Assignment One – 15%
Algorithms and Data Structures – COMP3506/7505 – Semester 2, 2024
Due: 3pm on Friday August 23 (week 5)
Summary
The main objective of this assignment is to get your hands dirty with some simple data structures
and algorithms to solve basic computational problems. These data structures will also come in handy
for your second assignment, so you should take your time to think about your implementations and
try to make them as efficient as possible.
1 Getting Started
Before we get into the nitty gritty, we will discuss the skeleton codebase that will form
the basis of your implementations, and provide some rules that must be followed when
implementing your solutions.
1.1 Codebase
The codebase contains a number of data structures stubs that you should implement, as well
as some scripts that allow your code to be tested. Figure 1 shows a snapshot of the project
directory tree with the different files categorized.
test_structures.py
test_warmup.py
test_kmers.py
structures
dynamic_array.py
linked_list.py
bit_vector.py
warmup
warmup.py
malloclabs
kmer_structure.py
analysis.txt
generate_dna.py
Figure 1 The directory tree is organized by task. Blue represents directories, Teal represents files
that contain implementations (but are not executable), and Orange represents executable files.
1.2 Implementation Rules
The following list outlines some important information regarding the skeleton code, and your
implementation. If you have any doubts, please ask on Ed discussion.
? The code is written in Python and, in particular, should be executed with Python 3
or higher. The EAIT student server, moss, has Python 3.11.* installed by default. We
recommend using moss for the development and testing of your assignment, but you can
use your own system if you wish.
2 COMP3506/7505 – Semester 2, 2024
? You are not allowed to use built-in methods or data structures – this is an algorithms and
data structures course, after all. If you want to use a dict (aka {}), you will need to imple-
ment that yourself. Lists can be used as “dumb arrays” by manually allocating space like
myArray = [None] * 10 but you may not use built-ins like append, clear, count,
copy, extend, index, insert, pop, remove, reverse, sort, min, max, and so
on. List slicing is also prohibited, as are functions like sorted, len, reversed, zip.
Be sensible – if you need the functionality provided by these methods, you may implement
them yourself. Similarly, don’t use any other collections or structures such as set or
tuple (for example; mytup = ("abc", 123)).
? You are not allowed to use libraries such as numpy, pandas, scipy, collections, and so
on.
? Exceptions: The only additional libraries you can use are random and math. You are
allowed to use range and enumerate to handle looping. You can also use for item in
my_list looping over simple lists.
2 Task 1: Data Structures (5 marks)
We’ll start off by implementing some fundamental data structures. You should write your
own tests. We will try to break your code via (hidden) corner cases. You have been warned.
Task 1.1: Doubly Linked List (1.5 Marks)
Your first task is to implement a doubly linked list — your first “pointer-based” data structure.
To get started, look at the linked_list.py file. You will notice that this file contains two
classes: the Node type, which stores a data payload, as well as a reference to the next node;
and the DoublyLinkedList type which tracks the head and tail of the list, as well as the number
of nodes in the list.
A basic set of functions that you need to support are provided as function templates, and
you will need to implement them. You will also notice that there may be some changes or
modifications required to the data structures to support the necessary operations – feel free
to add member variables or functions, but please do not change the names of the provided
functions as these will be used for marking.
You will need to implement your own tests and run them using:
python3 test_structures.py --linkedlist.
Task 1.2: Dynamic Array (2 Marks)
Unlike the linked list discussed above, which can store nodes at any abitrary location in
memory, we often prefer to have data items stored contiguously (consecutively in memory),
allowing us to access an element x at some index i in constant time. One such way to achieve
this is through the use of a dynamic array.
The file dynamic_array.py contains another skeleton for you to implement. You should
store your data in self._data, and you can add any other member variables to your Dy-
namicArray object. Each function that needs to be supported is provided as a stub. Your
implementations should be efficient and correct, and we have provided annotations to describe
the expected complexity. In this assignment, we have given you a slightly trickier ADT
than the classic append-only array discussed in the lectures. In particular, you must support
prepend operations — that is, allowing an element x to be placed at the front of the array —
in O(1) amortized time, worst case.
Assignment 1 3
You will need to implement your own tests and run them using:
python3 test_structures.py --dynamicarray
Task 1.3: Bitvector (1.5 marks)
In some applications, it is useful to track the state of a collection of objects using simple
Boolean (True or False) flags. A na?ve way to do this is to simply use a (dynamic) array,
storing bool types as the underlying data. However, Boolean types are usually represented
by a machine word (** or 64 bits), meaning that we waste a lot of space with this approach.1
An alternative approach is to use a bitvector , which stores an array of b-bit integers to
represent each item — unset bits (value 0) represent False, and set bits (value 1) represent
True. Clearly, this approach uses 64× less space than the na?ve approach, as a single b = 64
bit integer can track the state of 64 items.
