--- a/cws/cw03.tex Tue Dec 05 00:34:14 2017 +0000
+++ b/cws/cw03.tex Thu Dec 07 12:04:31 2017 +0000
@@ -45,6 +45,33 @@
28 29.81185
\end{filecontents}
+\begin{filecontents}{re-java9.data}
+1000 0.01410
+2000 0.04882
+3000 0.10609
+4000 0.17456
+5000 0.27530
+6000 0.41116
+7000 0.53741
+8000 0.70261
+9000 0.93981
+10000 0.97419
+11000 1.28697
+12000 1.51387
+14000 2.07079
+16000 2.69846
+20000 4.41823
+24000 6.46077
+26000 7.64373
+30000 9.99446
+34000 12.966885
+38000 16.281621
+42000 19.180228
+46000 21.984721
+50000 26.950203
+60000 43.0327746
+\end{filecontents}
+
\begin{document}
@@ -92,7 +119,7 @@
\subsection*{Disclaimer}
It should be understood that the work you submit represents
-your own effort! You have not copied from anyone else. An
+your \textbf{own} effort! You have not copied from anyone else. An
exception is the Scala code I showed during the lectures or
uploaded to KEATS, which you can freely use.\bigskip
@@ -359,28 +386,53 @@
30 seconds time limit?
\begin{center}
+\begin{tabular}{@{}cc@{}}
+\multicolumn{2}{c}{Graph: $(a^*)^*\cdot b$ and strings
+ $\underbrace{a\ldots a}_{n}$}\bigskip\\
+
\begin{tikzpicture}
\begin{axis}[
- title={Graph: $(a^*)^*\cdot b$ and strings
- $\underbrace{a\ldots a}_{n}$},
xlabel={$n$},
x label style={at={(1.05,0.0)}},
ylabel={time in secs},
+ y label style={at={(0.06,0.5)}},
enlargelimits=false,
xtick={0,5,...,30},
xmax=33,
- ymax=35,
- ytick={0,5,...,30},
+ ymax=45,
+ ytick={0,5,...,40},
scaled ticks=false,
axis lines=left,
width=6cm,
height=5.5cm,
legend entries={Python, Java 8},
- legend pos=outer north east]
+ legend pos=north west]
\addplot[blue,mark=*, mark options={fill=white}] table {re-python2.data};
\addplot[cyan,mark=*, mark options={fill=white}] table {re-java.data};
\end{axis}
\end{tikzpicture}
+ &
+\begin{tikzpicture}
+\begin{axis}[
+ xlabel={$n$},
+ x label style={at={(1.05,0.0)}},
+ ylabel={time in secs},
+ y label style={at={(0.06,0.5)}},
+ %enlargelimits=false,
+ %xtick={0,5000,...,30000},
+ xmax=65000,
+ ymax=45,
+ ytick={0,5,...,40},
+ scaled ticks=false,
+ axis lines=left,
+ width=6cm,
+ height=5.5cm,
+ legend entries={Java 9},
+ legend pos=north west]
+\addplot[cyan,mark=*, mark options={fill=white}] table {re-java9.data};
+\end{axis}
+\end{tikzpicture}
+\end{tabular}
\end{center}
\newpage
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/template3/bf.scala Thu Dec 07 12:04:31 2017 +0000
@@ -0,0 +1,151 @@
+// Part 2 about an Interpreter for the Brainf*** language
+//========================================================
+
+object CW8b {
+
+type Mem = Map[Int, Int]
+
+// (2a) Complete the functions for safely reading
+// and writing brainf*** memory. Safely read should
+// Return the value stored in the Map for a given memory
+// pointer, if it exists; otherwise it Returns 0. The
+// writing function generates a new Map with the
+// same data, except at the given memory pointer the
+// value v is stored.
+
+
+//def sread(mem: Mem, mp: Int) : Int = ...
+
+//def write(mem: Mem, mp: Int, v: Int) : Mem = ...
