--- a/progs/knight1.scala	Tue Nov 20 14:31:14 2018 +0000
+++ b/progs/knight1.scala	Thu Nov 22 17:19:23 2018 +0000
@@ -1,9 +1,19 @@
-// Part 1 about finding and counting Knight's tours
-//==================================================
+// 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) {
@@ -20,22 +30,22 @@
 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)
+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 = 
+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, -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))
+  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)))
@@ -62,6 +72,7 @@
 }
 
 // as far as tasks go
+// test cases for CW
 
 
 
@@ -79,11 +90,13 @@
 println("Number of tours starting from (0, 0)")
 
 for (dim <- 1 to 5) {
-  println(s"${dim} x ${dim} " + count_tours(dim, List((0, 0))))
+  println(s"${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 ${dim} " + count_all_tours(dim))
+  println(s"${dim} x ${dim} " + time_needed(0, count_all_tours(dim)))
 }
 
 for (dim <- 1 to 5) {
@@ -96,3 +109,49 @@
 }
 
 
+// 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))
+