--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_templates4/knight4.scala	Wed Nov 02 21:49:42 2022 +0000
@@ -0,0 +1,53 @@
+// Part 4 about finding a single tour on "mutilated" chessboards
+//==============================================================
+
+object M4d { // for preparing the jar
+
+type Pos = (Int, Int)
+type Path = List[Pos]
+
+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))}%4.0f ")
+    }
+    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, _))
+ 
+import scala.annotation.tailrec
+
+@tailrec
+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)
+  }
+}
+
+
+def one_tour_pred(dim: Int, path: Path, n: Int, pred: Pos => Boolean): Option[Path] = {
+  if (path.length == n) Some(path)
+  else
+    first(legal_moves(dim, path, path.head).filter(pred), (x: Pos) => one_tour_pred(dim, x::path, n, pred))
+}
+
+//print_board(8, one_tour_pred(8, List((0, 0)), 40, x => x._1 < 5).get)
+
+
+}