--- a/progs/knight3_sol.scala	Tue Nov 15 23:08:09 2016 +0000
+++ b/progs/knight3_sol.scala	Wed Nov 16 14:37:18 2016 +0000
@@ -1,65 +1,24 @@
-// Part 2 about finding a single tour for a board
-//================================================
-
-
-type Pos = (Int, Int)
-type Path = List[Pos]
+// Part 3 about finding a single tour using the Warnsdorf Rule
+//=============================================================
 
-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)
+// copy any function you need from files knight1.scala and
+// knight2.scala
 
-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 ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
-  legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length)
+type Pos = (Int, Int)    // a position on a chessboard 
+type Path = List[Pos]    // a path...a list of positions
 
+//(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 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)
-  }
-}
-
-
-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 ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = ..
 
-for (dim <- 1 to 7) {
-  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) ; "" }))
-}
-
+//(3b) Complete the function that searches for a single *closed* 
+// tour using the ordered moves function.
 
-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_closed_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) ; "" }))
-}
+//(3c) Sama as (3b) but searches for *open* tours.
+
+def first_tour_heuristic(dim: Int, path: Path): Option[Path] = ...