updated
authorChristian Urban <urbanc@in.tum.de>
Tue, 13 Dec 2016 13:02:52 +0000
changeset 86 f8a781322499
parent 85 fd3f8581ce85
child 87 9384b8c98014
child 96 abfcb6111d33
updated
cws/cw01.pdf
cws/cw01.tex
cws/cw02.pdf
cws/cw02.tex
cws/cw03.pdf
cws/cw03.tex
marking/knight1b_test.scala
marking/knight2b_test.scala
marking/knight3a_test.scala
marking/mark01b
marking/mark02
marking/mark02b
progs/knight1_sol.scala
progs/knight2_sol.scala
Binary file cws/cw01.pdf has changed
--- a/cws/cw01.tex	Thu Dec 08 12:50:54 2016 +0000
+++ b/cws/cw01.tex	Tue Dec 13 13:02:52 2016 +0000
@@ -21,7 +21,8 @@
 code! It has a different meaning in Scala, than in Java.
 Do not use \texttt{var}! This declares a mutable variable. Make sure the
 functions you submit are defined on the ``top-level'' of Scala, not
-inside a class or object. 
+inside a class or object. Also note that the running time of
+each part will be restricted to a maximum of 360 seconds. 
 
 
 \subsection*{Disclaimer}
Binary file cws/cw02.pdf has changed
--- a/cws/cw02.tex	Thu Dec 08 12:50:54 2016 +0000
+++ b/cws/cw02.tex	Tue Dec 13 13:02:52 2016 +0000
@@ -34,7 +34,9 @@
 copy any code you need from files \texttt{knight1.scala},
 \texttt{knight2.scala} and \texttt{knight3.scala}. Make sure the
 functions you submit are defined on the ``top-level'' of Scala, not
-inside a class or object.
+inside a class or object. Also note that the running time of
+each part will be restricted to a maximum of 360 seconds. 
+
  
 \subsection*{Disclaimer}
 
@@ -319,19 +321,19 @@
 \item[(3a)] Write a function ordered-moves that calculates a list of
   onward moves like in (1b) but orders them according to the
   Warnsdorf’s rule. That means moves with the fewest legal onward moves
-  should come first (in order to be tried out first).
+  should come first (in order to be tried out first). \hfill[1 Mark]
   
 \item[(3b)] Implement a first-closed-tour-heuristic function that searches for a
   \textbf{closed} tour on a $6\times 6$ board. It should use the
   first-function from (2a) and tries out onward moves according to
   the ordered-moves function from (3a). It is more likely to find
   a solution when started in the middle of the board (that is
-  position $(dimension / 2, dimension / 2)$).
+  position $(dimension / 2, dimension / 2)$). \hfill[1 Mark]
 
 \item[(3c)] Implement a first-tour-heuristic function for boards up to $50\times 50$.
   It is the same function  as in (3b) but searches for \textbf{open} tours. You have
   to be careful to write a tail-recursive version of the first-tour-heuristic
-  function otherwise you will get problems with stack-overflows.
+  function otherwise you will get problems with stack-overflows. \hfill[1 Mark]
 \end{itemize}  
 
 \end{document}
Binary file cws/cw03.pdf has changed
--- a/cws/cw03.tex	Thu Dec 08 12:50:54 2016 +0000
+++ b/cws/cw03.tex	Tue Dec 13 13:02:52 2016 +0000
@@ -20,7 +20,9 @@
 code! It has a different meaning in Scala, than in Java.  Do not use
 \texttt{var}! This declares a mutable variable.  Make sure the
 functions you submit are defined on the ``top-level'' of Scala, not
-inside a class or object.
+inside a class or object. Also note that the running time of
+each part will be restricted to a maximum of 360 seconds. 
+
 
 
 \subsection*{Disclaimer!!!!!!!!}
--- a/marking/knight1b_test.scala	Thu Dec 08 12:50:54 2016 +0000
+++ b/marking/knight1b_test.scala	Tue Dec 13 13:02:52 2016 +0000
@@ -4,16 +4,42 @@
 import ExecutionContext.Implicits.global
 import scala.language.postfixOps 
 
