diff -r 9b5165b8a762 -r 0587ef444547 progs/knight1_sol.scala
--- a/progs/knight1_sol.scala	Sat Mar 11 23:12:49 2023 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,107 +0,0 @@
-// 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)
-
-assert(is_legal(8, Nil)((3,4)) == true)
-assert(is_legal(8, List((4,1), (1,0)))((4,1)) == false)
-assert(is_legal(2, Nil)((0,0)) == true)
-
-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))
-
-assert(legal_moves(8, Nil, (2,2)) == 
-  List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))
-assert(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))
-assert(legal_moves(8, List((4,1), (1,0)), (2,2)) == 
-  List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))
-assert(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))
-assert(legal_moves(1, Nil, (0,0)) == List())
-assert(legal_moves(2, Nil, (0,0)) == List())
-assert(legal_moves(3, Nil, (0,0)) == List((1,2), (2,1)))
-
-
-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) = {
-  for (i <- (0 until dim).toList; 
-       j <- (0 until dim).toList) yield count_tours(dim, List((i, j)))
-}
-
-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
-}
-
-
-def add_pair_urban(x: Pos)(y: Pos): Pos = 
-  (x._1 + y._1, x._2 + y._2)
-
-def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = 
-  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
-
-def moves_urban(x: Pos): List[Pos] = 
-  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
-       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))
-
-def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = 
-  moves_urban(x).filter(is_legal_urban(dim, path))
-
-def correct_urban(dim: Int)(p: Path): Boolean = p match {
-  case Nil => true
-  case x::Nil => true
-  case x::y::p => if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false
-}
-
-enum_tours(5, List((0, 2))).map(correct_urban(5)).forall(_ == true)
-
-
-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)
-  }
-}
-
-