+
+
+// (2b) Implement the two jumping instructions in the
+// brainf*** language. In jumpRight, given a program and
+// a program counter move the counter to the right
+// until the command after the *matching* ]-command. Similarly,
+// jumpLeft implements the move to the left to just after
+// the *matching* [-command. The levels are used to find the
+// *matching* bracket.
+
+//def jumpRight(prog: String, pc: Int, level: Int) : Int = ...
+
+//def jumpLeft(prog: String, pc: Int, level: Int) : Int = ...
+
+
+
+// (2c) Complete the run function that interprets (runs) a brainf***
+// program: the arguments are a program, a program counter,
+// a memory counter and a brainf*** memory. It Returns the
+// memory at the stage when the execution of the brainf*** program
+// finishes. The interpretation finishes once the program counter
+// pc is pointing to something outside the program string.
+// If the pc points to a character inside the program, the pc,
+// memory pointer and memory need to be updated according to
+// rules of the brainf*** language. Then, recursively, the run
+// function continues with the command at the new program
+// counter.
+//
+// Implement the start function that calls run with the program
+// counter and memory counter set to 0.
+
+//def run(prog: String, pc: Int, mp: Int, mem: Mem) : Mem = ...
+
+//def start(prog: String, mem: Mem) = ...
+
+
+
+
+
+
+// some sample bf programs collected from the Internet
+//==================================================
+
+
+/*
+// first some contrived (small) programs
+
+// clears the 0-cell
+start("[-]", Map(0 -> 100))
+
+// copies content of the 0-cell to 1-cell
+start("[->+<]", Map(0 -> 10))
+
+// copies content of the 0-cell to 2-cell and 4-cell
+start("[>>+>>+<<<<-]", Map(0 -> 42))
+
+start("+++[>+++++<-]", Map(0 -> 10))
+
+
+// prints out numbers 0 to 9
+start("""+++++[->++++++++++<]>--<+++[->>++++++++++<<]>>++<<----------[+>.>.<+<]""", Map())
+
+
+// some more "useful" programs
+
+// hello world program 1
+start("""++++++++[>++++[>++>+++>+++>+<<<<-]>+>+>->>+[<]<-]>>.>---.+++++++
+ ..+++.>>.<-.<.+++.------.--------.>>+.>++.""", Map())
+
+// hello world program 2
+start("""++++++++++[>+++++++>++++++++++>+++>+<<<<-]>++.>+.+++++++..+++.>+
+ +.<<+++++++++++++++.>.+++.------.--------.>+.>.""", Map())
+
+
+// draws the Sierpinski triangle
+start("""++++++++[>+>++++<<-]>++>>+<[-[>>+<<-]+>>]>+[-<<<[
+ ->[+[-]+>++>>>-<<]<[<]>>++++++[<<+++++>>-]+<<++.[-]<<
