// Part 3 about finding a single tour using the Warnsdorf Rule
//=============================================================

//object CW8c { // for preparing the jar

type Pos = (Int, Int)
type Path = List[Pos]


// for measuring time in the JAR
def time_needed[T](code: => T) : T = {
  val start = System.nanoTime()
  val result = code
  val end = System.nanoTime()
  println(f"Time needed: ${(end - start) / 1.0e9}%3.3f secs.")
  result
}


def print_board(dim: Int, path: Path): Unit = {
  println
  for (i <- 0 until dim) {
    for (j <- 0 until dim) {
      print(f"${path.reverse.indexOf((i, j))}%4.0f ")
    }
    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, _))
 
def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
  legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length)

import scala.annotation.tailrec

@tailrec
def tour_on_mega_board_aux(dim: Int, paths: List[Path]): Option[Path] = paths match {
  case Nil => None
  case (path::rest) =>
    if (path.length == dim * dim) Some(path)
    else tour_on_mega_board_aux(dim, ordered_moves(dim, path, path.head).map(_::path) ::: rest)
}

def ttour_on_mega_board(dim: Int, path: Path): Option[Path] =
  tour_on_mega_board_aux(dim, List(path))


def tour_on_mega_board(dim: Int, path: Path) =
  time_needed(ttour_on_mega_board(dim: Int, path: Path))

//}
