diff -r 34feeb53c0ba -r 0315d9983cd0 main_marking4/knight1.scala
--- a/main_marking4/knight1.scala	Sun Jan 15 10:58:13 2023 +0000
+++ b/main_marking4/knight1.scala	Sat Mar 11 22:01:53 2023 +0000
@@ -1,119 +1,13 @@
-// Main Part 4 about finding Knight's tours
-//==========================================
-import scala.annotation.tailrec
-
-
-object M4a {
+// Part 1 about finding and counting Knight's tours
+//==================================================
 
-// If you need any auxiliary functions, feel free to 
-// implement them, but do not make any changes to the
-// templates below. Also have a look whether the functions
-// at the end of the file are of any help.
-
-
+object M4a {   // 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 = {
-  (x._1 < dim) && (x._2 < dim) && (!path.contains(x))
-}
-
-
-
-//(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 movesets = 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)
-  )
-  movesets.filter(is_legal(dim, path, _))
-}
-
-
-//some 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)))
-
-
-//(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 (dim <= 4) 0 else {
-    if (path.length >= (dim * dim)) 1 else {
-      val movesets = legal_moves(dim, path, path.head)
-      (for (move <- movesets) yield count_tours(dim, move :: path)).sum
-    }
-  }
-}
-
-def enum_tours(dim: Int, path: Path) : List[Path] = {
-  if (dim <= 4) Nil else {
-    if (path.length >= (dim * dim)) List(path) else {
-      val movesets = legal_moves(dim, path, path.head)
-      (for (move <- movesets) yield enum_tours(dim, move :: path)).flatten
-    }
-  }
-}
-
-
-//(4) 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.
-
-@tailrec
-def first(xs: List[Pos], f: Pos => Option[Path]) : Option[Path] = {
-  xs match {
-    case Nil => None
-    case head :: rest => {
-      val result = f(head)
-      if (result.isEmpty) first(rest, f) else result
-    }
-  }
-}
-
-
-// testcases
-//
-//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
-
-
-//(5) Implement a function that uses the first-function from (4) 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
@@ -122,14 +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()
@@ -141,7 +27,145 @@
   } 
 }
 
+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, _))
+
+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(8, Nil, (0,1)) == List((1,3), (2,2), (2,0)))
+//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)))
+
+
+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)
+  }
+}
 */
 
+
+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)
+
+
+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)
+//??val ts1 = time_needed(0,first_tour(8, List((1, 1))).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))
+
+
+
+
+
+}
+
+