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)
}