// 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)

}