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))))
//}