7......2.89.6...13..6....9..5.824.....891..........", | |
| 321 | 191 | "3...8.......7....51..............36...2..4....7...........6.13..452...........8..", | 
| 192 | "....14....3....2...7..........9...3.6.1.............8.2.....1.4....5.6.....7.8...", | |
| 193 | "4.....8.5.3..........7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......") | |
| 384 | 194 | |
| 329 | 195 | |
| 268 | 196 | |
| 197 | // for measuring time | |
| 198 | def time_needed[T](i: Int, code: => T) = {
 | |
| 199 | val start = System.nanoTime() | |
| 200 | for (j <- 1 to i) code | |
| 201 | val end = System.nanoTime() | |
| 301 | 202 | (end - start) / i / 1.0e9 | 
| 268 | 203 | } | 
| 204 | ||
| 205 | ||
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changeset | 206 | @main | 
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changeset | 207 | def test() = {
 | 
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changeset | 208 | val total = | 
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changeset | 209 |     (for ((game, i) <- hard_games.zipWithIndex) yield {
 | 
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changeset | 210 | val secs = time_needed(1, search(game)) | 
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changeset | 211 |       println(f"${i}%2.0f: ${game} |${secs}%2.3f secs")
 | 
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changeset | 212 | secs | 
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changeset | 213 | }).sum | 
| 301 | 214 | |
| 462 
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changeset | 215 |   println(f"\ntotal: ${total}%.3f secs")
 | 
| 268 | 216 | } | 
| 217 | ||
| 301 | 218 | |
| 219 | ||
| 462 
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changeset | 220 | // some numbers: | 
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changeset | 221 | // | 
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changeset | 222 | // single thread version 800 secs | 
| 446 | 223 | // | 
| 320 | 224 | // 4 cores parallel version on a moderate laptop 400 secs | 
| 225 | // 8 cores: 290 secs | |
| 446 | 226 | // 10 cores: 156 secs | 
| 320 | 227 | // 18 cores: 142 secs | 
| 301 | 228 |