diff -r eb188f9ac038 -r 9b45dd24271b testing3-bak/knight1.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3-bak/knight1.scala	Fri Nov 16 02:06:03 2018 +0000
@@ -0,0 +1,133 @@
+
+// Part 1 about finding and counting Knight's tours
+//==================================================
+
+object CW7a extends App{
+
+type Pos = (Int, Int)    // a position on a chessboard 
+type Path = List[Pos]    // a path...a list of positions
+
+//(1a) Complete the function that tests whether the position 
+//     is inside the board and not yet element in the path.
+
+//def is_legal(dim: Int, path: Path)(x: Pos) : Boolean = ...
+
+def is_legal(dim: Int, path: Path)(x: Pos) : Boolean = {
+  
+// if ((x._1<dim && x._2<dim) && (x._1>0 || x._2>0)) false else !path.contains(x)
+ 
+  if (x._1 < 0 || x._2 < 0) false 
+  else if (x._1 < dim && x._2 < dim && !path.contains(x)) true 
+  else false
+ 
+  
+}
+
+
+
+def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = {
+  
+  val allPossibleMoves = List((x._1+1, x._2+2), (x._1+2, x._2+1), (x._1+2, x._2-1), (x._1+1, x._2-2), (x._1-1, x._2-2), (x._1-2, x._2-1), (x._1-2, x._2+1), (x._1-1, x._2+2));
+ 
+  //val finalList = allPossibleMoves.filter((a=>a._1<dim && a._2<dim && x._1 >= 0 && a._2 >= 0));
+  
+  val finalList = for(pos<-allPossibleMoves if(is_legal(dim,path)(pos))) yield pos;
+  
+  // println("Space in board: " + dim*dim + " for dim: " + dim)
+   
+  
+  finalList.toList;
+    
+  
+}
+
+println(legal_moves(8, Nil, (2,2)))
+println(legal_moves(8, Nil, (7,7)))
+println(legal_moves(8, List((4,1), (1,0)), (2,2)))
+println(legal_moves(8, List((6,6)), (7,7)))
+println(legal_moves(1, Nil, (0,0)))
+println(legal_moves(2, Nil, (0,0)))
+println(legal_moves(3, Nil, (0,0)))
+
+println("=================================================================================")
+println("================================Comparision output===============================")
+println("=================================================================================")
+
+println(legal_moves(8, Nil, (2,2)) == List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))
+println(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))
+println(legal_moves(8, List((4,1), (1,0)), (2,2)) == List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))
+println(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))
+println(legal_moves(1, Nil, (0,0)) == Nil)
+println(legal_moves(2, Nil, (0,0)) == Nil)
+println(legal_moves(3, Nil, (0,0)) == List((1,2), (2,1)))
+
+
+def count_tours(dim: Int, path: Path) : Int = {
+     
+  val allMovesFromCurrentPosition = legal_moves(dim, path, path.head);
+  
+  if (path.length == dim*dim) 1 else  {
+    
+    if (allMovesFromCurrentPosition.size == 0 ) 0  else {
+      
+      allMovesFromCurrentPosition.map( element => count_tours(dim, element::path)).sum
+      
+      
+    }
+    
+  }
+  
+}
+    
+  
+
+println ( count_tours(5, List((0,0))) )
+
+def enum_tours(dim: Int, path: Path) : List[Path] = {
+  
+     val allMovesFromCurrentPosition = legal_moves(dim, path, path.head);
+  
+  if (path.length == dim*dim) List(path) else  {
+    
+  allMovesFromCurrentPosition.map( element => enum_tours(dim, element::path)).flatten ;
+      
+      
+      }
+    }
+  println ( enum_tours(6, List((0,2))).size)
+}
+
+
+
+
+
+ 
+ 
+//(1b) Complete the function that calculates for a position 
+//     all legal onward moves that are not already in the path. 
+//     The moves should be ordered in a "clockwise" manner.
+ 
+//def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = ...
+
+
+
+
+//some test cases
+//
+//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)))
+
+
+//(1c) Complete the two recursive functions below. 
+//     They exhaustively search for knight's tours starting from the 
+//     given path. The first function counts all possible tours, 
+//     and the second collects all tours in a list of paths.
+
+//def count_tours(dim: Int, path: Path) : Int = ...
+
+
+//def enum_tours(dim: Int, path: Path) : List[Path] = ...