# HG changeset patch # User Christian Urban # Date 1544881614 0 # Node ID 50a3b874008a004430133edc475803f33d7a6e6a # Parent 178438912e5fa655bfdec3c82b195296fa2f575b updated diff -r 178438912e5f -r 50a3b874008a TAs --- a/TAs Fri Dec 14 20:01:49 2018 +0000 +++ b/TAs Sat Dec 15 13:46:54 2018 +0000 @@ -53,6 +53,18 @@ 232 submissions +CW9, Part 1 + + late (231) +140 => 6 137 +53 => 5 56 +15 => 4 16 +5 => 3 5 +4 => 2 4 +0 => 1 0 +14 => 0 13 +-------- +231 submissions ======================= diff -r 178438912e5f -r 50a3b874008a cws/cw04.pdf Binary file cws/cw04.pdf has changed diff -r 178438912e5f -r 50a3b874008a cws/cw04.tex --- a/cws/cw04.tex Fri Dec 14 20:01:49 2018 +0000 +++ b/cws/cw04.tex Sat Dec 15 13:46:54 2018 +0000 @@ -514,7 +514,7 @@ \end{lstlisting} \noindent -where the command \texttt{ldc} loads a constant onto a stack, and \texttt{imul}, +where the command \texttt{ldc} loads a constant onto the stack, and \texttt{imul}, \texttt{isub} and \texttt{iadd} are commands acting on the stack. Clearly this is the arithmetic expression in postfix notation.\bigskip diff -r 178438912e5f -r 50a3b874008a cws/cw05.pdf Binary file cws/cw05.pdf has changed diff -r 178438912e5f -r 50a3b874008a cws/cw05.tex --- a/cws/cw05.tex Fri Dec 14 20:01:49 2018 +0000 +++ b/cws/cw05.tex Sat Dec 15 13:46:54 2018 +0000 @@ -12,9 +12,6 @@ \begin{document} -% BF IDE -% https://www.microsoft.com/en-us/p/brainf-ck/9nblgggzhvq5 - \section*{Coursework 10 (Scala)} This coursework is worth 10\%. It is about a small programming @@ -101,7 +98,15 @@ be implemented in brainf***. It just takes a lot of determination and quite a lot of memory resources. Some relatively sophisticated sample programs in brainf*** are given in the file \texttt{bf.scala}, including -a brainf*** program for the Sierpinski triangle and the Mandelbrot set.\bigskip +a brainf*** program for the Sierpinski triangle and the Mandelbrot set. +There seems to be even a dedicated Windows IDE for bf programs, though +I am not sure whether this is just an elaborate April fools' joke---judge +yourself: + +\begin{center} +\url{https://www.microsoft.com/en-us/p/brainf-ck/9nblgggzhvq5} +\end{center} + \noindent As mentioned above, brainf*** has 8 single-character commands, namely diff -r 178438912e5f -r 50a3b874008a progs/lecture1.scala --- a/progs/lecture1.scala Fri Dec 14 20:01:49 2018 +0000 +++ b/progs/lecture1.scala Sat Dec 15 13:46:54 2018 +0000 @@ -140,6 +140,8 @@ */ +val name: String = "leo" + // Pairs/Tuples //============== diff -r 178438912e5f -r 50a3b874008a progs/lecture5.scala --- a/progs/lecture5.scala Fri Dec 14 20:01:49 2018 +0000 +++ b/progs/lecture5.scala Sat Dec 15 13:46:54 2018 +0000 @@ -180,7 +180,7 @@ // input type: String // output type: Int -Integer.parseInt("123456") +Integer.parseInt("123u456") /* Note, in the previous lectures I did not show the type consraint * I <% Seq[_] , which means that the input type I can be @@ -241,7 +241,7 @@ val NumParser = RegexParser("[0-9]+".r) def StringParser(s: String) = RegexParser(Regex.quote(s).r) -println(NumParser.parse_all("12345")) +NumParser.parse_all("12u345") println(NumParser.parse_all("12u45")) @@ -266,7 +266,7 @@ } -val NumParserInt = NumParser ==> (s => s.toInt) +val NumParserInt = NumParser ==> (s => 2 * s.toInt) NumParser.parse_all("12345") NumParserInt.parse_all("12345") @@ -288,7 +288,7 @@ lazy val F: Parser[String, Int] = ("(" ~ E ~ ")") ==> { case ((x, y), z) => y } | NumParserInt -println(E.parse_all("1+3+4")) + println(E.parse_all("4*2+3")) println(E.parse_all("4*(2+3)")) println(E.parse_all("(4)*((2+3))")) @@ -331,7 +331,7 @@ // // http://www.latkin.org/blog/2017/05/02/when-the-scala-compiler-doesnt-help/ -List(1, 2, 3) contains "your mom" +List(1, 2, 3).contains("your mom") // I like best about Scala that it lets me often write // concise, readable code. And it hooks up with the diff -r 178438912e5f -r 50a3b874008a testing3/knight1.scala --- a/testing3/knight1.scala Fri Dec 14 20:01:49 2018 +0000 +++ b/testing3/knight1.scala Sat Dec 15 13:46:54 2018 +0000 @@ -1,121 +1,13 @@ -// Part 1 about finding Knight's