COMP9021

Assignment 2
COMP9021, Trimester 1, 2019

  1. General matter
    1.1. Aims. The purpose of the assignment is to:
    design and implement an interface based on the desired behaviour of an application program;
    practice the use of Python syntax;
    develop problem solving skills.
    1.2. Submission. Your program will be stored in a file named tangram.py. After you have developed and
    tested your program, upload it using Ed (unless you worked directly in Ed). Assignments can be submitted
    more than once; the last version is marked. Your assignment is due by April 28, 11:59pm.
    1.3. Assessment. The assignment is worth 10 marks. It is going to be tested against a number of input files.
    For each test, the automarking script will let your program run for 30 seconds.
    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.
    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 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.
    1
    2
  2. Background
    The game of tangram consists in creating shapes out of pieces. We assume that each piece has its own colour,
    different to the colour of any other piece in the set we are working with. Just for reference, here is the list of
    colours that are available to us (you will not make use of this list):
    https://www.w3.org/TR/2011/RE...
    A representation of the pieces will be stored in an .xml file thanks to a simple, fixed syntax.
    2.1. Pieces. Here is an example of the contents of the file pieces_A.xml, typical of the contents of any file of
    this kind (so only the number of pieces, the colour names, and the various coordinates can differ from one such
    file to another–we do not bother with allowing for variations, in the use of space in particular).









    Opened in a browser, pieces_A.xml displays as follows:
    Note that the coordinates are nonnegative integers. This means that the sets of pieces we consider rule out
    those of the traditional game of tangram, where √
  3. is involved everywhere...
    We require every piece to be a convex polygon. An .xml file should represent a piece with n sides (n ≥ 3)
    by an enumeration of n pairs of coordinates, those of consecutive vertices, the first vertex being arbitrary, and
    the enumeration being either clockwise or anticlockwise.
    The pieces can have a different orientation and be flipped over. For instance, the file pieces_AA.xml whose
    contents is




    3





    and which displays as
    represents the same set of pieces (the fact that the latter appear as smaller than the former is just due to the
    different scaling of the included pdf’s; the sizes of the pieces are actually the same in terms of the coordinates
    of their vertices).
    The pieces can overlap, but that does not concern us. In practice, we will just use representations where the
    pieces do not overlap as that allows us to visualise the pieces properly when we open the corresponding .xml
    file, but it is just for convenience and irrelevant to the tasks we tackle.
    2.2. Shapes. A representation of a shape is provided thanks to an .xml file with the same structure, storing
    the coordinates of the vertices of just one polygon.
    The file shape_A_1.xml whose contents is



    and which displays as
    is such an example. The file shape_A_2.xml whose contents is



    and which displays as
    4
    is another such example.
    Contrary to pieces, shapes are not assumed to be convex polygons. Still they are assumed to be simple
    polygons (the boundary of a simple polygon does not cross itself; in particular, it cannot consist of at least 2
    polygons that are connected by letting two of them just “touch” each other at one of their vertices–e.g., two
    rectangles such that the upper right corner of one rectangle is the lower left corner of the other rectangle; that
    is not allowed).
    Whereas you will have to check that the representation of the pieces in an .xml file satisfies our constraints,
    you will not have to do so for the representation of a shape; you can assume that any shape we will be dealing
    with satisfies our constraints.
    2.3. Tangrams. The first shape can be built from our set of pieces, in many ways. Here is one, given by the
    file tangram_A_1_a.xml whose contents is









    and which displays as follows.
    Here is another one, given by the file tangram_A_1_b.xml whose contents is







    5


    and which displays as follows.
    The second shape can also be built from our set of pieces, in many ways. Here is one, given by the file
    tangram_A_2_a.xml whose contents is









    and which displays as follows.
    Here is another one, given by the file tangram_A_2_b.xml whose contents is









    and which displays as follows.
    6
    7
  4. First task (3 marks)
    You have to check that the pieces represented in an .xml file satisfy our constraints. So you have to check
    that each piece is convex, and if it represents a polygon with n sides (n ≥ 3) then the representation consists
    of an enumeration of the n vertices, either clockwise or anticlockwise. Here is the expected behaviour of your
    program.
    $ python3
    ...

    from tangram import *
    file = open('pieces_A.xml')
    coloured_pieces = available_coloured_pieces(file)
    are_valid(coloured_pieces)
    True
    file = open('pieces_AA.xml')
    coloured_pieces = available_coloured_pieces(file)
    are_valid(coloured_pieces)
    True
    file = open('incorrect_pieces_1.xml')
    coloured_pieces = available_coloured_pieces(file)
    are_valid(coloured_pieces)
    False
    file = open('incorrect_pieces_2.xml')
    coloured_pieces = available_coloured_pieces(file)
    are_valid(coloured_pieces)
    False
    file = open('incorrect_pieces_3.xml')
    coloured_pieces = available_coloured_pieces(file)
    are_valid(coloured_pieces)
    False
    file = open('incorrect_pieces_4.xml')
    coloured_pieces = available_coloured_pieces(file)
    are_valid(coloured_pieces)
    False
    Note that the function are_valid() does not print out True or False, but returns True or False.
    8
  5. Second task (3 marks)
    You have to check whether the sets of pieces represented in two .xml files are identical, allowing for pieces
    to be flipped over and allowing for different orientations. Here is the expected behaviour of your program.
    $ python3
    ...

    from tangram import *
    file = open('pieces_A.xml')
    coloured_pieces_1 = available_coloured_pieces(file)
    file = open('pieces_AA.xml')
    coloured_pieces_2 = available_coloured_pieces(file)
    are_identical_sets_of_coloured_pieces(coloured_pieces_1, coloured_pieces_2)
    True
    file = open('shape_A_1.xml')
    coloured_pieces_2 = available_coloured_pieces(file)
    are_identical_sets_of_coloured_pieces(coloured_pieces_1, coloured_pieces_2)
    False
    Note that the function identical_sets_of_coloured_pieces() does not print out True or False, but
    returns True or False.
    9
  6. Third task (4 marks)
    You have to check whether the pieces represented in an .xml file are a solution to a tangram puzzle represented
    in another .xml file. Here is the expected behaviour of your program.
    $ python3
    ...

    from tangram import *
    file = open('shape_A_1.xml')
    shape = available_coloured_pieces(file)
    file = open('tangram_A_1_a.xml')
    tangram = available_coloured_pieces(file)
    is_solution(tangram, shape)
    True
    file = open('tangram_A_2_a.xml')
    tangram = available_coloured_pieces(file)
    is_solution(tangram, shape)
    False
    Note that the function is_solution() does not print out True or False, but returns True or False.

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