The file bit_vector.py contains another skeleton for you to implement. Note that it
uses a composition based design where a DynamicArray object is used to store the underlying
data. Each function that needs to be supported is provided as a stub. Your implementations
should be efficient and correct, and we have provided annotations to describe the expected
complexity. We describe two of the more exotic operations that should be supported in more
detail below.
You will need to implement your own tests and run them using:
python3 test_structures.py --bitvector.
Bitvector Operations: Shift
The shift operator handles both left and right shifts, depending on the sign of the dist
parameter. If the dist parameter is positive, we do a left shift by dist. A left shift moves all
bits in the bitvector left by dist positions, replacing empty positions with 0 bits. For example,
the following demonstrates the before (top) and after (bottom) of a left shift by dist = 2:
1011000100011
1100010001100
Notice that the two most significant bits have fallen off (the leftmost 10 on the first bitvector).
The right shifts work the same way, but we move the bits dist positions to the right (and the
least significant bits will fall off).
Bitvector Operations: Rotate
The rotate operator works exactly the same way as the shift operator, except it ensures that
any bits that fall off the end are rotated back onto the start of the bitvector. Using the same
example as above with dist = 2:
1011000100011
1100010001110
1 For the interested student: Most statically typed languages would represent a Boolean value as a
machine word (that is, ** or 64 bits) for convenience. Python is a dynamically typed language, and
each object actually carries a bunch of metadata around with it, and may be something like 24 bytes.
However, every True or False used is merely a reference to one of these two objects (there is only real
True and one real False object instantiated in the runtime). Nonetheless, here, we will pretend that
each Bool usually costs a machine word. In C, for example, a bool would use 8 bits (one byte), the
minimal addressable size.
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3 Task 2: Algorithmic Thinking Warm-Up (5 Marks)
Next, we are going to work on some simple warm up problems. These are designed to build
your problem solving skills. Some of them may appear tricky at first; you are encouraged
to sit down and think about them (a pen and a piece of paper will help). Do not be afraid
to get creative, as there may be multiple ways to solve each problem. Each problem will
be assessed on three tiers of tests — see the warmup.py file for more details, and test with
test_warmup.py (you need to implement your own tests).
3.1 The Main Character
You are given a string S. You need to simply return the first position of a repeated character
(indexed from zero), or ?1 if there are no repeats.
S = hello → 3.
S = world → ?1.
 S = algorithmsarefun → 10.
S = ooooohigetitnow → 1.
Here’s the catch: S can be built from an alphabet containing 2** possible characters,
represented as integers in the range [0, 2** ? 1]. Hint: You should use one of your data
structures from part one to help you solve this problem efficiently!
3.2 Sum-Thing Odd
You are given an unsorted list L containing n unique integers. Let min(L) and max(L)
represent the smallest and largest integers in L. Your task is to find the sum of the missing
odd integers in the range [min(L),max(L)].
 Consider L = ?6, 4, 9?: min(L) = 4 and max(L) = 9. Your range of interest is thus [4, 9].
The sum of the missing odd integers will be 5 + 7 = 12.
 Consider L = ?10, 1, 7, 17?: min(L) = 1 and max(L) = 17. Your range of interest is [1, 17].
The sum of missing odds in this range will be 3 + 5 + 9 + 11 + 13 + 15 = 56.
3.3 It’s cool, k?
A natural number is k-cool if it can be represented as the sum of unique non-negative powers
of k. For example:
? 17 is 4-cool because 40 + 42 = 17;
? 128 is 2-cool because 27 = 128;
? 11 is 10-cool because 100 + 101 = 11.
Given n and k, you must return the n th largest k-cool natural number. Two alternative
ways to say this:
? Return the n th smallest number that can be created by summing non-negative integer
powers of k; or
? If you created all combinations of sums of powers of k and sorted them into ascending
order, we want you to return the n th one.
Clearly, the first k-cool number is always 1 (k0 = 1) and the second k-cool number is always
k1 = k. Since we will test some very large numbers (up to 101,000,000), you should return the
number modulo 1016 + 61.
Assignment 1 5
3.4 Your Number is Up
Alice and Bob are playing a numbers game. The game starts with an unsorted list of integers,
L, with n = |L| guaranteed to be even. On each turn, they both remove one number from L.
