--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/knight1.scala	Wed Nov 02 13:22:40 2016 +0000
@@ -0,0 +1,76 @@
+import scala.util._
+
+class Computation[A,B](value: A, function: A => B) {
+  lazy val result = function(value)
+}
+
+
+def print_board(n: Int)(steps: List[(Int, Int)]): Unit = {
+  println
+  for (i <- 0 until n) {
+    for (j <- 0 until n) {
+      print(f"${steps.indexOf((i, j))}%3.0f ")
+    }
+    println
+  } 
+}
+
+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)(steps: List[(Int, 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)).filterNot(steps.contains(_))
+}
+
+def ordered_moves(n: Int)(steps: List[(Int, Int)])(x : (Int, Int)): List[(Int, Int)] = 
+  moves(n)(steps)(x).sortBy(moves(n)(steps)(_).length)
+
+moves(8)(Nil)(1,3)
+ordered_moves(8)(Nil)(1,3)
+ordered_moves(8)(List((2, 4), (2, 6)))(1,3)
+
+def first[A, B](xs: List[A], f: A => Set[B]): Set[B] = xs match {
+  case Nil => Set()
+  case x::xs => {
+    val result = f(x)
+    if (result == Set()) first(xs, f) else result
+  }
+}
+
+// non-circular tour
+def tour(n: Int)(steps: List[(Int, Int)]): Option[List[(Int, Int)]] = {
+  if (steps.length ==  n * n) Some(steps) 
+  else 
+    { val list = moves(n)(steps)(steps.head) map (x => new Computation(x, ((x:(Int, Int)) => tour(n)(x::steps))))
+      val found = list.par find (_.result.isDefined)
+      found map (_.result.get)
+    }
+}
+
+val n = 6
+println(s"simple tour: n = $n")
+
+val starts = for (i <- (0 until n).toList; 
+                  j <- (0 until n).toList) yield new Computation ((i, j), ((x:(Int, Int)) => tour(n)(x::Nil)))
+
+val found = starts.par find (_.result.isDefined)
+print_board(n)((found map (_.result.get)).get)
+
+//for measuring time
+def time_needed[T](i: Int, code: => T) = {
+  val start = System.nanoTime()
+  for (j <- 1 to i) code
+  val end = System.nanoTime()
+  (end - start)/(i * 1.0e9)
+}
+
+//for (i <- 1 to 20) {
+//  println(i + ": " + "%.5f".format(time_needed(2, matches(EVIL1(i), "a" * i))))
+//}
+
+
+