--- a/progs/knight3_sol.scala	Wed Nov 16 15:05:40 2016 +0000
+++ b/progs/knight3_sol.scala	Wed Nov 16 23:34:05 2016 +0000
@@ -1,24 +1,65 @@
 // Part 3 about finding a single tour using the Warnsdorf Rule
 //=============================================================
 
-// copy any function you need from files knight1.scala and
-// knight2.scala
+
+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
+  } 
+}
 
-type Pos = (Int, Int)    // a position on a chessboard 
-type Path = List[Pos]    // a path...a list of positions
+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)
 
-//(3a) Complete the function that calculates a list of onward
-// moves like in (1b) but orders them according to the Warnsdorf’s 
-// rule. That means moves with the fewest legal onward moves 
-// should come first.
+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 ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
+  legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length)
+
 
-def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = ..
+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)
+  }
+}
 
-//(3b) Complete the function that searches for a single *closed* 
-// tour using the ordered moves function.
+
+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))
+}
 
-def first_closed_tour_heuristic(dim: Int, path: Path): Option[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) ; "" }))
+}
+
 
-//(3c) Sama as (3b) but searches for *open* tours.
+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))
+}
 
-def first_tour_heuristic(dim: Int, path: Path): Option[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) ; "" }))
+}