diff -r 9b5165b8a762 -r 0587ef444547 Attic/knight2.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Attic/knight2.scala	Sat Mar 11 23:22:05 2023 +0000
@@ -0,0 +1,81 @@
+// Part 2 about finding a single tour for a board
+//================================================
+
+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](n: Int, code: => T) : T = {
+  val start = System.nanoTime()
+  for (i <- 0 until n) code
+  val result = code
+  val end = System.nanoTime()
+  println("Time needed: " + (end - start) / 1.0e9 + " secs.")
+  result
+}
+
+
+def print_board(dim: Int, path: Path): Unit = {
+  println
+  for (i <- 0 until dim) {
+    for (j <- 0 until dim) {
+      print(f"${path.reverse.indexOf((i, j))}%3.0f ")
+    }
+    println
+  } 
+}
+
+def add_pair(x: Pos)(y: Pos): Pos = 
+  (x._1 + y._1, x._2 + y._2)
+
+def is_legal(dim: Int, path: Path)(x: Pos): Boolean = 
+  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
+
+def moves(x: Pos): List[Pos] = 
+  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
+       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x))
+
+def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
+  moves(x).filter(is_legal(dim, path))
+
+
+def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match {
+  case Nil => None
+  case x::xs => {
+    val result = f(x)
+    if (result.isDefined) result else first(xs, f)
+  }
+}
+
+first(List((1, 0),(2, 0),(3, 0),(4, 0)), (x => if (x._1 > 3) Some(List(x)) else None))
+first(List((1, 0),(2, 0),(3, 0)), (x => if (x._1 > 3) Some(List(x)) else None))
+
+
+
+def first_tour(dim: Int, path: Path): Option[Path] = {
+  if (path.length == dim * dim) Some(path)
+  else
+    first(legal_moves(dim, path, path.head), (x: Pos) => first_tour(dim, x::path))
+}
+
+/*
+for (dim <- 1 to 8) {
+  val t = first_tour(dim, List((0, 0)))
+  println(s"${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))
+
+