| author | Christian Urban <christian.urban@kcl.ac.uk> | 
| Fri, 12 Sep 2025 10:36:07 +0100 | |
| changeset 492 | 17e6f46260bd | 
| parent 464 | 1b1330cde075 | 
| permissions | -rw-r--r-- | 
| 268 | 1  | 
// Sudoku  | 
2  | 
//========  | 
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3  | 
||
| 492 | 4  | 
// you can call the parallel version with  | 
5  | 
//  | 
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// scala -cp scala-parallel-collections_3-1.0.4.jar sudoku.scala  | 
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| 301 | 7  | 
//  | 
| 492 | 8  | 
// or with java directly  | 
| 301 | 9  | 
//  | 
| 492 | 10  | 
// java -cp .:scala3-library_3-3.2.2.jar:scala-parallel-collections_3-1.0.4.jar Sudoku  | 
| 301 | 11  | 
|
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462
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
12  | 
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| 268 | 13  | 
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14  | 
import scala.collection.parallel.CollectionConverters._  | 
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15  | 
||
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type Pos = (Int, Int)  | 
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val emptyValue = '.'  | 
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val maxValue = 9  | 
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19  | 
||
20  | 
val allValues = "123456789".toList  | 
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21  | 
val indexes = (0 to 8).toList  | 
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||
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||
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def empty(game: String) = game.indexOf(emptyValue)  | 
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def isDone(game: String) = empty(game) == -1  | 
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| 383 | 27  | 
//def emptyPosition(game: String) : Pos =  | 
28  | 
// (empty(game) % maxValue, empty(game) / maxValue)  | 
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def emptyPosition(game: String) = {
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val e = empty(game)  | 
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(e % maxValue, e / maxValue)  | 
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}  | 
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||
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def get_row(game: String, y: Int) = indexes.map(col => game(y * maxValue + col))  | 
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def get_col(game: String, x: Int) = indexes.map(row => game(x + row * maxValue))  | 
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||
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def get_box(game: String, pos: Pos): List[Char] = {
 | 
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def base(p: Int): Int = (p / 3) * 3  | 
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val x0 = base(pos._1)  | 
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val y0 = base(pos._2)  | 
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for (x <- (x0 until x0 + 3).toList;  | 
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y <- (y0 until y0 + 3).toList) yield game(x + y * maxValue)  | 
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}  | 
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def update(game: String, pos: Int, value: Char): String =  | 
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game.updated(pos, value)  | 
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def toAvoid(game: String, pos: Pos): List[Char] =  | 
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(get_col(game, pos._1) ++ get_row(game, pos._2) ++ get_box(game, pos))  | 