-lazy val f = Future {
-  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_all_tours(dim: Int) = {
+  for (i <- (0 until dim).toList; 
+       j <- (0 until dim).toList) yield count_tours(dim, List((i, j)))
 }
 
-Await.result(f, 120 second)
+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
+}
+
+
+lazy val f = Future {
+  assert(count_all_tours(1) == List(1))
+  assert(count_all_tours(2) == List(0, 0, 0, 0))
+  assert(count_all_tours(3) == List(0, 0, 0, 0, 0, 0, 0, 0, 0))
+  assert(count_all_tours(4) == List(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))
+  assert(count_all_tours(5) == List(304, 0, 56, 0, 304, 0, 56, 0, 56, 0, 56, 0, 64, 0, 56, 0, 56, 0, 56, 0, 304, 0, 56, 0, 304))
+
+  val ts = enum_tours(5, List((0, 2)))
+  assert(ts.map(correct_urban(5)).forall(_ == true) == true)
+  assert(ts.length == 56)  
+}
+
+Await.result(f, 360 second)
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/marking/knight2b_test.scala	Tue Dec 13 13:02:52 2016 +0000
@@ -0,0 +1,38 @@
+
+import scala.concurrent._
+import scala.concurrent.duration._
+import ExecutionContext.Implicits.global
+import scala.language.postfixOps 
+
+
+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
+}
+
+
+lazy val f = Future {
+
+  val ts1 = first_tour(8, List((0, 0))).get
+  assert(correct_urban(8)(ts1) == true)
+
+  val ts2 = first_tour(4, List((0, 0)))
+  assert(ts2 == None)  
+}
+
+Await.result(f, 300 second)
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/marking/knight3a_test.scala	Tue Dec 13 13:02:52 2016 +0000
@@ -0,0 +1,15 @@
+
+import scala.concurrent._
+import scala.concurrent.duration._
+import ExecutionContext.Implicits.global
+import scala.language.postfixOps 
+
+lazy val f = Future {
+
+assert( ordered_moves(8, List((3,4), (3,2)), (1, 3)) == List((0,1), (0,5), (2,1), (2,5)))
+assert( ordered_moves(8, List((4,0)), (0,0)) == List((2,1), (1,2)))
+assert( ordered_moves(8, List((0,4)), (0,0)) == List((1,2), (2,1)))
+
+}
+
+Await.result(f, 120 second)
--- a/marking/mark01b	Thu Dec 08 12:50:54 2016 +0000
+++ b/marking/mark01b	Tue Dec 13 13:02:52 2016 +0000
@@ -39,7 +39,7 @@
 
 if (scala_compile drumb.scala)
 then
-  echo "  --> success" | tee -a $out
+  echo "  --> yes" | tee -a $out
   tsts=$(( 0 ))
 else
   echo "  --> scala did not run drumb.scala" | tee -a $out
--- a/marking/mark02	Thu Dec 08 12:50:54 2016 +0000
+++ b/marking/mark02	Tue Dec 13 13:02:52 2016 +0000
@@ -6,7 +6,7 @@
 echo "" > $out
 
 echo "Below is the feedback and provisional mark for your submission" >> $out
-echo "for CW 7.  Please note all marks are provisional until" >> $out
+echo "for CW 7, Part 1.  Please note all marks are provisional until" >> $out
 echo "ratified by the assessment board -- this is not an official" >> $out
 echo "results transcript." >> $out
 echo "" >> $out
@@ -33,38 +33,57 @@
 # marks for CW2
 marks=$(( 0 ))
 
-# var, comments test
-echo "knight1.scala contains any vars, returns etc?" | tee -a $out
+# knights1: var, comments test
+
+echo "knight1.scala does not contain vars, returns etc?" | tee -a $out
 
 if (scala_vars knight1.scala)
 then
   echo "  --> fail" | tee -a $out
   tsts0=$(( 1 ))
 else
-  echo "  --> success" | tee -a $out
+  echo "  --> yes" | tee -a $out
   tsts0=$(( 0 )) 
 fi
 
