EightQueen.scala

object EightQueen {
    def queens(n: Int): Set[List[Int]] = {
        def placeQueens(k: Int): Set[List[Int]] = {
            if (k == 0) Set(List.empty)
            else {
                for {
                    queens <- placeQueens(k - 1)
                    col <- 0 until n
                    if (isSafe(col, queens)) 
                } yield col :: queens
            }
        }
        placeQueens(n)
    }

    def isSafe(col: Int, queens: List[Int]): Boolean = {
       val row = queens.length
       val queensWithRow = (row - 1 to 0 by - 1) zip queens
       queensWithRow forall {
           case (r, c) => col != c && math.abs(col - c) != row - r
       }
    }

    def show(queens: List[Int]) = {
        val lines = 
            for(col <- queens.reverse) 
            yield Vector.fill(queens.length)("* ").updated(col, "X ").mkString
            "\n" + (lines mkString "\n")
    }
    def main(args: Array[String]) = {
        println((queens(8) map show) mkString "\n")
    }
}