--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3-bak/knight2.scala	Fri Nov 16 02:06:03 2018 +0000
@@ -0,0 +1,61 @@
+// Part 2 about finding a single tour for a board
+//================================================
+
+object CW7b {
+
+type Pos = (Int, Int)    // a position on a chessboard 
+type Path = List[Pos]    // a path...a list of positions
+
+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))
+}
+
+/* 
+val ts1 = first_tour(8, List((0, 0))).get
+  assert(correct_urban(8)(ts1) == true)
+
+val ts2 = first_tour(4, List((0, 0)))
+assert(ts2 == None)  
+
+print_board(8, first_tour(8, List((0, 0))).get)
+*/
+
+}
+