--- a/testing2/knight1.scala Tue Dec 05 00:34:14 2017 +0000
+++ b/testing2/knight1.scala Thu Dec 07 12:04:31 2017 +0000
@@ -1,91 +1,133 @@
+
// Part 1 about finding and counting Knight's tours
//==================================================
-object CW7a {
+object CW7a extends App{
type Pos = (Int, Int) // a position on a chessboard
type Path = List[Pos] // a path...a list of positions
-def print_board(dim: Int, path: Path): Unit = {
- println
- for (i <- 0 until dim) {
- for (j <- 0 until dim) {
- print(f"${path.reverse.indexOf((j, dim - i - 1))}%3.0f ")
- }
- println
- }
-}
+//(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 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)
-
-assert(is_legal(8, Nil)((3,4)) == true)
-assert(is_legal(8, List((4,1), (1,0)))((4,1)) == false)
-assert(is_legal(2, Nil)((0,0)) == true)
+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 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 count_tours(dim: Int, path: Path): Int = {
- if (path.length == dim * dim) 1
- else
- (for (x <- legal_moves(dim, path, path.head)) yield count_tours(dim, x::path)).sum
-}
-
-def count_tours(dim: Int, path : Path) : Int = {
+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));
- if (path.length == dim * dim) {1}
- else
- val x = for (m <- legal_moves(dim,path,path.head)) yield {
+ val finalList = for(pos<-allPossibleMoves if(is_legal(dim,path)(pos))) yield pos;
+
+ // println("Space in board: " + dim*dim + " for dim: " + dim)
+
+
+ finalList.toList;
- count_tours(dim,m::path)
- }
- x.sum
}
-def enum_tours(dim: Int, path: Path): List[Path] = {
- if (path.length == dim * dim) List(path)
- else
- (for (x <- legal_moves(dim, path, path.head)) yield enum_tours(dim, x::path)).flatten
-}
+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_all_tours(dim: Int) = {
- for (i <- (0 until dim).toList;
- j <- (0 until dim).toList) yield count_tours(dim, List((i, j)))
+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
+
+
+ }
+
+ }
+
}
+
+
-def enum_all_tours(dim: Int): List[Path] = {
- (for (i <- (0 until dim).toList;
- j <- (0 until dim).toList) yield enum_tours(dim, List((i, j)))).flatten
+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)
}
-/*
-for (dim <- 1 to 5) {
- println(s"${dim} x ${dim} " + count_tours(dim, List((0, 0))))
-}
+
+
+
-for (dim <- 1 to 5) {
- println(s"${dim} x ${dim} " + count_all_tours(dim))
-}
+
+
+//(1b) Complete the function that calculates for a position
+// all legal onward moves that are not already in the path.
+// The moves should be ordered in a "clockwise" manner.
+
+//def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = ...
+
+
+
-for (dim <- 1 to 5) {
- val ts = enum_tours(dim, List((0, 0)))
- println(s"${dim} x ${dim} ")
- if (ts != Nil) {
- print_board(dim, ts.head)
- println(ts.head)
- }
-}
-*/
+//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] = ...