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solution to the n-queens problem based on "Programming in Scala"
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| // Solves the n-queens problem for an arbitrary board size | |
| // Run for a board size of ten: scala nqueen.scala 10 | |
| object Nqueen { | |
| type Queen = (Int, Int) | |
| type Solutions = List[List[Queen]] | |
| def main(args: Array[String]) { | |
| val size: Int = args match { | |
| case Array() => sys.error("Provide a board size") | |
| case Array(n) => n.toInt | |
| } | |
| def placeQueens(n: Int): Solutions = n match { | |
| case 0 => List(Nil) | |
| case _ => for { | |
| queens <- placeQueens(n -1) | |
| y <- 1 to size | |
| queen = (n, y) | |
| if (isSafe(queen, queens)) | |
| } yield queen :: queens | |
| } | |
| val solutions = placeQueens(size) | |
| println(solutions.size + " solutions found") | |
| // print the board of the first solution | |
| for (queen <- solutions.head; x <- 1 to size) { | |
| if (queen._2 == x) print("Q ") else print(". ") | |
| if (x == size) println() | |
| } | |
| } | |
| def isSafe(queen: Queen, others: List[Queen]) = | |
| others forall (!isAttacked(queen, _)) | |
| def isAttacked(q1: Queen, q2: Queen) = | |
| q1._1 == q2._1 || | |
| q1._2 == q2._2 || | |
| (q2._1-q1._1).abs == (q2._2-q1._2).abs | |
| } |
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