Assignment 2

COMP9021, Session 2, 2018

1 General presentation

You will design and implement a program that will

• analyse the various characteristics of a maze, represented by a particular coding of its basic con-

stituents 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.

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:

2 Examples

2.1 First example

The file named maze_1.txt has the following contents.

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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 as

argument to pdflatex to produce a file named maze_1.pdf that views as follows.

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2.2 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 as

argument to pdflatex to produce a file named maze_2.pdf that views as follows.

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2.3 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.

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3 Detailed description

3.1 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.

3.2 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):

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...

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.

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• A gate is any pair of consecutive points on one of the four sides of the maze that are not connected.

• An inaccessible inner point is an inner point that cannot be reached from any gate.

• An accessible area is a maximal set of inner points that can all be accessed from the same gate (so

the number of accessible inner points is at most equal to the number of gates).

• A set of accessible cul-de-sacs that are all connected is a maximal set S of connected inner points

that can all be accessed from the same gate g and such that for all points p in S, if p has been

accessed from g for the first time, then either p is in a dead end or moving on without ever getting

back leads into a dead end.

• An entry-exit path with no intersections not to cul-de-sacs is a maximal set S of connected inner

points that go from a gate to another (necessarily different) gate and such that for all points p in

S, there is only one way to move on from p without getting back and without entering a cul-de-sac.

Pay attention to the expected format, including spaces.

If the input is correct and represents a maze, then executing maze = Maze(some_filename) followed by

maze.display() should have the effect of producing a file named some_filename.tex that can be given

as argument to pdflatex to generate a file named some_filename.pdf. The provided examples will

show you what some_filename.tex should contain.

• Walls are drawn in blue. There is a command for every longest segment that is part of a wall.

Horizontal segments are drawn starting with the topmost leftmost segment and finishing with

the bottommost rightmost segment. Then vertical segments are drawn starting with the topmost

leftmost segment and finishing with the bottommost rightmost segment.

• Pillars are drawn as green circles.

• Inner points in accessible cul-de-sacs are drawn as red crosses.

• The paths with no intersection not to cul-de-sacs are drawn as dashed yellow lines. There is a

command for every longest segment on such a path. Horizontal segments are drawn starting with

the topmost leftmost segment and finishing with the bottommost rightmost segment, with those

segments that end at a gate sticking out by 0.25 cm. Then vertical segments are drawn starting

with the topmost leftmost segment and finishing with the bottommost rightmost segment, with

those segments that end at a gate sticking out by 0.25 cm.

Pay attention to the expected format, including spaces and blank lines. Lines that start with % are

comments; there are 4 such lines, that have to be present even when there is no item to be displayed of

the kind described by the comment. The output of your program redirected to a file will be compared

with the expected output saved in a file (of a different name of course) using the diff command. For

your program to pass the associated test, diff should silently exit, which requires that the contents of

both files be absolutely identical, character for character, including spaces and blank lines. Check your

program on the provided examples using the associated .tex files, renaming them as they have the names

of the files expected to be generated by your program.

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4 Submission and assessment

4.1 Submission

Your program will be stored in a file which has to be named maze.py. Your code can be submitted

more than once on Ed; the last version and only the last version will be run, tested and marked. Your

assignment is due by October 28, 11:59pm.

4.2 Assessment

The automarking script will let each both assessed methods of your program run for 30 seconds. Still

you should not take advantage of this and strive for a solution that gives an immediate output.

Late assignments will be penalised: the mark for a late submission will be the minimum of the awarded

mark and 10 minus the number of full and partial days that have elapsed from the due date.

4.3 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 routinely 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.

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