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

//=============================================================

object CW8c { 

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))

}