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53  | 
||
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def candidates(game: String, pos: Pos): List[Char] =  | 
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allValues.diff(toAvoid(game, pos))  | 
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||
| 
462
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
57  | 
// search for all solutions  | 
| 268 | 58  | 
def search(game: String): List[String] = {
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59  | 
if (isDone(game)) List(game)  | 
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else  | 
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| 464 | 61  | 
candidates(game, emptyPosition(game)).par.  | 
| 268 | 62  | 
map(c => search(update(game, empty(game), c))).toList.flatten  | 
63  | 
}  | 
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||
| 447 | 65  | 
|
| 
462
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
66  | 
// search for single solution  | 
| 325 | 67  | 
def search1T(games: List[String]): Option[String] = games match {
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68  | 
case Nil => None  | 
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  case game::rest => {
 | 
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if (isDone(game)) Some(game)  | 
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71  | 
    else {
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val cs = candidates(game, emptyPosition(game))  | 
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search1T(cs.map(c => update(game, empty(game), c)) ::: rest)  | 
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74  | 
}  | 
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75  | 
}  | 
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}  | 
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||
| 329 | 78  | 
def pretty(game: String): String =  | 
| 383 | 79  | 
  "\n" + (game.grouped(maxValue).mkString(",\n"))
 | 
| 329 | 80  | 
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||
| 301 | 82  | 
// a list of hard games according to Andrew Coles and Peter Norvig  | 
| 268 | 83  | 
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val hard_games =  | 
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| 321 | 85  | 
  List("52...6.........7.13...........4..8..6......5...........418.........3..2...87.....",
 | 
| 301 | 86  | 
"6.....8.3.4.7.................5.4.7.3..2.....1.6.......2.....5.....8.6......1....",  | 
87  | 
"48.3............71.2.......7.5....6....2..8.............1.76...3.....4......5....",  | 
|
88  | 
"......52..8.4......3...9...5.1...6..2..7........3.....6...1..........7.4.......3.",  | 
|
89  | 
"6.2.5.........3.4..........43...8....1....2........7..5..27...........81...6.....",  | 
|
90  | 
".524.........7.1..............8.2...3.....6...9.5.....1.6.3...........897........",  | 
|
91  | 
"6.2.5.........4.3..........43...8....1....2........7..5..27...........81...6.....",  | 
|
| 384 | 92  | 
".923.........8.1...........1.7.4...........658.........6.5.2...4.....7.....9.....",  | 
| 301 | 93  | 
"85...24..72......9..4.........1.7..23.5...9...4...........8..7..17..........36.4.",  | 
| 268 | 94  | 
"..53.....8......2..7..1.5..4....53...1..7...6..32...8..6.5....9..4....3......97..",  | 
95  | 
"12..4......5.69.1...9...5.........7.7...52.9..3......2.9.6...5.4..9..8.1..3...9.4",  | 
|
96  | 
"...57..3.1......2.7...234......8...4..7..4...49....6.5.42...3.....7..9....18.....",  | 
|
97  | 
"7..1523........92....3.....1....47.8.......6............9...5.6.4.9.7...8....6.1.",  | 
|
98  | 
"1....7.9..3..2...8..96..5....53..9...1..8...26....4...3......1..4......7..7...3..",  | 
|
99  | 
"1...34.8....8..5....4.6..21.18......3..1.2..6......81.52..7.9....6..9....9.64...2",  | 
|
100  | 