 
 # compilation test
-if  [ $tsts0 -eq 0 ]
+
+if [ $tsts0 -eq 0 ]
 then    
   echo "knight1.scala runs?" | tee -a $out
 
   if (scala_compile knight1.scala.bak)
   then
-    echo "  --> success" | tee -a $out
+    echo "  --> yes" | tee -a $out
     tsts1=$(( 0 ))
   else
     echo "  --> scala did not run knight1.scala" | tee -a $out
     tsts1=$(( 1 )) 
   fi
+else
+  tsts1=$(( 1 ))   
 fi
 
 ### knight1a test
 
 if [ $tsts1 -eq 0 ]
 then
+    echo " is_legal(8, Nil) (3,4) == true " | tee -a $out
+    echo " is_legal(8, (4,1) (1,0)) (4,1) == false " | tee -a $out
+    echo " is_legal(2, Nil) (0,0) == true" | tee -a $out                          
+
+    if (scala_assert "knight1.scala.bak" "../../../marking/knight1c_test.scala")
+    then
+        echo "  --> success" | tee -a $out
+        marks=$(( marks + 1 ))
+    else
+        echo "  --> test failed" | tee -a $out
+    fi
+fi
+
+if [ $tsts1 -eq 0 ]
+then
   echo " legal_moves(8, Nil, (2,2)) = (3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)" | tee -a $out
   echo " legal_moves(8, Nil, (7,7)) = (6,5), (5,6)" | tee -a $out
   echo " legal_moves(8, (4,1), (1,0), (2,2)) = (3,4), (4,3), (3,0), (0,1), (0,3), (1,4)" | tee -a $out
@@ -73,7 +92,7 @@
   echo " legal_moves(2, Nil, (0,0)) = Nil" | tee -a $out
   echo " legal_moves(3, Nil, (0,0)) = (1,2), (2,1)" | tee -a $out
   
-  if (scala_assert "knight1.scala" "../../../marking/knight1_test.scala")
+  if (scala_assert "knight1.scala.bak" "../../../marking/knight1_test.scala")
   then
     echo "  --> success" | tee -a $out
     marks=$(( marks + 1 ))
@@ -82,44 +101,126 @@
   fi
 fi
 
+### knight1b test
+
+if [ $tsts1 -eq 0 ]
+then
+  echo " all_tours from every position on the board" | tee -a $out
+  echo " dim = 1: 1" | tee -a $out
+  echo "       2: 0,0,0,0" | tee -a $out
+  echo "       3: 0,0,0,0,0,0,0,0,0" | tee -a $out
+  echo "       4: 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0" | tee -a $out
+  echo "       5: 304,0,56,0,304,0,56,0,56,0,56,0,64,0,56,0,56,0,56,0,304,0,56,0,304" | tee -a $out
+  echo " enum_tours(5, (0,2) ) = 56 and all correct?" | tee -a $out
+  
+  if (scala_assert "knight1.scala.bak" "../../../marking/knight1b_test.scala") 
+  then
+    echo "  --> success" | tee -a $out
+    marks=$(( marks + 2 ))
+  else
+    echo "  --> test failed" | tee -a $out
+  fi
+fi
+
+
+
+# knights2: var, comments test
+
+echo "knight2.scala does not contain vars, returns etc?" | tee -a $out
+
+if (scala_vars knight2.scala)
+then
+  echo "  --> fail" | tee -a $out
+  tsts0=$(( 1 ))
+else
+  echo "  --> yes" | tee -a $out
+  tsts0=$(( 0 )) 
+fi
+
+
+# compilation test
+if  [ $tsts0 -eq 0 ]
+then    
+  echo "knight2.scala runs?" | tee -a $out
+
+  if (scala_compile knight2.scala.bak)
+  then
+    echo "  --> yes" | tee -a $out
+    tsts1=$(( 0 ))
+  else
+    echo "  --> scala did not run knight2.scala" | tee -a $out
+    tsts1=$(( 1 )) 
+  fi
+else
+  tsts1=$(( 1 ))     
+fi
+
 ### knight2 test
 