If Alice removes an even number, it is added to her score. If she removes an odd number,
her score remains unchanged. The opposite is true for Bob (removing an odd number adds
to his score; removing an even number keeps his score unchanged). After n turns, the array
is exhausted, and the winner is determined by the player with the largest score — A draw is
also possible. Given L, you must return the winner, and their score, assuming both Alice
and Bob play optimally. You can assume that Alice always gets the first turn.
3.5 Getting Lit
A straight road of length k is illuminated by n light poles. Each light pole is represented
by a natural number i, where i represents the total distance from the start of the road to
the given pole. Each light is capable of illuminating a radius r. Given an unsorted list L of
poles, you need to return the minimal radius r such that the entire length of the road, k, is
illuminated. You may assume that the width of the road is infinitely small.2
k =12
L = 4, 7, 8, 1 .
0 3 6 9 12
r is too small!
0 3 6 9 12
r
r is too big!
0 3 6 9 12
r
r is just right.
0 3 6 9 12
r
Figure 2 A sketch of getting lit with n = 4 light poles.
2 Yes, we know it’s not a very useful road, but it makes your assignment easier. See also: https:
//w.wiki/Ajs5
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4 Task 3: Problem Solving with Data Structures (5 marks)
You are an algorithms specialist working at SIGSEGVTM, a world leader in high perform-
ance algorithmic solutions. You have been contracted by a bioinformatics company called
MallocLabs who require a bespoke system to help them deal with a growing amount of
genomic data they need to index. Their lead Bioinformatician, Barry Malloc, has provided
you with the following overview of the data and the system requirements. Your job is to
design and implement an appropriate data structure — and related algorithms — to match
Barry’s requirements. Barry has kindly placed the required time bounds in the function
stubs — you should carefully consider these when designing your data structure.
4.1 Data Representation
DNA data is represented as a string S of length |S| over an alphabet Σ = {A, C, G, T}.
Each character represents a different base (Adenine, Cytosine, Guanine, and Thymine). For
example, a sequence S with |S| = ** might look like
S = GTCGTGAAGTCGGTTCCTTCAATGGTTAAACC.
Since sequences can be very long, we can break them up into k-mers, all possible substrings
of length k. For example, there are 10 individual 23-mers of S:
GTCGTGAAGTCGGTTCCTTCAAT
TCGTGAAGTCGGTTCCTTCAATG
CGTGAAGTCGGTTCCTTCAATGG
GTGAAGTCGGTTCCTTCAATGGT
TGAAGTCGGTTCCTTCAATGGTT
GAAGTCGGTTCCTTCAATGGTTA
AAGTCGGTTCCTTCAATGGTTAA
AGTCGGTTCCTTCAATGGTTAAA
GTCGGTTCCTTCAATGGTTAAAC
TCGGTTCCTTCAATGGTTAAACC
In general, a sequence of length |S| will contain |S|?k+1 k-mers, and there are a total of |Σ|k
unique possible k-mers (in our case, |Σ| = 4). You are provided with a tool generate_dna.py
that can generate n sequences of length |S| for you to experiment with; it is probably easiest
to simply write them out to a file, and use the file as input to your testing program.
4.2 Required Functionality
At run-time, your program will be given two arguments that specify a path to a file containing
DNA sequences, as well as the value of k we are interested in working with. For example,
you might be given a file containing 50, 000 sequences of length 200, and k = 31. We will
always use str types to represent k-mers. The data structure used to solve the following
requirements is up to you, and should be designed based on the functionality requested. You
may need to use one or more of the structures implemented in part one for example, but the
final choice is yours. Implement in kmer_structure.py and test with test_kmers.py (you
need to implement your own tests).
Assignment 1 7
Storage and Modification: 2 marks
The first set of functions you need to support allow for reading and modifying data. They
are specified as follows:
? read: Given a file containing DNA sequences, break them into individual k-mers, and
store them in your data structure;
? batch_insert(L): Given a list of k-mers L, insert them into your data structure;
? batch_delete(L): Given a list of k-mers L, delete all occurences of them from your data
structure.
Note that there may be some duplicate k-mers in your data structure. You must keep track
of duplicates and their frequency, as these will be required for answering some query types in
the next section.
Queries: 3 marks
Your data structure also needs to support the following query types.
? freqgeq(n): Return a list of unique k-mers that occur at least n times;
? count(q): Return the number of times a k-mer q occurs;
? countgeq(q): Return the total number of k-mers that are ≥ q; that is, you need to sum
the frequencies of all k-mers lexicographically greater than or equal to q;
? compatible(q): Return the total number of k-mers that are compatible with q.
