--- a/progs/knight3.scala	Tue Nov 15 23:08:09 2016 +0000
+++ b/progs/knight3.scala	Wed Nov 16 14:37:18 2016 +0000
@@ -1,45 +1,65 @@
-import scala.util._
+// Part 3 about finding a single tour using the Warnsdorf Rule
+//=============================================================
+
 
-def print_board(n: Int)(steps: List[(Int, Int)]): Unit = {
-  for (i <- 0 until n) {
-    for (j <- 0 until n) {
-      print(f"${steps.indexOf((i, j))}%3.0f ")
+type Pos = (Int, Int)
+type Path = List[Pos]
+
+def print_board(dim: Int, path: Path): Unit = {
+  println
+  for (i <- 0 until dim) {
+    for (j <- 0 until dim) {
+      print(f"${path.reverse.indexOf((i, j))}%3.0f ")
     }
     println
   } 
-  //readLine()
-  System.exit(0)
-}
-
-def add_pair(x: (Int, Int))(y: (Int, Int)) = 
-  (x._1 + y._1, x._2 + y._2)
-
-def is_legal(n: Int)(x: (Int, Int)) = 
-  0 <= x._1 && 0 <= x._2 && x._1 < n && x._2 < n
-
-def moves(n: Int)(x: (Int, Int)): List[(Int, Int)] = {
-  List((1, 2),(2, 1),(2, -1),(1, -2),
-       (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)).filter(is_legal(n))
 }
 
-def ordered_moves(n: Int)(steps: List[(Int, Int)])(x : (Int, Int)): List[(Int, Int)] = 
-  moves(n)(x).sortBy((x: (Int, Int)) => moves(n)(x).filterNot(steps.contains(_)).length)
+def add_pair(x: Pos)(y: Pos): Pos = 
+  (x._1 + y._1, x._2 + y._2)
 
-moves(8)(1,3)
-ordered_moves(8)(Nil)(1,3)
-ordered_moves(8)(List((2, 4), (2, 6)))(1,3)
+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))
 
-// non-circle tour parallel
-def tour(n: Int)(steps: List[(Int, Int)]): Unit = {
-  if (steps.length ==  n * n && moves(n)(steps.head).contains(steps.last))
-    print_board(n)(steps)
-  else 
-    for (x <- moves(n)(steps.head).par; if (!steps.contains(x))) tour(n)(x :: steps)
+def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
+  moves(x).filter(is_legal(dim, path))
+
+def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
+  legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length)
+
+
+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)
+  }
 }
 
-val n = 7
-println(s"circle tour parallel: n = $n")
+
+def first_closed_tour_heuristics(dim: Int, path: Path): Option[Path] = {
+  if (path.length == dim * dim && moves(path.head).contains(path.last)) Some(path)
+  else
+    first(ordered_moves(dim, path, path.head), (x: Pos) => first_closed_tour_heuristics(dim, x::path))
+}
+
+for (dim <- 1 to 6) {
+  val t = first_closed_tour_heuristics(dim, List((dim / 2, dim / 2)))
+  println(s"${dim} x ${dim} closed: " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))
+}
 
-val starts = for (i <- 0 until n; j <- 0 until n) yield (i, j)
 
-starts.par.foreach((x:(Int, Int)) => tour(n)(List(x))) 
+def first_tour_heuristics(dim: Int, path: Path): Option[Path] = {
+  if (path.length == dim * dim) Some(path)
+  else
+    first(ordered_moves(dim, path, path.head), (x: Pos) => first_tour_heuristics(dim, x::path))
+}
+
+for (dim <- 1 to 50) {
+  val t = first_tour_heuristics(dim, List((dim / 2, dim / 2)))
+  println(s"${dim} x ${dim}: " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))
+}