-#if [ $tsts -eq 0 ]
+if [ $tsts1 -eq 0 ]
+then
+  echo " Let f = (x:(Int, Int)) => if (x._1 > 3) Some(List(x)) else None " | tee -a $out
+  echo "  first((1,0),(2,0),(3,0),(4,0), f) == Some(List((4,0)))" | tee -a $out
+  echo "  first((1,0),(2,0),(3,0), f) == None" | tee -a $out
+
+  if (scala_assert "knight2.scala.bak" "../../../marking/knight2_test.scala") 
+  then
+    echo "  --> success" | tee -a $out
+    marks=$(( marks + 1 ))
+  else
+    echo "  --> test failed" | tee -a $out
+  fi
+fi
+
+### knight2b test
+
+if [ $tsts1 -eq 0 ]
+then
+  echo " is first_tour(8,  (0, 0)) ok? " | tee -a $out
+  echo " is first_tour(4,  (0, 0)) == None " | tee -a $out
+
+  if (scala_assert "knight2.scala.bak" "../../../marking/knight2b_test.scala") 
+  then
+    echo "  --> success" | tee -a $out
+    marks=$(( marks + 2 ))
+  else
+    echo "  --> test failed" | tee -a $out
+  fi
+fi
+
+
+# knights3: var, comments test
+#
+#echo "knight3.scala does not contain vars, returns etc?" | tee -a $out
+
+#if (scala_vars knight3.scala)
 #then
-#  echo "  legal_moves(8, Nil, (2,2) = (3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)" | tee -a $out
-#  echo "  List(List(Some(0.07596697626574789), None), " | tee -a $out
-#  echo "       List(Some(-0.152620823795232), None)," | tee -a $out
-#  echo "       List(Some(0.20126676681483952), Some(0.9277165354330709))," | tee -a $out
-#  echo "       List(Some(0.09141762603007778), Some(2.119679764725104)))" | tee -a $out
-#  
-#  if (scala_assert "drumb.scala" "../drumb_test2.scala") 
-#  then
-#    echo "  --> success" | tee -a $out
-#    marks=$(( marks + 1 ))
-#  else
-#    echo "  --> test failed" | tee -a $out
-#  fi
+#  echo "  --> fail" | tee -a $out
+#  tsts0=$(( 1 ))
+#else
+#  echo "  --> success" | tee -a $out
+#  tsts0=$(( 0 )) 
 #fi
 
-### knight3 test
 
-#if [ $tsts -eq 0 ]
-#then
-#  echo "  yearly_yield(IBM + BIDU, 04 - 08, 100, 0) - 107).abs <= 2 " | tee -a $out
-#  echo "  yearly_yield(IBM + BIDU, 04 - 08, 100, 1) -  85).abs <= 2 " | tee -a $out
-#  echo "  yearly_yield(IBM + BIDU, 04 - 08, 100, 2) - 156).abs <= 2 " | tee -a $out
-#  echo "  yearly_yield(IBM + BIDU, 04 - 08, 100, 3) - 210).abs <= 2 " | tee -a $out
-#  echo "  investment(List(\"IBM\", \"BIDU\"), 2004 to 2008, 100) - 298).abs <= 10" | tee -a $out
-#  
-#  if (scala_assert "drumb.scala" "../drumb_test3.scala") 
+# compilation test
+#if  [ $tsts0 -eq 0 ]
+#then    
+#  echo "knight3.scala runs?" | tee -a $out
+#
+#  if (scala_compile knight3.scala.bak)
 #  then
 #    echo "  --> success" | tee -a $out
-#    marks=$(( marks + 1 ))
+#    tsts1=$(( 0 ))
 #  else
-#    echo "  --> test failed" | tee -a $out
+#    echo "  --> scala did not run knight3.scala" | tee -a $out
+#    tsts1=$(( 1 )) 
 #  fi
+#else
+#  tsts1=$(( 1 ))     
 #fi
 
