1. General Matters

1.1 Aim

The purpose of this assignment is to design and implement a program that will:

.    analyse the various characteristics of a maze, represented by a particular coding of its basic constituents into numbers stored in a file whose contents is read, and

.    either display those characteristics, or

.    output some Latex code in a file, from which a pictorial representation of the maze can be produced.

.    use object-oriented programming.

1.2 Marking

This assignment is worth 13 marks distributed approximately as follows:

Your program will be tested against several inputs.  For each test, the automarking script will let your program run for 30 seconds.  The outputs of your program should be exactly as indicated.

1.3 Due Date and Submission

Your program will be stored in a file named maze.py. The assignment can be submitted more than once. The last version just before the due date and time will be marked (unless you submit late in which case the last late version will be marked).

Assignment 2 is due Week 11 Monday 22 April 2024 @ 10:00am (Sydney time)

Note that late submission with 5% penalty per day is allowed up to 5 days from the due date, that is, any late submission after Week 11 Saturday 27 April 2024 @ 10:00am will be discarded.

Make sure not to change the filename maze.py while submitting by clicking on [Mark] button in Ed. It is your responsibility to check that your submission did go through properly using Submissions link in Ed otherwise your mark will be zero for Assignment 2.

Please note that the testing is done in two steps. You can test part 1 of the assignment in “Assignment 2: for testing of part 1 and for submission” on the sample inputs.

Your submission will NOT be downloaded from “Assignment 2: NOT for submission, for testing of part 2 ONLY” for marking. You can ONLY test part 2 of the assignment in “Assignment 2: NOT for submission, for testing of part 2 ONLY” on the sample inputs.

Please also note that your submission for BOTH PART 1 AND PART 2 will be downloaded from “Assignment 2: for testing of part 1 and for submission” for marking.

1.4 Reminder on Plagiarism Policy

You are permitted, indeed encouraged, to discuss ways to solve the assignment with other people.

Such discussions must be in terms of algorithms, not code. But you must implement the solution on your own. Submissions are scanned for similarities that occur when students copy and modify other people’s work or work very closely together on a single implementation. Severe penalties apply.

2. Description

The representation of the maze is based on a coding with the four digits 0, 1, 2 and 3 such that:

.  0 codes points that are connected to neither their right nor below neighbours

.  1 codes points that are connected to their right neighbours but not to their below ones:

.  2 codes points that are connected to their below neighbours but not to their right ones:

.  3 codes points that are connected to both their right and below neighbours:

A point that is connected to none of their left, right, above, and below neighbours represents a

pillar:

Analysing the maze will allow you to also represent:

. cul-de-sacs:

.  certain kinds of paths:

3. Examples

3.1 First example

The file named maze_1.txt has the following contents:

1   0    2    2    1    2    3    0

3    2    2    1    2    0    2    2

3   0    1    1    3    1    0    0

2   0    3    0    0    1    2    0

3    2    2    0    1    2    3    2

1   0    0    1    1    0    0    0

Here is a possible interaction:

$ python3

...

>>> from maze import  *

>>> maze = Maze('maze_1.txt')

>>> maze.analyse()

The  maze  has  12  gates.

The  maze  has  8  sets  of  walls  that  are  all  connected.

The  maze  has  2  inaccessible  inner  points.

The maze has 4 accessible areas.

The maze has 3 sets of accessible cul-de-sacs that are all connected.

The maze has a unique entry-exit path with no intersection not to cul-de-sacs. >>>  maze.display()

The effect of executing maze.display() is to  produce a file  named  maze_1.tex that can  be given asargument to pdflatex to produce a file named maze_1.pdf that views as follows.

3.2 Second example

The file named maze_2.txt has the following contents.

022302120222

222223111032

301322130302

312322232330

001000100000

Here is a possible interaction:

$ python3

...

>>> from maze import  *

>>> maze = Maze('maze_2.txt')

>>> maze.analyse()

The  maze  has  20  gates.

The  maze  has  4  sets  of  walls  that  are  all  connected.

The  maze  has  4  inaccessible  inner  points.

The maze has 13 accessible areas.

The maze has 11 sets of accessible cul-de-sacs that are all  connected.

The maze has 5 entry-exit paths with no intersections not to cul-de-sacs. >>>  maze.display()

The effect of executing maze.display() is to  produce a file  named  maze_2.tex that can  be given asargument to pdflatex to produce a file named maze_2.pdf that views as follows.

3.3 Third example

The file named labyrinth.txt has the following contents.

31111111132

21122131202

33023022112

20310213122

31011120202

21230230112

30223031302

03122121212

22203110322

22110311002

11111101110

Here is a possible interaction:

$ python3

...

