--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/knight1_sol.scala	Mon Nov 14 03:25:14 2016 +0000
@@ -0,0 +1,73 @@
+// Part 1 about finding and counting Knight's tours
+//==================================================
+
+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"${path.reverse.indexOf((j, dim - i - 1))}%3.0f ")
+    }
+    println
+  } 
+}
+
+def add_pair(x: Pos)(y: Pos): Pos = 
+  (x._1 + y._1, x._2 + y._2)
+
+def is_legal(dim: Int, path: Path)(x: Pos): Boolean = 
+  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
+
+def moves(x: Pos): List[Pos] = 
+  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
+       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x))
+
+def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
+  moves(x).filter(is_legal(dim, path))
+
+legal_moves(8, Nil, (2,2))
+legal_moves(8, Nil, (7,7))
+
+
+def count_tours(dim: Int, path: Path): Int = {
+  if (path.length == dim * dim) 1
+  else 
+    (for (x <- legal_moves(dim, path, path.head)) yield count_tours(dim, x::path)).sum
+}
+
+def enum_tours(dim: Int, path: Path): List[Path] = {
+  if (path.length == dim * dim) List(path)
+  else 
+    (for (x <- legal_moves(dim, path, path.head)) yield enum_tours(dim, x::path)).flatten
+}
+
+def count_all_tours(dim: Int): Int = {
+  (for (i <- (0 until dim).toList; 
+        j <- (0 until dim).toList) yield count_tours(dim, List((i, j)))).sum
+}
+
+def enum_all_tours(dim: Int): List[Path] = {
+  (for (i <- (0 until dim).toList; 
+        j <- (0 until dim).toList) yield enum_tours(dim, List((i, j)))).flatten
+}
+
+for (dim <- 1 to 5) {
+  println(s"${dim} x ${dim} " + count_tours(dim, List((0, 0))))
+}
+
+for (dim <- 1 to 5) {
+  println(s"${dim} x ${dim} " + count_all_tours(dim))
+}
+
+for (dim <- 1 to 5) {
+  val ts = enum_tours(dim, List((0, 0)))
+  println(s"${dim} x ${dim} ")   
+  if (ts != Nil) {
+    print_board(dim, ts.head)
+    println(ts.head)
+  }
+}
+
+