We provide some further information on the compatibility query as follows. A given k-mer q
is called compatible with k-mer b if the last two characters in q are the complement of the
first two characters in b. In genomics, the pair A and T is complementary, as is the pair C
and G. So, for example, CCTGATG is compatible with ACTTGCG:
q = CCTGATG
| |
ACTTGCG
Note that we always assume we are matching the end of the input query k-mer q with the
start of all other k-mers.
Analysis: 2 marks (COMP7505 Students Only)
If you are a COMP7505 student, you must also answer the questions posed in the plain text
file called analysis.txt (inside the malloclabs directory).COMP3506 students are encouraged
to do this too, but they will not be assessed on this component. Please keep your answers
succinct, but make sure to include all details that may be relevant. If in doubt, err on the
side of more detail.
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5 Assessment
This section briefly describes how your assignment will be assessed.
5.1 Mark Allocation
Marks will be provided based on an extensive (hidden) set of unit tests. These tests will do
their best to break your data structure in terms of time and/or correctness, so you need to
pay careful attention to the efficiency and the validity of your code. Each test passed will
carry some weight, and your autograder score will be computed based on the outcome of the
test suite. If you did not rigorously test your programs/code, you should go back and do so!
As the famous poet Ice Cube once said: check yourself before you wreck yourself.
The marks (percentages) provided in each task above are indicative of the total score
available for each part, but marks may be taken off for poor coding style including lack of
commenting, inefficient solutions, and incorrect solutions. Our code quality checks are not as
strict as PEP8, but we assume typical best practices are used such as informative variable
and function names, commenting, and breaking long lines. While the overall grade/score
will be calculated mathematically, an indicative rubric is provided as follows:
? Excellent: Passes at least **% of test cases, failing only sophisticated or tricky tests;
well structured and commented code; appropriate design choices; appropriate application
of data structures/algorithms for solving Tasks 2/3.
? Good: Passes at least 80% of test cases, failing one or two simple tests; well structured
and commented code; good design choices with some minor improvements possible;
good application of data structures/algorithms for solving Task 2/3 with some minor
improvements possible.
? Satisfactory: Passes at least 70% of test cases; code is reasonably well structured with
some comments; most design choices are reasonable but significant room for improvement;
reasonable application of data structures/algorithms for solving Task 2/3, but significant
improvements possible.
? Poor: Passes less than 70% of test cases; code is difficult to read, not well structured, or
lacks comments; design choices do not demonstrate a sound understanding of the desired
functionality; little or no suitable application of data structures or algorithms towards
solving Task 2/3.
5.2 Plagiarism and Generative AI
If you want to actually learn something in this course, our recommendation is that you avoid
using Generative AI tools: You need to think about what you are doing, and why, in order
to put the theory (what we talk about in the lectures and tutorials) into practical knowledge
that you can use, and this is often what makes things “click” when learning. Mindlessly
lifting code from an AI engine won’t teach you how to solve algorithms problems, and if
you’re not caught here, you’ll be caught soon enough by prospective employers.
If you are still tempted, note that we will be running your assignments through sophistic-
ated software similarity checking systems against a number of samples including including
your classmates and our own solutions (including a number that have been developed with
AI assistance). If we believe you may have used AI extensively in your solution, you may
be called in for an interview to walk through your code. Note also that the final exam
may contain questions or scenarios derived from those presented in the assignment work, so
cheating could weaken your chances of successfully passing the exam.
Assignment 1 9
As part of your submission, you must create a file called statement.txt. In that file,
you must provide attribution to any sources or tools used to help you with your assignment,
including any prompts provided to AI tooling. If you did not use any such tooling, you can
make a statement outlining that fact. Failing to submit this file will yield you zero marks.
6 Submission
You need to submit your solution to Gradescope under the Assignment 1: Autograder link in
your dashboard. Please use the appropriate link as there is a separate submission for 3506
and 7505 students. Once you submit your solution, a series of tests will be conducted and
the results of the public tests will be provided to you. However, the assessment will also
include a number of additional hidden tests, so you should make sure you test your solutions
extensively. You may resubmit as often as you like before the deadline, but we are imposing
a limit of ten submissions per 24 hour period. Please write your own tests!
Structure
The easiest way to submit your solution is to submit a .zip file. The autograder expects a
specific directory structure for your solution, and the tests will fail if you do not use this
structure. In particular, you should use the same structure as the skeleton codebase that
was provided. You should also have the statement.txt and analysis.txt (for COMP7505
students). Submissions without the statement.txt will be given zero marks, and the
autograder will notify you of this.
7 Resources
We provide a number of useful git and/or unix resources to help you get started. Please go
onto the Blackboard LMS and see the Learning Resources > Resources directory for more
information.
8 Changelog
? V1.0: Initial release.