tours -//===================================== +// Part 1 about finding and counting Knight's tours +//================================================== -// If you need any auxiliary function, feel free to -// implement it, but do not make any changes to the -// templates below. Also have a look whether the functions -// at the end are of any help. - - +//object CW8a { // for preparing the jar type Pos = (Int, Int) // a position on a chessboard type Path = List[Pos] // a path...a list of positions -//(1) Complete the function that tests whether the position x -// is inside the board and not yet element in the path. -def is_legal(dim: Int, path: Path, x: Pos) : Boolean = { - if ((x._1 < dim && x._2 < dim) && !(path.contains(x))) - true - else - false -} - - - -//(2) Complete the function that calculates for a position x -// 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] = { - val legalMovesList = 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)) - - for (i <- legalMovesList - if (is_legal(dim, path, i))) - yield i - -} - - -//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))) - - -//(3) 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 = { - if (path.size == (dim ^ 2)){ - List(path).size - } else { - val totalTours = legal_moves(dim, path, path.head) - totalTours.map(element => count_tours(dim, element :: path)).sum - } -} - -def enum_tours(dim: Int, path: Path) : List[Path] = { - if (path.size == (dim ^ 2)){ - List(path) - } else { - val totalEnums = legal_moves(dim, path, path.head) - totalEnums.map(element => enum_tours(dim, element :: path)).flatten - } -} - - -//(5) Implement a first-function that finds the first -// element, say x, in the list xs where f is not None. -// In that case Return f(x), otherwise None. If possible, -// calculate f(x) only once. - -def first(xs: List[Pos], f: Pos => Option[Path]) : Option[Path] = { - if (xs eq Nil) { - None - } else { - if (f(xs.head) != None) { - f(xs.head) - } else { - first(xs.tail, f) - } - } - -} - - -// test cases -//def foo(x: (Int, Int)) = if (x._1 > 3) Some(List(x)) else None -// -//first(List((1, 0),(2, 0),(3, 0),(4, 0)), foo) // Some(List((4,0))) -//first(List((1, 0),(2, 0),(3, 0)), foo) // None - - - - -//(6) Implement a function that uses the first-function from (5) for -// trying out onward moves, and searches recursively for a -// knight tour on a dim * dim-board. - - -//def first_tour(dim: Int, path: Path) : Option[Path] = ... - - - - - - -/* Helper functions - - -// for measuring time +// for measuring time in the JAR def time_needed[T](code: => T) : T = { val start = System.nanoTime() val result = code @@ -124,11 +16,6 @@ result } -// can be called for example with -// time_needed(count_tours(dim, List((0, 0)))) -// in order to print out the time that is needed for -// running count_tours - // for printing a board def print_board(dim: Int, path: Path): Unit = { println @@ -140,5 +27,144 @@ } } +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) +// testcases +//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 add_pair(x: Pos, y: Pos): Pos = + (x._1 + y._1, x._2 + y._2) + +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, _)) + +// 1 mark + +def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = + moves(x).filter(is_legal(dim, path, _)) + +// testcases +//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))) + +// 2 marks + +def tcount_tours(dim: Int, path: Path): Int = { + if (path.length == dim * dim) 1 + else + (for (x <- legal_moves(dim, path, path.head)) yield tcount_tours(dim, x::path)).sum +} + +def count_tours(dim: Int, path: Path) = + time_needed(tcount_tours(dim: Int, path: Path)) + + +def tenum_tours(dim: Int, path: Path): List[Path] = { + if (path.length == dim * dim) List(path) + else + (for (x <- legal_moves(dim, path, path.head)) yield tenum_tours(dim, x::path)).flatten +} + +def enum_tours(dim: Int, path: Path) = + time_needed(tenum_tours(dim: Int, path: Path)) + +// test cases + +/* +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 +} + + +println("Number of tours starting