import scala.util._

class Computation[A,B](value: A, function: A => B) {

  lazy val result = function(value)

}

def print_board(n: Int)(steps: List[(Int, Int)]): Unit = {

  println

  for (i <- 0 until n) {

    for (j <- 0 until n) {

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

    }

    println

  } 

}

def add_pair(x: (Int, Int))(y: (Int, Int)) = 

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

def is_legal(n: Int)(x: (Int, Int)) = 

  0 <= x._1 && 0 <= x._2 && x._1 < n && x._2 < n

def moves(n: Int)(steps: List[(Int, Int)])(x: (Int, Int)): List[(Int, Int)] = {

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

       (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)).filter(is_legal(n)).filterNot(steps.contains(_))

}

def ordered_moves(n: Int)(steps: List[(Int, Int)])(x : (Int, Int)): List[(Int, Int)] = 

  moves(n)(steps)(x).sortBy(moves(n)(steps)(_).length)

moves(8)(Nil)(1,3)

ordered_moves(8)(Nil)(1,3)

ordered_moves(8)(List((2, 4), (2, 6)))(1,3)

def first[A, B](xs: List[A], f: A => Set[B]): Set[B] = xs match {

  case Nil => Set()

  case x::xs => {

    val result = f(x)

    if (result == Set()) first(xs, f) else result

  }

}

// non-circular tour

def tour(n: Int)(steps: List[(Int, Int)]): Option[List[(Int, Int)]] = {

  if (steps.length ==  n * n) Some(steps) 

  else 

    { val list = moves(n)(steps)(steps.head) map (x => new Computation(x, ((x:(Int, Int)) => tour(n)(x::steps))))

      val found = list.par find (_.result.isDefined)

      found map (_.result.get)

    }

}

val n = 6

println(s"simple tour: n = $n")

val starts = for (i <- (0 until n).toList; 

                  j <- (0 until n).toList) yield new Computation ((i, j), ((x:(Int, Int)) => tour(n)(x::Nil)))

val found = starts.par find (_.result.isDefined)

print_board(n)((found map (_.result.get)).get)

//for measuring time

def time_needed[T](i: Int, code: => T) = {

  val start = System.nanoTime()

  for (j <- 1 to i) code

  val end = System.nanoTime()

  (end - start)/(i * 1.0e9)

}

//for (i <- 1 to 20) {

//  println(i + ": " + "%.5f".format(time_needed(2, matches(EVIL1(i), "a" * i))))

//}