// Part 1 about finding and counting Knight's tours

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

object CW7a extends App{

type Pos = (Int, Int)    // a position on a chessboard 

type Path = List[Pos]    // a path...a list of positions

//(1a) Complete the function that tests whether the position 

//     is inside the board and not yet element in the path.

//def is_legal(dim: Int, path: Path)(x: Pos) : Boolean = ...

def is_legal(dim: Int, path: Path)(x: Pos) : Boolean = {

// if ((x._1<dim && x._2<dim) && (x._1>0 || x._2>0)) false else !path.contains(x)

  if (x._1 < 0 || x._2 < 0) false 

  else if (x._1 < dim && x._2 < dim && !path.contains(x)) true 

  else false

}

def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = {

  val allPossibleMoves = List((x._1+1, x._2+2), (x._1+2, x._2+1), (x._1+2, x._2-1), (x._1+1, x._2-2), (x._1-1, x._2-2), (x._1-2, x._2-1), (x._1-2, x._2+1), (x._1-1, x._2+2));

  //val finalList = allPossibleMoves.filter((a=>a._1<dim && a._2<dim && x._1 >= 0 && a._2 >= 0));

  val finalList = for(pos<-allPossibleMoves if(is_legal(dim,path)(pos))) yield pos;

  // println("Space in board: " + dim*dim + " for dim: " + dim)

  finalList.toList;

}

println(legal_moves(8, Nil, (2,2)))

println(legal_moves(8, Nil, (7,7)))

println(legal_moves(8, List((4,1), (1,0)), (2,2)))

println(legal_moves(8, List((6,6)), (7,7)))

println(legal_moves(1, Nil, (0,0)))

println(legal_moves(2, Nil, (0,0)))

println(legal_moves(3, Nil, (0,0)))

println("=================================================================================")

println("================================Comparision output===============================")

println("=================================================================================")

println(legal_moves(8, Nil, (2,2)) == List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))

println(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))

println(legal_moves(8, List((4,1), (1,0)), (2,2)) == List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))

println(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))

println(legal_moves(1, Nil, (0,0)) == Nil)

println(legal_moves(2, Nil, (0,0)) == Nil)

println(legal_moves(3, Nil, (0,0)) == List((1,2), (2,1)))

def count_tours(dim: Int, path: Path) : Int = {

  val allMovesFromCurrentPosition = legal_moves(dim, path, path.head);

  if (path.length == dim*dim) 1 else  {

    if (allMovesFromCurrentPosition.size == 0 ) 0  else {

      allMovesFromCurrentPosition.map( element => count_tours(dim, element::path)).sum

    }

  }

}

println ( count_tours(5, List((0,0))) )

def enum_tours(dim: Int, path: Path) : List[Path] = {

     val allMovesFromCurrentPosition = legal_moves(dim, path, path.head);

  if (path.length == dim*dim) List(path) else  {

  allMovesFromCurrentPosition.map( element => enum_tours(dim, element::path)).flatten ;

      }

    }

  println ( enum_tours(6, List((0,2))).size)

}

//(1b) Complete the function that calculates for a position 

//     all legal onward moves that are not already in the path. 

//     The moves should be ordered in a "clockwise" manner.

//def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = ...

//some test cases

//

//assert(legal_moves(8, Nil, (2,2)) == 

//  List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))

//assert(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))

//assert(legal_moves(8, List((4,1), (1,0)), (2,2)) == 

//  List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))

//assert(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))

//(1c) Complete the two recursive functions below. 

//     They exhaustively search for knight's tours starting from the 

//     given path. The first function counts all possible tours, 

//     and the second collects all tours in a list of paths.

//def count_tours(dim: Int, path: Path) : Int = ...

//def enum_tours(dim: Int, path: Path) : List[Path] = ...