>>> from maze import  *

>>> maze = Maze('labyrinth.txt')

>>> maze.analyse()

The  maze  has  2

gates.

The  maze  has  2  sets  of  walls  that  are  all  connected.

The  maze  has  no  inaccessible  inner  point.

The maze has a unique accessible area.

The maze has 8 sets of accessible cul-de-sacs that are all connected.

The maze has a unique entry-exit path with no intersection not to cul-de-sacs. >>>  maze.display()

The effect of executing maze.display() is to produce a file named labyrinth.tex that can be given as argument to pdflatex to produce a file named labyrinth.pdf that views as follows.

4. Detailed  description

4.1 Input

The  input  is  expected  to  consist  of ydim lines  of xdim members  of {0, 1, 2, 3}, where xdim and ydim are  at least equal to 2 and at most equal to 31 and 41, respectively, with possibly lines consisting of spaces only that will be ignored and with possibly spaces anywhere on the lines with digits. If n is the xth   digit of the yth  line with digits, with 0 ≤ x < xdim and 0 ≤ y < ydim ,  then

. n is to  be  associated with a point situated x ×0.5 cm to the right and y ×0.5 cm  below an origin,

. n is to be connected to the point 0.5 cm to its right just in case n = 1 or n = 3, and

. n is to be connected to the point 0.5 cm below itself just in case n = 2 or n = 3.

The last digit on every line with digits cannot be equal to 1 or 3, and the digits on the last line with digits cannot be equal to 2 or 3, which ensures that the input encodes a maze, that is, a grid of width (xdim -   1) × 0.5 cm and of height (ydim - 1) × 0.5 cm (hence of maximum width 15 cm and of maximum height 20 cm), with possibly gaps on the sides and inside. A point not connected to any of its neighbours is thought of as a pillar; a point connected to at least one of its neighbours is thought of as part of a wall.

We talk about inner point to refer to a point that lies (x + 0.5) × 0.5 cm to the right of and (y + 0.5) × 0.5

cm below the origin with 0 ≤ x < xdim − 1 and 0 ≤ y < ydim − 1.

4.2 Output

Consider executing from the Python prompt the statement from maze import * followed by the state- ment maze = Maze(some_filename). In case  some_filename does  not  exist  in  the  working  directory, then Python  will  raise  a  FileNotFoundError  exception,  that  does  not  need  to  be  caught.  Assume  that some_filename does exist (in the working directory). If the input is incorrect in that it does not contain only digits in  {0, 1, 2, 3} besides  spaces,  or in that it contains either too few or too many nonblank lines,or in that some nonblank lines contain too many or too few digits, or in that two of its nonblank lines do not contain the same number of digits, then the effect of executing maze = Maze(some_filename) should be to generate a MazeError exception that reads

Traceback  (most  recent  call  last):

...

maze.MazeError:  Incorrect  input.

If the previous conditions hold but the further conditions spelled out above for the input to qualify as a maze (that is, the condition on the last digit on every line with digits and the condition on the digits on the last line) do not hold, then the effect of executing maze = Maze(some_filename) should be to generate a MazeError exception that reads

Traceback  (most  recent  call  last):

...

maze. MazeError:  Input  does  not  represent  a  maze.

If the input is correct and represents a maze, then executing maze =  Maze(some_filename) should have the effect of outputting a first line that reads one of

The  maze  has  no  gate.

The maze has  a  single  gate.

The  maze  has  N  gates.

with N an appropriate integer at least equal to 2, a second line that reads one of

The maze  has  no  wall.

The  maze  has  walls that  are  all  connected.

The  maze  has  N  sets  of  walls  that  are  all  connected.

with N an appropriate integer at least equal to 2, a third line that reads one of

The maze has no inaccessible inner point.

The  maze  has a  unique  inaccessible  inner

point.The  maze  has  N  inaccessible  inner  points.

with N an appropriate integer at least equal to 2, a fourth line that reads one of

The maze has no accessible area.

The  maze  has a  unique accessible

area.

The  maze  has  N  accessible  areas.

with N an appropriate integer at least equal to 2, a fifth line that reads one of

The maze has no accessible cul-de-sac.

The maze has accessible cul-de-sacs that are all  connected.

The maze has N  sets of accessible cul-de-sacs that are all  connected.

with N an appropriate integer at least equal to 2, and a sixth line that reads one of

The maze has no entry-exit path with no intersection not to cul-de-sacs.

The  maze  has  a  unique  entry-exit  path  with  no  intersection  not  to  cul-de-sacs. The  maze  has  N entry-exit  paths  with  no  intersections  not  to  cul-de-sacs.

with N an appropriate integer at least equal to 2.