+
 ## final marks
-echo "Overall mark for CW 2" | tee -a $out
+echo "Overall mark for CW 2, Part 1 " | tee -a $out
 echo "$marks" | tee -a $out
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/marking/mark02b	Tue Dec 13 13:02:52 2016 +0000
@@ -0,0 +1,74 @@
+#!/bin/bash
+set -e
+
+out=${1:-output}
+
+echo "" > $out
+
+echo "Below is the feedback and provisional mark for your submission" >> $out
+echo "for CW 7, Part 2.  Please note all marks are provisional until" >> $out
+echo "ratified by the assessment board -- this is not an official" >> $out
+echo "results transcript." >> $out
+echo "" >> $out
+
+function scala_vars {
+   (egrep 'var|return|ListBuffer|mutable' "$1" 2> /dev/null 1> /dev/null)
+}
+
+
+# compilation tests
+
+function scala_compile {
+  (scala "$1" 2> /dev/null 1> /dev/null) 
+}
+
+
+# functional tests
+
+function scala_assert {
+  (scala -i "$1" "$2" -e "" 2> /dev/null 1> /dev/null)
+}
+
+
+# marks for CW2b
+marks=$(( 0 ))
+
+
+# knights3: var, comments test
+#
+echo "knight3.scala does not contain vars, returns etc?" | tee -a $out
+
+if (scala_vars knight3.scala)
+then
+  echo "  --> fail" | tee -a $out
+  tsts0=$(( 1 ))
+else
+  echo "  --> yes" | tee -a $out
+  tsts0=$(( 0 )) 
+fi
+
+
+# compilation test
+if  [ $tsts0 -eq 0 ]
+then    
+  echo "knight3.scala runs?" | tee -a $out
+
+  if (scala_compile knight3.scala.bak)
+  then
+    echo "  --> yes" | tee -a $out
+    tsts1=$(( 0 ))
+  else
+    echo "  --> scala knight3.scala did not run successfully" | tee -a $out
+    tsts1=$(( 1 )) 
+  fi
+else
+  tsts1=$(( 1 ))     
+fi
+
+
+
+
+
+## final marks
+echo "Overall mark for CW 7, Part 2" | tee -a $out
+echo "$marks" | tee -a $out
--- a/progs/knight1_sol.scala	Thu Dec 08 12:50:54 2016 +0000
+++ b/progs/knight1_sol.scala	Tue Dec 13 13:02:52 2016 +0000
@@ -20,6 +20,10 @@
 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))
@@ -50,9 +54,9 @@
     (for (x <- legal_moves(dim, path, path.head)) yield enum_tours(dim, x::path)).flatten
 }
 
-def count_all_tours(dim: Int): Int = {
-  (for (i <- (0 until dim).toList; 
-        j <- (0 until dim).toList) yield count_tours(dim, List((i, j)))).sum
+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] = {
@@ -60,6 +64,29 @@
         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))))
 }
--- a/progs/knight2_sol.scala	Thu Dec 08 12:50:54 2016 +0000
+++ b/progs/knight2_sol.scala	Tue Dec 13 13:02:52 2016 +0000
@@ -36,6 +36,10 @@
   }
 }
 
+first(List((1, 0),(2, 0),(3, 0),(4, 0)), (x => if (x._1 > 3) Some(List(x)) else None))
+first(List((1, 0),(2, 0),(3, 0)), (x => if (x._1 > 3) Some(List(x)) else None))
+
+
 
 def first_tour(dim: Int, path: Path): Option[Path] = {
   if (path.length == dim * dim) Some(path)
@@ -49,7 +53,36 @@
   println(s"${dim} x ${dim} " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))
 }
 */
+
+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
+}
+
+
+
  
+val ts1 = first_tour(8, List((0, 0))).get
+  assert(correct_urban(8)(ts1) == true)
+
+val ts2 = first_tour(4, List((0, 0)))
+assert(ts2 == None)  
+
 print_board(8, first_tour(8, List((0, 0))).get)