diff -r 6d25ccbb3cf2 -r 84917f2e16cd testing2/knight1.scala
--- a/testing2/knight1.scala	Tue Dec 05 00:34:14 2017 +0000
+++ b/testing2/knight1.scala	Thu Dec 07 12:04:31 2017 +0000
@@ -1,91 +1,133 @@
+
 // Part 1 about finding and counting Knight's tours
 //==================================================
 
-object CW7a {
+object CW7a extends App{
 
 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
-  } 
-}
+//(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 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 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 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))
-
-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 count_tours(dim: Int, path : Path) : Int = {
+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));
   
-  if (path.length == dim * dim) {1}
-  else 
-  val x = for (m <- legal_moves(dim,path,path.head)) yield {
+  val finalList = for(pos<-allPossibleMoves if(is_legal(dim,path)(pos))) yield pos;
+  
+  // println("Space in board: " + dim*dim + " for dim: " + dim)
+   
+  
+  finalList.toList;
     
-    count_tours(dim,m::path)
-  }
-  x.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
-}
+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_all_tours(dim: Int) = {
-  for (i <- (0 until dim).toList; 
-       j <- (0 until dim).toList) yield count_tours(dim, List((i, j)))
+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
+      
+      
+    }
+    
+  }
+  
 }
+    
+  
 
-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
+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)
 }
 
-/*
-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))
-}
+ 
+ 
+//(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] = ...
+
+
+
 
-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)
-  }
-}
-*/ 
+//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] = ...