"...92......68.3...19..7...623..4.1....1...7....8.3..297...8..91...5.72......64...",  | 
|
101  | 
".6.5.4.3.1...9...8.........9...5...6.4.6.2.7.7...4...5.........4...8...1.5.2.3.4.",  | 
|
102  | 
"7.....4...2..7..8...3..8.799..5..3...6..2..9...1.97..6...3..9...3..4..6...9..1.35",  | 
|
103  | 
"....7..2.8.......6.1.2.5...9.54....8.........3....85.1...3.2.8.4.......9.7..6....",  | 
|
104  | 
"52...6.........7.13...........4..8..6......5...........418.........3..2...87.....",  | 
|
105  | 
"6.....8.3.4.7.................5.4.7.3..2.....1.6.......2.....5.....8.6......1....",  | 
|
106  | 
"48.3............71.2.......7.5....6....2..8.............1.76...3.....4......5....",  | 
|
107  | 
"......52..8.4......3...9...5.1...6..2..7........3.....6...1..........7.4.......3.",  | 
|
108  | 
"6.2.5.........3.4..........43...8....1....2........7..5..27...........81...6.....",  | 
|
109  | 
".524.........7.1..............8.2...3.....6...9.5.....1.6.3...........897........",  | 
|
110  | 
"6.2.5.........4.3..........43...8....1....2........7..5..27...........81...6.....",  | 
|
111  | 
".923.........8.1...........1.7.4...........658.........6.5.2...4.....7.....9.....",  | 
|
112  | 
"6..3.2....5.....1..........7.26............543.........8.15........4.2........7..",  | 
|
113  | 
".6.5.1.9.1...9..539....7....4.8...7.......5.8.817.5.3.....5.2............76..8...",  | 
|
114  | 
"..5...987.4..5...1..7......2...48....9.1.....6..2.....3..6..2.......9.7.......5..",  | 
|
115  | 
"3.6.7...........518.........1.4.5...7.....6.....2......2.....4.....8.3.....5.....",  | 
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116  | 
"1.....3.8.7.4..............2.3.1...........958.........5.6...7.....8.2...4.......",  | 
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117  | 
"6..3.2....4.....1..........7.26............543.........8.15........4.2........7..",  | 
|
118  | 
"....3..9....2....1.5.9..............1.2.8.4.6.8.5...2..75......4.1..6..3.....4.6.",  | 
|
119  | 
"45.....3....8.1....9...........5..9.2..7.....8.........1..4..........7.2...6..8..",  | 
|
120  | 
".237....68...6.59.9.....7......4.97.3.7.96..2.........5..47.........2....8.......",  | 
|
121  | 
"..84...3....3.....9....157479...8........7..514.....2...9.6...2.5....4......9..56",  | 
|
122  | 
".98.1....2......6.............3.2.5..84.........6.........4.8.93..5...........1..",  | 
|
123  | 
"..247..58..............1.4.....2...9528.9.4....9...1.........3.3....75..685..2...",  | 
|
124  | 
".2.3......63.....58.......15....9.3....7........1....8.879..26......6.7...6..7..4",  | 
|
125  | 
"1.....7.9.4...72..8.........7..1..6.3.......5.6..4..2.........8..53...7.7.2....46",  | 
|
126  | 
"4.....3.....8.2......7........1...8734.......6........5...6........1.4...82......",  | 
|
127  | 
".......71.2.8........4.3...7...6..5....2..3..9........6...7.....8....4......5....",  | 
|
128  | 
"6..3.2....4.....8..........7.26............543.........8.15........8.2........7..",  | 
|
129  | 
".47.8...1............6..7..6....357......5....1..6....28..4.....9.1...4.....2.69.",  | 
|
130  | 
"......8.17..2........5.6......7...5..1....3...8.......5......2..4..8....6...3....",  | 
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131  | 
"38.6.......9.......2..3.51......5....3..1..6....4......17.5..8.......9.......7.32",  | 
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132  | 
"...5...........5.697.....2...48.2...25.1...3..8..3.........4.7..13.5..9..2...31..",  | 
|
133  | 
".2.......3.5.62..9.68...3...5..........64.8.2..47..9....3.....1.....6...17.43....",  | 
|
134  | 
".8..4....3......1........2...5...4.69..1..8..2...........3.9....6....5.....2.....",  | 
|
135  | 
"..8.9.1...6.5...2......6....3.1.7.5.........9..4...3...5....2...7...3.8.2..7....4",  | 
|
136  | 
"1.....3.8.6.4..............2.3.1...........958.........5.6...7.....8.2...4.......",  | 
|
137  | 
