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COMP7505 Algorithms and Data Structures
创建日期：2024-08-24 15:05:28
标签： COMP7505
Algorithms and Data Structures
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Algorithms and Data Structures – COMP3506/7505 
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 naïve 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 (32 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 naïve 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, 32 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.
COMP3506/7505
4 COMP3506/7505 – Semester 2, 2024
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 232 possible characters,
represented as integers in the range [0, 232 − 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
COMP3506/7505
6 COMP3506/7505 – Semester 2, 2024
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| = 32 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.
COMP3506/7505
8 COMP3506/7505 – Semester 2, 2024
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 90% 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.
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MATH20602 COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 CIVL2010 ECMT2150 CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 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FN1024 MATH0094 MANG 6554 ECOS3003 ELEC6252 C2511C PHY328 EC1060 ECON32202 COMP4002-E1 MATH3063 EFIMM0124 QBUS2310 ECON4411 FUNDAMENTALS ACCT20001 18YX RPM COMP 2711 QBUS6600 BUSS5221 ST3189 FIT1047 MAT344 EGB375 MATH60013 MATH96011 COMP3557 MAST20029 ECM159 EAE1011 ENSCEN 105 SECTION A STA 141C SOSE 2022 PAM006 COMP0048 M40007 ISOM2500 CMPE 142 A06472 MCC150 ACST 8083 GEOG6087 ECON920 FINM7008 ENVENG 4110 COMPSCI 361 ENGRCEE 21 PHYS 1112 ACF2100 ECMM108 COMPS267F MAT00050M MAST30025 CSIT970 MSCI 224 INT202 PUBL0054 MSDM5004 BMAN 21020 BMAN21020 MGMT1002 MATH11150 LAWS7023 ACTL30002 CIVL3340 MATH1002 ECON 8069 COMPSCI 351 IBUS7302 STAT4528 CHEM1101 STAT3925 BUSN 7008 Comp 3120 ECOS2040 SWEN90010 ENGN6528 ECM158 ECON20022 COMP6452 Calculation CITS1401 S1889112 BUS 351 ACTL30008 FIT2091 ECON6002 IBUS6020 PHI 001 ECON30290 MATH7501 ECON10004 MFIN7017 ISYS90043 LAWS7012 ECON30025 COMP30023 COMM1190 ECOM20001 GSBS6009 STAT 337 EMET8002 ECOM90001 ECOM30001 FINC 2012 BUSINESS ENGCV512 ECO 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