--- a/testing3/knight1.scala Fri Dec 14 20:01:49 2018 +0000
+++ b/testing3/knight1.scala Sat Dec 15 13:46:54 2018 +0000
@@ -1,121 +1,13 @@
-// Part 1 about finding Knight's tours
-//=====================================
+// Part 1 about finding and counting Knight's tours
+//==================================================
-// If you need any auxiliary function, feel free to
-// implement it, but do not make any changes to the
-// templates below. Also have a look whether the functions
-// at the end are of any help.
-
-
+//object CW8a { // for preparing the jar
type Pos = (Int, Int) // a position on a chessboard
type Path = List[Pos] // a path...a list of positions
-//(1) Complete the function that tests whether the position x
-// is inside the board and not yet element in the path.
-def is_legal(dim: Int, path: Path, x: Pos) : Boolean = {
- if ((x._1 < dim && x._2 < dim) && !(path.contains(x)))
- true
- else
- false
-}
-
-
-
-//(2) Complete the function that calculates for a position x
-// 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] = {
- val legalMovesList = 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))
-
- for (i <- legalMovesList
- if (is_legal(dim, path, i)))
- yield i
-
-}
-
-
-//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)))
-
-
-//(3) 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 = {
- if (path.size == (dim ^ 2)){
- List(path).size
- } else {
- val totalTours = legal_moves(dim, path, path.head)
- totalTours.map(element => count_tours(dim, element :: path)).sum
- }
-}
-
-def enum_tours(dim: Int, path: Path) : List[Path] = {
- if (path.size == (dim ^ 2)){
- List(path)
- } else {
- val totalEnums = legal_moves(dim, path, path.head)
- totalEnums.map(element => enum_tours(dim, element :: path)).flatten
- }
-}
-
-
-//(5) Implement a first-function that finds the first
-// element, say x, in the list xs where f is not None.
-// In that case Return f(x), otherwise None. If possible,
-// calculate f(x) only once.
-
-def first(xs: List[Pos], f: Pos => Option[Path]) : Option[Path] = {
- if (xs eq Nil) {
- None
- } else {
- if (f(xs.head) != None) {
- f(xs.head)
- } else {
- first(xs.tail, 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) // Some(List((4,0)))
-//first(List((1, 0),(2, 0),(3, 0)), foo) // None
-
-
-
-
-//(6) Implement a function that uses the first-function from (5) for
-// trying out onward moves, and searches recursively for a
-// knight tour on a dim * dim-board.
-
-
-//def first_tour(dim: Int, path: Path) : Option[Path] = ...
-
-
-
-
-
-
-/* Helper functions
-
-
-// for measuring time
+// for measuring time in the JAR
def time_needed[T](code: => T) : T = {
val start = System.nanoTime()
val result = code
@@ -124,11 +16,6 @@
result
}
-// can be called for example with
-// time_needed(count_tours(dim, List((0, 0))))
-// in order to print out the time that is needed for
-// running count_tours
-
// for printing a board
def print_board(dim: Int, path: Path): Unit = {
println
@@ -140,5 +27,144 @@
}
}
+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)
+// testcases
+//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, _))
+
+// testcases
+//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 tcount_tours(dim: Int, path: Path): Int = {
+ if (path.length == dim * dim) 1
+ else
+ (for (x <- legal_moves(dim, path, path.head)) yield tcount_tours(dim, x::path)).sum
+}
+
+def count_tours(dim: Int, path: Path) =
+ time_needed(tcount_tours(dim: Int, path: Path))
+
+
+def tenum_tours(dim: Int, path: Path): List[Path] = {
+ if (path.length == dim * dim) List(path)
+ else
+ (for (x <- legal_moves(dim, path, path.head)) yield tenum_tours(dim, x::path)).flatten
+}
+
+def enum_tours(dim: Int, path: Path) =
+ time_needed(tenum_tours(dim: Int, path: Path))
+
+// test cases
+
+/*
+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 ${dim} ")
+ if (ts != Nil) {
+ print_board(dim, ts.head)
+ println(ts.head)
+ }
+}
*/
+
+// 1 mark
+
+def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match {
+ case Nil => None
+ case x::xs => {
+ val result = f(x)
+ if (result.isDefined) result else first(xs, f)
+ }
+}
+
+// test cases
+//def foo(x: (Int, Int)) = if (x._1 > 3) Some(List(x)) else None
+//
+//first(List((1, 0),(2, 0),(3, 0),(4, 0)), foo)
+//first(List((1, 0),(2, 0),(3, 0)), foo)
+
+
+// 1 mark
+
+def tfirst_tour(dim: Int, path: Path): Option[Path] = {
+ if (path.length == dim * dim) Some(path)
+ else
+ first(legal_moves(dim, path, path.head), (x:Pos) => tfirst_tour(dim, x::path))
+}
+
+def first_tour(dim: Int, path: Path) =
+ time_needed(tfirst_tour(dim: Int, path: Path))
+
+
+/*
+for (dim <- 1 to 8) {
+ val t = first_tour(dim, List((0, 0)))
+ println(s"${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))
+
+
+//}
+
+