from (0, 0)") + +for (dim <- 1 to 5) { + println(s"${dim} x ${dim} " + time_needed(0, count_tours(dim, List((0, 0))))) +} + +println("Number of tours starting from all fields") + +for (dim <- 1 to 5) { + println(s"${dim} x ${dim} " + time_needed(0, count_all_tours(dim))) +} + +for (dim <- 1 to 5) { + val ts = enum_tours(dim, List((0, 0))) + println(s"${dim} x ${dim} ") + if (ts != Nil) { + print_board(dim, ts.head) + println(ts.head) + } +} */ + +// 1 mark + +def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match { + case Nil => None + case x::xs => { + val result = f(x) + if (result.isDefined) result else first(xs, f) + } +} + +// test cases +//def foo(x: (Int, Int)) = if (x._1 > 3) Some(List(x)) else None +// +//first(List((1, 0),(2, 0),(3, 0),(4, 0)), foo) +//first(List((1, 0),(2, 0),(3, 0)), foo) + + +// 1 mark + +def tfirst_tour(dim: Int, path: Path): Option[Path] = { + if (path.length == dim * dim) Some(path) + else + first(legal_moves(dim, path, path.head), (x:Pos) => tfirst_tour(dim, x::path)) +} + +def first_tour(dim: Int, path: Path) = + time_needed(tfirst_tour(dim: Int, path: Path)) + + +/* +for (dim <- 1 to 8) { + val t = first_tour(dim, List((0, 0))) + println(s"${dim} x ${dim} " + (if (t == None) "" else { print_board(dim, t.get) ; "" })) +} +*/ + +// 15 secs for 8 x 8 +//val ts1 = time_needed(0,first_tour(8, List((0, 0))).get) + +// no result for 4 x 4 +//val ts2 = time_needed(0, first_tour(4, List((0, 0)))) + +// 0.3 secs for 6 x 6 +//val ts3 = time_needed(0, first_tour(6, List((0, 0)))) + +// 15 secs for 8 x 8 +//time_needed(0, print_board(8, first_tour(8, List((0, 0))).get)) + + +//} + + diff -r 178438912e5f -r 50a3b874008a testing3/knight2.scala --- a/testing3/knight2.scala Fri Dec 14 20:01:49 2018 +0000 +++ b/testing3/knight2.scala Sat Dec 15 13:46:54 2018 +0000 @@ -64,6 +64,9 @@ def first_closed_tour_heuristics(dim: Int, path: Path) = time_needed(tfirst_closed_tour_heuristics(dim: Int, path: Path)) +def first_closed_tour_heuristic(dim: Int, path: Path) = + time_needed(tfirst_closed_tour_heuristics(dim: Int, path: Path)) + // heuristic cannot be used to search for closed tours on 7 x 7 an beyond //for (dim <- 1 to 6) { @@ -82,6 +85,8 @@ def first_tour_heuristics(dim: Int, path: Path) = time_needed(tfirst_tour_heuristics(dim: Int, path: Path)) +def first_tour_heuristic(dim: Int, path: Path) = + time_needed(tfirst_tour_heuristics(dim: Int, path: Path)) // will be called with boards up to 30 x 30 diff -r 178438912e5f -r 50a3b874008a testing3/knight2_test.sh --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/testing3/knight2_test.sh Sat Dec 15 13:46:54 2018 +0000 @@ -0,0 +1,177 @@ +#!/bin/bash + +# to make the script fail safely +set -euo pipefail + + +out=${1:-output} + +echo "" > $out + +echo "Below is the feedback and provisional marks for your submission" >> $out +echo "for assignment 8 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 "" >> $out + +# marks for CW8 part 2 +marks=$(( 0 )) + +# compilation tests + +function scala_compile { + (ulimit -t 30; JAVA_OPTS="-Xmx1g" scala -nc "$1" 2>> $out 1>> $out) +} + +# functional tests + + +function scala_assert { + (ulimit -t 30; JAVA_OPTS="-Xmx1g" scala -nc -i "$1" "$2" -e "") #2> /dev/null 1> /dev/null) +} + +function scala_assert_slow { + (ulimit -t 120; JAVA_OPTS="-Xmx1g" scala -nc -i "$1" "$2" -e "" 2> /dev/null 1> /dev/null) +} + + + +# purity test + +function scala_vars { + (egrep '\bvar\b|\breturn\b|\.par|ListBuffer|mutable|new Array' "$1" 2> /dev/null 1> /dev/null) +} + + +# knights2: purity test +# +echo -e "knight2.scala does not contain vars, returns, Arrays, ListBuffers etc?" | tee -a $out + + +if (scala_vars knight2.scala) +then + echo -e " --> test failed" | tee -a $out + tsts0=$(( 0 )) +else + echo -e " --> success" | tee -a $out + tsts0=$(( 0 )) +fi + + +# compilation test +if [ $tsts0 -eq 0 ] +then + echo -e "knight2.scala runs?" | tee -a $out + + if (scala_compile knight2.scala) + then + echo -e " --> success" | tee -a $out + tsts1=$(( 0 )) + else + echo -e " --> SCALA DID NOT RUN KNIGHT2.SCALA\n" >> $out + tsts1=$(( 1 )) + fi +else + tsts1=$(( 1 )) +fi + +# ordered move test + +if [ $tsts1 -eq 0 ] +then + echo -e " ordered_moves(8, List((3,4), (3,2)), (1,3)) == List((0,1), (0,5), (2,1), (2,5))" | tee -a $out + echo -e " ordered_moves(8, List((4,0)), (0,0)) == List((2,1), (1,2))" | tee -a $out + echo -e " ordered_moves(8, List((0,4)), (0,0)) == List((1,2), (2,1))" | tee -a $out + + if (scala_assert "knight2.scala" "knight_test6.scala") + then + echo -e " --> success" | tee -a $out + marks=$(( marks + 1 )) + else + echo -e " --> \n ONE TEST FAILED\n" >> $out + fi +fi + + +# first-closed-tour test + +if [ $tsts1 -eq 0 ] +then + echo -e " first_closed_tour_heuristic(6, List((3,3))) found and correct?" | tee -a $out + + if (scala_assert "knight2.scala" "knight_test7.scala") + then + echo -e " --> success" | tee -a $out + marks=$(( marks + 1 )) + else + echo -e " --> \n ONE TEST FAILED\n" >> $out + fi +fi + + + +if [ $tsts1 -eq 0 ] +then + echo -e " first_tour_heuristic(8, List((0,0))) found and correct?" | tee -a $out + echo -e " first_tour_heuristic(30, List((0,0))) found and correct?" | tee -a $out + + if (scala_assert "knight2.scala" "knight_test8.scala") + then + echo -e " --> success" | tee -a $out + marks=$(( marks + 1 )) + else + echo -e " --> \n ONE TEST FAILED\n" >> $out + fi +fi + + +# knights3: purity test +# +echo -e "knight3.scala does not contain vars, returns, Arrays, ListBuffers etc?" | tee -a $out + + +if (scala_vars knight3.scala) +then + echo " --> test failed" | tee -a $out + tsts0=$(( 0 )) +else + echo " --> success" | 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) + then + echo " --> success" | tee -a $out + tsts1=$(( 0 )) + else + echo -e " --> SCALA DID NOT RUN KNIGHT3.SCALA\n" >> $out + tsts1=$(( 1 )) + fi +else + tsts1=$(( 1 )) +fi + + +if [ $tsts1 -eq 0 ] +then + echo -e " tour_on_mega_board(70, List((0,0))) found and correct?" | tee -a $out + + if (scala_assert "knight3.scala" "knight_test9.scala") + then + echo -e " --> success" | tee -a $out + marks=$(( marks + 1 )) + else + echo -e " --> \n ONE TEST FAILED\n" >> $out + fi +fi + + +## final marks +echo "Overall mark for CW 8, Part 2" | tee -a $out +echo "$marks" | tee -a $out diff -r 178438912e5f -r 50a3b874008a testing3/knight_test6.scala --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/testing3/knight_test6.scala Sat Dec 15 13:46:54 2018 +0000 @@ -0,0 +1,19 @@ + + +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))) + + + +/* +import scala.concurrent._ +import scala.concurrent.duration._ +import ExecutionContext.Implicits.global +import scala.language.postfixOps + +lazy val f = Future { +} + +Await.result(f, 120 second) +*/ diff -r 178438912e5f -r 50a3b874008a testing3/knight_test7.scala --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/testing3/knight_test7.scala Sat Dec 15 13:46:54 2018 +0000 @@ -0,0 +1,31 @@ + +//type Pos = (Int, Int) +//type Path = List[Pos] + +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 +} + +def correct_closed_urban(dim: Int)(p: Path) = + correct_urban(6)(p) && moves_urban(p.head).contains(p.last) + + +val tsc = first_closed_tour_heuristic(6, List((3, 3))).get +assert(correct_closed_urban(6)(tsc) == true) + diff -r 178438912e5f -r 50a3b874008a testing3/knight_test8.scala --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/testing3/knight_test8.scala Sat Dec 15 13:46:54 2018 +0000 @@ -0,0 +1,31 @@ + +//type Pos = (Int, Int) +//type Path = List[Pos] + +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 ts8 = first_tour_heuristic(8, List((0,0))).get +assert(correct_urban(8)(ts8) == true) + +val ts30 = first_tour_heuristic(30, List((0,0))).get +assert(correct_urban(30)(ts30) == true) + diff -r 178438912e5f -r 50a3b874008a testing3/knight_test9.scala --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/testing3/knight_test9.scala Sat Dec 15 13:46:54 2018 +0000 @@ -0,0 +1,28 @@ + +//type Pos = (Int, Int) +//type Path = List[Pos] + +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 ts70 = tour_on_mega_board(70, List((0,0))).get +assert(correct_urban(70)(ts70) == true) +