Solve the N-queens problem in Scala

object Example {
  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
  }

  def isSafe(queen: (Int, Int), queens: List[(Int, Int)]) = {
    queens.forall(!inCheck(_, queen))
  }

    def queens(k: Int): List[List[(Int, Int)]] = {
      // solve the nth row
      def placeQueens(n: Int): List[List[(Int, Int)]] = {
        if (n == 0) {
          List(List())
        }
        else {
          for {
            queens: List[(Int, Int)] <- placeQueens(n - 1)
            column <- 1 to k
            queen = (n, column)
            if (isSafe(queen, queens))
          } yield queen :: queens
        }
      }
      placeQueens(k)
    }
}


object Test {

  import Example._

  isSafe((1, 1), List((2, 3), (3, 2)))
  inCheck((1, 1), (2, 3))
  List[Int]().forall(_ > 3) // vacuously true
  queens(4)

}