// Part 4 about finding a single tour on "mutilated" chessboards
//==============================================================

object M4d { // for preparing the jar

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.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, _))
 
import scala.annotation.tailrec

@tailrec
def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match {
  case Nil => None
  case x::xs => {
    val result = f(x)
    if (result.isDefined) result else first(xs, f)
  }
}


def one_tour_pred(dim: Int, path: Path, n: Int, pred: Pos => Boolean): Option[Path] = {
  if (path.length == n) Some(path)
  else
    first(legal_moves(dim, path, path.head).filter(pred), (x: Pos) => one_tour_pred(dim, x::path, n, pred))
}

//print_board(8, one_tour_pred(8, List((0, 0)), 40, x => x._1 < 5).get)


}