"1....6.8..64..........4...7....9.6...7.4..5..5...7.1...5....32.3....8...4........",  | 
|
138  | 
"249.6...3.3....2..8.......5.....6......2......1..4.82..9.5..7....4.....1.7...3...",  | 
|
139  | 
"...8....9.873...4.6..7.......85..97...........43..75.......3....3...145.4....2..1",  | 
|
140  | 
"......8.16..2........7.5......6...2..1....3...8.......2......7..3..8....5...4....",  | 
|
141  | 
".476...5.8.3.....2.....9......8.5..6...1.....6.24......78...51...6....4..9...4..7",  | 
|
142  | 
".....7.95.....1...86..2.....2..73..85......6...3..49..3.5...41724................",  | 
|
143  | 
".4.5.....8...9..3..76.2.....146..........9..7.....36....1..4.5..6......3..71..2..",  | 
|
144  | 
".834.........7..5...........4.1.8..........27...3.....2.6.5....5.....8........1..",  | 
|
145  | 
"..9.....3.....9...7.....5.6..65..4.....3......28......3..75.6..6...........12.3.8",  | 
|
146  | 
".26.39......6....19.....7.......4..9.5....2....85.....3..2..9..4....762.........4",  | 
|
147  | 
"2.3.8....8..7...........1...6.5.7...4......3....1............82.5....6...1.......",  | 
|
148  | 
"6..3.2....1.....5..........7.26............843.........8.15........8.2........7..",  | 
|
149  | 
"1.....9...64..1.7..7..4.......3.....3.89..5....7....2.....6.7.9.....4.1....129.3.",  | 
|
150  | 
".........9......84.623...5....6...453...1...6...9...7....1.....4.5..2....3.8....9",  | 
|
151  | 
".2....5938..5..46.94..6...8..2.3.....6..8.73.7..2.........4.38..7....6..........5",  | 
|
152  | 
"9.4..5...25.6..1..31......8.7...9...4..26......147....7.......2...3..8.6.4.....9.",  | 
|
153  | 
"...52.....9...3..4......7...1.....4..8..453..6...1...87.2........8....32.4..8..1.",  | 
|
154  | 
"53..2.9...24.3..5...9..........1.827...7.........981.............64....91.2.5.43.",  | 
|
155  | 
"1....786...7..8.1.8..2....9........24...1......9..5...6.8..........5.9.......93.4",  | 
|
156  | 
"....5...11......7..6.....8......4.....9.1.3.....596.2..8..62..7..7......3.5.7.2..",  | 
|
157  | 
".47.2....8....1....3....9.2.....5...6..81..5.....4.....7....3.4...9...1.4..27.8..",  | 
|
158  | 
"......94.....9...53....5.7..8.4..1..463...........7.8.8..7.....7......28.5.26....",  | 
|
159  | 
".2......6....41.....78....1......7....37.....6..412....1..74..5..8.5..7......39..",  | 
|
160  | 
"1.....3.8.6.4..............2.3.1...........758.........7.5...6.....8.2...4.......",  | 
|
161  | 
"2....1.9..1..3.7..9..8...2.......85..6.4.........7...3.2.3...6....5.....1.9...2.5",  | 
|
162  | 
"..7..8.....6.2.3...3......9.1..5..6.....1.....7.9....2........4.83..4...26....51.",  | 
|
163  | 
"...36....85.......9.4..8........68.........17..9..45...1.5...6.4....9..2.....3...",  | 
|
164  | 
"34.6.......7.......2..8.57......5....7..1..2....4......36.2..1.......9.......7.82",  | 
|
165  | 
"......4.18..2........6.7......8...6..4....3...1.......6......2..5..1....7...3....",  | 
|
166  | 
".4..5..67...1...4....2.....1..8..3........2...6...........4..5.3.....8..2........",  | 
|
167  | 
".......4...2..4..1.7..5..9...3..7....4..6....6..1..8...2....1..85.9...6.....8...3",  | 
|
168  | 
"8..7....4.5....6............3.97...8....43..5....2.9....6......2...6...7.71..83.2",  | 
|
169  | 
".8...4.5....7..3............1..85...6.....2......4....3.26............417........",  | 
|
170  | 
"....7..8...6...5...2...3.61.1...7..2..8..534.2..9.......2......58...6.3.4...1....",  | 
|
171  | 
"......8.16..2........7.5......6...2..1....3...8.......2......7..4..8....5...3....",  | 
|
172  | 
".2..........6....3.74.8.........3..2.8..4..1.6..5.........1.78.5....9..........4.",  | 
|
173  | 
".52..68.......7.2.......6....48..9..2..41......1.....8..61..38.....9...63..6..1.9",  | 
|
174  | 
"....1.78.5....9..........4..2..........6....3.74.8.........3..2.8..4..1.6..5.....",  | 
|
175  | 
"1.......3.6.3..7...7...5..121.7...9...7........8.1..2....8.64....9.2..6....4.....",  | 
|
176  | 
