Queens

queens.scala

object queens extends App {

  def queens(n: Int): List[List[(Int, Int)]] = {
    def placeQueens(k: Int): List[List[(Int, Int)]] = {
      if (k == 0)
        List(List())
      else for {
        queens <- placeQueens(k - 1)
        col <- 1 to n
        queen = (k, col)
        if queens forall (q => !inCheck(queen, q))
      } yield queen :: queens
    }
    placeQueens(n)
  }

  def inCheck(q1: (Int, Int), q2: (Int, Int)) =
    q1._1 == q2._1 ||
    q1._2 == q2._2 ||
    (q1._1 - q2._1).abs == (q1._2 - q2._2).abs

  println(for (n <- 1 to 10) yield queens(n).length)
}