--- a/progs/knight1.scala Sat Mar 11 23:12:49 2023 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,157 +0,0 @@
-// Part 1 about finding Knight's tours
-//=====================================
-
-type Pos = (Int, Int) // a position on a chessboard
-type Path = List[Pos] // a path...a list of positions
-
-// for measuring time
-def time_needed[T](code: => T) : T = {
- val start = System.nanoTime()
- val result = code
- val end = System.nanoTime()
- println(f"Time needed: ${(end - start) / 1.0e9}%3.3f secs.")
- result
-}
-
-// for printing a board
-def print_board(dim: Int, path: Path): Unit = {
- println
- for (i <- 0 until dim) {
- for (j <- 0 until dim) {
- print(f"${path.reverse.indexOf((j, dim - i - 1))}%3.0f ")
- }
- println
- }
-}
-
-
-// 1 mark
-
-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 add_pair(x: Pos, y: Pos): Pos =
- (x._1 + y._1, x._2 + y._2)
-
-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, _))
-
-// 1 mark
-
-def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] =
- moves(x).filter(is_legal(dim, path, _))
-
-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)))
-assert(legal_moves(1, Nil, (0,0)) == List())
-assert(legal_moves(2, Nil, (0,0)) == List())
-assert(legal_moves(3, Nil, (0,0)) == List((1,2), (2,1)))
-
-// 2 marks
-
-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 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
-}
-
-// as far as tasks go
-// test cases for CW
-
-
-
-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 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("Number of tours starting from (0, 0)")
-
-for (dim <- 1 to 5) {
- println(s"${dim} x ${dim} " + time_needed(0, count_tours(dim, List((0, 0)))))
-}
-
-println("Number of tours starting from all fields")
-
-for (dim <- 1 to 5) {
- println(s"${dim} x ${dim} " + time_needed(0, count_all_tours(dim)))
-}
-
-for (dim <- 1 to 5) {
- val ts = enum_tours(dim, List((0, 0)))
- println(s"${dim} x ${dim} ")
- if (ts != Nil) {
- print_board(dim, ts.head)
- println(ts.head)
- }
-}
-
-
-// 1 mark
-
-def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match {
- case Nil => None
- case x::xs => {
- val result = f(x)
- if (result.isDefined) result else first(xs, f)
- }
-}
-
-// test cases
-def foo(x: (Int, Int)) = if (x._1 > 3) Some(List(x)) else None
-
-first(List((1, 0),(2, 0),(3, 0),(4, 0)), foo)
-first(List((1, 0),(2, 0),(3, 0)), foo)
-
-
-// 1 mark
-
-def first_tour(dim: Int, path: Path): Option[Path] = {
- if (path.length == dim * dim) Some(path)
- else
- first(legal_moves(dim, path, path.head), (x: Pos) => first_tour(dim, x::path))
-}
-
-
-
-/*
-for (dim <- 1 to 8) {
- val t = first_tour(dim, List((0, 0)))
- println(s"${dim} x ${dim} " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))
-}
-*/
-
-// 15 secs for 8 x 8
-val ts1 = time_needed(0,first_tour(8, List((0, 0))).get)
-
-// no result for 4 x 4
-val ts2 = time_needed(0, first_tour(4, List((0, 0))))
-
-// 0.3 secs for 6 x 6
-val ts3 = time_needed(0, first_tour(6, List((0, 0))))
-
-// 15 secs for 8 x 8
-time_needed(0, print_board(8, first_tour(8, List((0, 0))).get))
-