"4...7.1....19.46.5.....1......7....2..2.3....847..6....14...8.6.2....3..6...9....",  | 
|
177  | 
"......8.17..2........5.6......7...5..1....3...8.......5......2..3..8....6...4....",  | 
|
178  | 
"963......1....8......2.5....4.8......1....7......3..257......3...9.2.4.7......9..",  | 
|
179  | 
"15.3......7..4.2....4.72.....8.........9..1.8.1..8.79......38...........6....7423",  | 
|
180  | 
"..........5724...98....947...9..3...5..9..12...3.1.9...6....25....56.....7......6",  | 
|
181  | 
"....75....1..2.....4...3...5.....3.2...8...1.......6.....1..48.2........7........",  | 
|
182  | 
"6.....7.3.4.8.................5.4.8.7..2.....1.3.......2.....5.....7.9......1....",  | 
|
183  | 
"....6...4..6.3....1..4..5.77.....8.5...8.....6.8....9...2.9....4....32....97..1..",  | 
|
184  | 
".32.....58..3.....9.428...1...4...39...6...5.....1.....2...67.8.....4....95....6.",  | 
|
185  | 
"...5.3.......6.7..5.8....1636..2.......4.1.......3...567....2.8..4.7.......2..5..",  | 
|
186  | 
".5.3.7.4.1.........3.......5.8.3.61....8..5.9.6..1........4...6...6927....2...9..",  | 
|
187  | 
"..5..8..18......9.......78....4.....64....9......53..2.6.........138..5....9.714.",  | 
|
188  | 
"..........72.6.1....51...82.8...13..4.........37.9..1.....238..5.4..9.........79.",  | 
|
189  | 
"...658.....4......12............96.7...3..5....2.8...3..19..8..3.6.....4....473..",  | 
|
190  | 
".2.3.......6..8.9.83.5........2...8.7.9..5........6..4.......1...1...4.22..7..8.9",  | 
|
191  | 
".5..9....1.....6.....3.8.....8.4...9514.......3....2..........4.8...6..77..15..6.",  | 
|
192  | 
".....2.......7...17..3...9.8..7......2.89.6...13..6....9..5.824.....891..........",  | 
|
| 321 | 193  | 
"3...8.......7....51..............36...2..4....7...........6.13..452...........8..",  | 
194  | 
"....14....3....2...7..........9...3.6.1.............8.2.....1.4....5.6.....7.8...",  | 
|
195  | 
"4.....8.5.3..........7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......")  | 
|
| 384 | 196  | 
|
| 329 | 197  | 
|
| 268 | 198  | 
|
199  | 
// for measuring time  | 
|
200  | 
def time_needed[T](i: Int, code: => T) = {
 | 
|
201  | 
val start = System.nanoTime()  | 
|
202  | 
for (j <- 1 to i) code  | 
|
203  | 
val end = System.nanoTime()  | 
|
| 301 | 204  | 
(end - start) / i / 1.0e9  | 
| 268 | 205  | 
}  | 
206  | 
||
207  | 
||
| 
462
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
208  | 
@main  | 
| 
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
209  | 
def test() = {
 | 
| 
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
210  | 
val total =  | 
| 
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
211  | 
    (for ((game, i) <- hard_games.zipWithIndex) yield {
 | 
| 
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
212  | 
val secs = time_needed(1, search(game))  | 
| 
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
213  | 
      println(f"${i}%2.0f: ${game} |${secs}%2.3f secs")
 | 
| 
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
214  | 
secs  | 
| 
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
215  | 
}).sum  | 
| 301 | 216  | 
|
| 
462
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
217  | 
  println(f"\ntotal: ${total}%.3f secs")
 | 
| 268 | 218  | 
}  | 
219  | 
||
| 301 | 220  | 
|
221  | 
||
| 
462
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
222  | 
// some numbers:  | 
| 
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
223  | 
//  | 
| 
 
c9fa27e4906a
updated to scala 3
 
Christian Urban <christian.urban@kcl.ac.uk> 
parents: 
447 
diff
changeset
 | 
224  | 
// single thread version 800 secs  | 
| 446 | 225  | 
//  | 
| 320 | 226  | 
// 4 cores parallel version on a moderate laptop 400 secs  | 
227  | 
// 8 cores: 290 secs  | 
|
| 446 | 228  | 
// 10 cores: 156 secs  | 
| 320 | 229  | 
// 18 cores: 142 secs  | 
| 301 | 230  |