type Pos = (Int, Int)

type Path = List[Pos]

def print_board(dim: Int, path: Path): Unit = {

  println

  for (i <- 0 until dim) {

    for (j <- 0 until dim) {

      print(f"${path.indexOf((i, j))}%3.0f ")

    }

    println

  } 

}

def add_pair(x: Pos)(y: Pos): Pos = 

  (x._1 + y._1, x._2 + y._2)

def is_legal(dim: Int, path: Path)(x: Pos): Boolean = 

  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)

def moves(x: Pos): List[Pos] = {

  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),

       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x))

}

def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = 

  moves(x).filter(is_legal(dim, path))

// non-circle tours

/*

def tour(dim: Int, path: List[Pos]): List[List[Pos]] = {

  if (path.length ==  dim * dim) // && moves(n)(path.head).contains(path.last)) 

    List(path)

  else 

    (for (x <- legal_moves(dim, path, path.head)) yield tour(dim, x::path)).flatten

}

*/

def tour(dim: Int, path: Path): Int = {

  if (path.length == dim * dim) 1

  else 

    (for (x <- legal_moves(dim, path, path.head) yield tour(dim, x::path))).sum

}

def dtour(dim: Int): List[List[Pos]] = {

  var counter = 100000000

  def etour(dim: Int, path: List[Pos]): List[List[Pos]] = {

    counter = counter - 1

    if (counter <= 0) List() else

      if (path.length == dim * dim) List(path)

      else 

        (for (x <- legal_moves(dim, path, path.head)) yield etour(dim, x::path)).flatten

  }

  (for (i <- (0 until dim).toList; 

        j <- (0 until dim).toList) yield etour(dim, List((i, j)))).flatten

}

//val n = 8

val n = 5

println(s"number simple tours: n = $n")

//println(etour(n, List((0, 0))).size)

for (d <- 9 to 9) {

  println(s"${d} x ${d} " + dtour(d).length)

}