--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Attic/knight.scala	Sat Mar 11 23:22:05 2023 +0000
@@ -0,0 +1,87 @@
+import scala.util._
+
+def print_board(n: Int)(steps: List[(Int, Int)]): Unit = {
+  for (i <- 0 until n) {
+    for (j <- 0 until n) {
+      print(f"${steps.indexOf((i, j))}%3.0f ")
+    }
+    println
+  } 
+  //readLine()
+  //System.exit(0)
+  throw new Exception("\n")
+}
+
+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)(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))
+}
+
+def ordered_moves(n: Int)(steps: List[(Int, Int)])(x : (Int, Int)): List[(Int, Int)] = 
+  moves(n)(x).sortBy((x: (Int, Int)) => moves(n)(x).filterNot(steps.contains(_)).length)
+
+moves(8)(1,3)
+ordered_moves(8)(Nil)(1,3)
+ordered_moves(8)(List((2, 4), (2, 6)))(1,3)
+
+// non-circle tour parallel
+def tour(n: Int)(steps: List[(Int, Int)]): Unit = {
+  if (steps.length ==  n * n)
+    print_board(n)(steps)
+  else 
+    for (x <- moves(n)(steps.head); if (!steps.contains(x))) tour(n)(x :: steps)
+}
+
+// non-circle tour
+def ctour(n: Int)(steps: List[(Int, Int)]): Unit = {
+  if (steps.length ==  n * n && moves(n)(steps.head).contains(steps.last))
+    print_board(n)(steps)
+  else 
+    for (x <- moves(n)(steps.head); if (!steps.contains(x))) ctour(n)(x :: steps)
+}
+
+
+def faster_tour(n: Int)(steps: List[(Int, Int)]): Unit = {
+  if (steps.length ==  n * n && moves(n)(steps.head).contains(steps.last))
+    print_board(n)(steps)
+  else 
+    for (x <- ordered_moves(n)(steps)(steps.head); if (!steps.contains(x))) faster_tour(n)(x :: steps)
+}
+
+
+val n1 = 5
+println(s"simple tour: n = $n1")
+
+Try {
+  for (i <- 0 until n1; j <- 0 until n1) {
+    tour(n1)(List((i, j))) 
+  }
+}
+
+
+val n2 = 6
+println(s"circle tour: n = $n2")
+
+Try {
+  for (i <- 0 until n2; j <- 0 until n2) {
+    ctour(n2)(List((i, j))) 
+  }
+}
+
+
+val n3 = 8
+println(s"fast circle tour: n = $n3")
+
+Try {
+  for (i <- 0 until n3; j <- 0 until n3) {
+    faster_tour(n3)(List((i, j))) 
+  }
+}
+
+println("finished")