--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/knight6.scala	Sat Nov 12 22:28:14 2016 +0000
@@ -0,0 +1,72 @@
+import scala.util._
+
+type Pos = (Int, Int)
+
+
+def print_board(n: Int)(steps: List[Pos]): Unit = {
+  for (i <- 0 until n) {
+    for (j <- 0 until n) {
+      print(f"${steps.reverse.indexOf((i, j))}%3.0f ")
+    }
+    println
+  } 
+}
+
+def add_pair(x: Pos)(y: Pos) = 
+  (x._1 + y._1, x._2 + y._2)
+
+def dist(n: Int)(y: Pos) = 
+  (n / 2 - y._1).abs + (n / 2 - y._2).abs
+
+def is_legal(n: Int)(x: Pos) = 
+  0 <= x._1 && 0 <= x._2 && x._1 < n && x._2 < n
+
+def moves(n: Int)(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)).filter(is_legal(n))
+}
+
+def moves_filtered(n: Int)(steps: List[Pos])(x: Pos): List[Pos] = {
+  moves(n)(x).filterNot(steps.contains(_))
+}
+
+def ordered_moves(n: Int)(steps: List[Pos])(x: Pos): List[Pos] = 
+  moves_filtered(n)(steps)(x).sortBy((x: Pos) => (moves_filtered(n)(steps)(x).length, dist(n)(x)))
+
+/*def first[A, B](xs: List[A], f: A => Option[B]): Option[B] = xs match {
+  case Nil => None
+  case x::xs => {
+    val result = f(x)
+    if (result.isDefined) result else first(xs, f)
+  }
+}*/
+
+def first[A, B](xs: List[A], f: A => Option[B]): Option[B] =
+  xs.par.flatMap(f(_)).headOption
+
+// non-circle tours, including distance
+def tour(n: Int)(steps: List[Pos]): Option[List[Pos]] = {
+  if (steps.length ==  n * n) //&& moves(n)(steps.head).contains(steps.last)) 
+    Some(steps)
+  else first(ordered_moves(n)(steps)(steps.head), (x: Pos) => tour(n)(x::steps))
+}
+
+//val n = 8
+val n = 6
+println(s"number simple tours: n = $n")
+
+println(print_board(n)((tour(n)(List((0, 0)))).get))
+//println((for (i <- 0 until n; j <- 0 until n) yield tour(n)(List((i, j)))).flatten.distinct.size) 
+
+
+
+
+
+/*
+def first[A, B](xs: List[A], f: A => Option[B]): Option[B] =
+  xs.view.flatMap(f(_)).headOption
+*/
+
+/*
+
+*/