+ ]>.>+[>>]>+]""", Map())
+
+//Fibonacci numbers below 100
+start("""+++++++++++
+ >+>>>>++++++++++++++++++++++++++++++++++++++++++++
+ >++++++++++++++++++++++++++++++++<<<<<<[>[>>>>>>+>
+ +<<<<<<<-]>>>>>>>[<<<<<<<+>>>>>>>-]<[>++++++++++[-
+ <-[>>+>+<<<-]>>>[<<<+>>>-]+<[>[-]<[-]]>[<<[>>>+<<<
+ -]>>[-]]<<]>>>[>>+>+<<<-]>>>[<<<+>>>-]+<[>[-]<[-]]
+ >[<<+>>[-]]<<<<<<<]>>>>>[+++++++++++++++++++++++++
+ +++++++++++++++++++++++.[-]]++++++++++<[->-<]>++++
+ ++++++++++++++++++++++++++++++++++++++++++++.[-]<<
+ <<<<<<<<<<[>>>+>+<<<<-]>>>>[<<<<+>>>>-]<-[>>.>.<<<
+ [-]]<<[>>+>+<<<-]>>>[<<<+>>>-]<<[<+>-]>[<+>-]<<<-]""", Map())
+
+
+//outputs the square numbers up to 10000
+start("""++++[>+++++<-]>[<+++++>-]+<+[
+ >[>+>+<<-]++>>[<<+>>-]>>>[-]++>[-]+
+ >>>+[[-]++++++>>>]<<<[[<++++++++<++>>-]+<.<[>----<-]<]
+ <<[>>>>>[>>>[-]+++++++++<[>-<-]+++++++++>[-[<->-]+[<<<]]<[>+<-]>]<<-]<<-]""", Map())
+
+
+//Collatz numbers (need to be typed in)
+start(""">,[[----------[
+ >>>[>>>>]+[[-]+<[->>>>++>>>>+[>>>>]++[->+<<<<<]]<<<]
+ ++++++[>------<-]>--[>>[->>>>]+>+[<<<<]>-],<]>]>>>++>+>>[
+ <<[>>>>[-]+++++++++<[>-<-]+++++++++>[-[<->-]+[<<<<]]<[>+<-]>]
+ >[>[>>>>]+[[-]<[+[->>>>]>+<]>[<+>[<<<<]]+<<<<]>>>[->>>>]+>+[<<<<]]
+ >[[>+>>[<<<<+>>>>-]>]<<<<[-]>[-<<<<]]>>>>>>>
+ ]>>+[[-]++++++>>>>]<<<<[[<++++++++>-]<.[-]<[-]<[-]<]<,]""", Map())
+
+
+// infinite Collatz (never stops)
+start(""">>+>+<[[->>[>>]>>>[>>]+[<<]<<<[<<]>[>[>>]>>+>[>>]<+<[<<]<<<[<
+ <]>-]>[>>]>>[<<<<[<<]>+>[>>]>>-]<<<<[<<]+>>]<<[+++++[>+++++++
+ +<-]>.<++++++[>--------<-]+<<]>>[>>]+[>>>>[<<+>+>-]<-[>+<-]+<
+ [<<->>-[<<+>>[-]]]>>>[<<<+<<+>>>>>-]<<<[>>>+<<<-]<<[[-]>+>>->
+ [<+<[<<+>>-]<[>+<-]<[>+<-]>>>>-]<[>+<-]+<[->[>>]<<[->[<+++>-[
+ <+++>-[<+++>-[<[-]++>>[-]+>+<<-[<+++>-[<+++>-[<[-]+>>>+<<-[<+
+ ++>-[<+++>-]]]]]]]]]<[>+<-]+<<]>>>+<[->[<+>-[<+>-[<+>-[<+>-[<
+ +>-[<+>-[<+>-[<+>-[<+>-[<[-]>>[-]+>+<<-[<+>-]]]]]]]]]]]<[>+<-
+ ]+>>]<<[<<]>]<[->>[->+>]<[-[<+>-[<->>+<-[<+>-[<->>+<-[<+>-[<-
+ >>+<-[<+>-[<->>+<-[<+>-[<->>+<-[<+>-[<->>+<-[<+>-[<->>+<-[<+>
+ -[<->>+<-[<+>-[<->>+<-[<+>-]]]]]]]]]]]]]]]]]]]>[<+>-]<+<[<+++
+ +++++++>-]<]>>[<+>->>]<<[>+>+<<-]>[<+>-]+>[<->[-]]<[-<<-]<<[<
+ <]]++++++[>+++++++<-]>++.------------.[-]>[>>]<<[+++++[>+++++
+ +++<-]>.<++++++[>--------<-]+<<]+<]>[<+>-]<]>>>[>>]<<[>[-]<-<
+ <]++++++++++.[-]<<<[<<]>>>+<[->[<+>-[<+>-[<+>-[<+>-[<+>-[<+>-
+ [<+>-[<+>-[<+>-[<[-]>>[-]+>+<<-]]]]]]]]]]<[>+<-]+>>]<<[<<]>>]""", Map())
+
+
+*/
+
+}
--- 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] = ...