? V2.0: Release with code; changed directory structure to match code. Clarified k-cool
further. Fixed an unfortunate typo.
? V3.0: Add clarifications section to the end of the spec to track any additonal changes or
clarifications from Ed or other discussions.
? V3.1: Remove some of the clarifying discussion about linked list nodes, since the API
was changed in the v3.0 code skeleton and the discussion is no longer relevant.
? V4.0: Further clarifications in the section below. No further changes.
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9 Clarifications
This section is introduced in V3.0 of the spec. It will be used to track any additional
clarifications on the spec or functionality.
Corner Cases
Here we clarify some corner cases and expected behaviour.
DoublyLinkedList
? What happens if I call set_head (or set_tail) on an empty list? In this case, do nothing.
These functions simply change the data of the head or tail if they do already exist. The
v3 skeleton code docstrings now capture this functionality.
BitVector
? If the dist provided to shift is greater than the bitvector length, what happens? The
bitvector would simply become filled with 0’s as everything will be shifted off.
? What about the case where we call rotate with a dist value larger than the length?
You will just keep rotating until done; rotating a bitvector of length l by l or 2l or 3l will
end up with the same bitvector as before the rotation. Modulus is your friend...
Node API
In our test suite, we will not be checking individual linked list Node types in isolation. What we
will be checking is that the linked list API works as expected; we will be traversing/modifying
your linked list (via the public DoublyLinkedList methods) and comparing the behaviour with
what a correct implementation does.
So, to be clear, we will never take a single Node type and check what is in prev or next
for example. This means you may even modify the Node API as it is only accessed internally
from the DoublyLinkedList; just ensure it is still compatible with the DoublyLinkedList
API.
Banned Code
Our philosophy for banning specific python functionality is to avoid the situation where some
complex operations are being hidden by syntactic sugar. For example, consider:
my_list = [1, 6, 105, 4, 9]
x = 4
if x in my_list:
print ("Yay!")
This innocent looking code is actually hiding an O(n) execution, where n is the length of
my_list. That’s because Python allows us to search for an item using nice syntax like if x
in my_list. That’s why we would prefer you to write something like:
...
for item in my_list:
if x == item:
print ("Yay!")
Even though this is longer, it clearly demonstrates that the list is being iterated over.
Some examples of things that are OK or not:
Assignment 1 11
? Generators: These are OK, because they hide annoying/ugly complexity, but do not mask
the fact that they are used for iteration.
? Dictionaries: Clearly not OK, because you need to be able to implement a map data
structure to get this behaviour. Same for Sets. (More in Week 5/6/7).
? Dunder methods: These are OK, as you will need to implement them anyway (and indeed,
you will implement __str__ for example).
In general: If you want to use something, you need to implement it yourself, not use an “out
of the box” implementation.
Why Moss?
You do not need to use Moss. We recommend you do because it provides a shared platform
for us to help if anything goes wrong. However, you are more than welcome to develop/test
your work elsewhere.
More about Bitvectors
A key principle in this assignment is that the data structure being implemented should
behave the way a user expects. This is different to the question of how the data is stored (in
what sort of container, in what order, ...) as a user doesn’t care about that. We do care, as
the designer of the data structure, so we endeavour to make things as efficient as possible
while maintaining correctness.
In terms of bitvectors, we cannot answer questions like should I append a bit to the most
significant bit, or the least significant bit? or should I store my bits little or big endian? –
What really matters is that a user appending the sequence 1 0 1 0 will get back a 1 if they
ask for the value of the bit at index 0, and a 0 back if they ask for the value of the bit at
index 3. If they then flip all of the bits, and prepend a 0, they should get a 0 back if they ask
for the value at index 0, and a 0 if they ask for the element at index 1 (this was previously
the first 1 we appended, but it has now been flipped). When these operations happen, it
is up to you to design how it works under the hood. The API should behave like a user
interacting with the DynamicArray using only 0 and 1’s, except that it should be much more
space efficient.
I’m Overwhelmed
This is a tough assignment, and it will take time. If you are overwhelmed, our advice is to
simplify the API you support for each structure. For example, instead of supporting both
append and prepend, just focus on supporting append efficiently. Similarly, ignore reverse for
now. This will at least allow you to build an efficient “append-only” list that you can use in
the assignment. You will of course lose some marks, but you will be able to move on and
capitalise in the other sections. For the warmup problems, just focus on solving them – even
if it is inefficient at first – as you will get marks just for giving correct (albeit slow) solutions
on small inputs.
Finally, please seek support; we have Ed, office hours, assignment help sessions. But we
cannot help you if you do not seek help.
COMP3506/7505

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