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COMP3121/9101 Assignment
创建日期：2024-05-20 17:51:33
标签： COMP3121
Assignment

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COMP3121/9101  Assignment 

Due Friday 3rd March at 5pm Sydney time
In this assignment we review some basic algorithms and data structures, and we apply the divide-
and-conquer paradigm. There are three problems each worth 20 marks, for a total of 60 marks.
Partial credit will be awarded for progress towards a solution. We’ll award one mark for a response
of “one sympathy mark please” for a whole question, but not for parts of a question.
Any requests for clarification of the assignment questions should be submitted using the Ed forum.
We will maintain a FAQ thread for this assignment.
For each question requiring you to design an algorithm, you must justify the correctness of your
algorithm. If a time bound is specified in the question, you also must argue that your algorithm
meets this time bound. The required time bound always applies to the worst case unless otherwise
specified.
You must submit your response to each question as a separate PDF document on Moodle. You
can submit as many times as you like. Only the last submission will be marked.
Your solutions must be typed, not handwritten. We recommend that you use LaTeX, since:
• as a UNSW student, you have a free Professional account on Overleaf, and
• we will release a LaTeX template for each assignment question.
Other typesetting systems that support mathematical notation (such as Microsoft Word) are also
acceptable.
Your assignment submissions must be your own work.
• You may make reference to published course material (e.g. lecture slides, tutorial solutions)
without providing a formal citation. The same applies to material from COMP2521/9024.
• You may make reference to either of the recommended textbooks with a citation in any
format.
• You may reproduce general material from external sources in your own words, along with a
citation in any format. ‘General’ here excludes material directly concerning the assignment
question. For example, you can use material which gives more detail on certain properties of
a data structure, but you cannot use material which directly answers the particular question
asked in the assignment.
• You may discuss the assignment problems privately with other students. If you do so, you
must acknowledge the other students by name and zID in a citation.
• However, you must write your submissions entirely by yourself.
– Do not share your written work with anyone except COMP3121/9101 staff, and do not
store it in a publicly accessible repository.
– The only exception here is UNSW Smarthinking, which is the university’s official writing
support service.

Question 1
You have recently been hired to work for a large social media company. The company has staff
shortages due to a recent firing spree, and you have been tasked with designing the recommendation
algorithm used on the front page! After thinking for several days, you have figured out a way to
measure a user’s popularity, and now need to design an efficient algorithm to calculate it.
For a given user with n posts, you have access to an integer array V = [v1, v2, . . . , vn], where vi
is the number of views the user’s ith post has in thousands. Since these view counts are used to
order posts on a user’s profile page, they are already sorted, in descending order. The popularity
of a user is the largest value of p such that the user has at least p posts that each have at least p
thousand views.
For example, suppose a user has n = 6 posts, and a view count array V = [7, 6, 5, 4, 4, 1]. Then
they have at least 4 posts each with at least 4,000 views (indeed, they have five such posts), so
p = 4 satisfies the criterion. You can confirm that the criterion is also satisfied for p = 3, but it is
not satisfied for p = 5 since there are only three qualifying posts. The user’s popularity index is
in fact 4, because p = 4 is the largest value for which the criterion holds.
1.1 [7 marks] Before you are given full access to the codebase, you need to try and implement
your new popularity measure on top of the existing code. Given the integer n and the integer array
V for a user as well as an integer value p ≤ n, you must determine whether that user’s popularity
is at least p. This snippet of code runs every single time the page gets loaded, so it needs to be
very efficient.
Design an algorithm that runs in O(1) time and checks whether a user’s popularity is at least
p.
1.2 [13 marks] The code you modified was written by a now-fired intern, and would simply try
every value of p until it found one that worked, for every user. Now that the company has grown
to serve millions of users, your boss has demanded that you develop a faster algorithm. Given the
integer n and the integer array V for a user, you must efficiently compute the user’s popularity
index p.
Design an algorithm that runs in O(log n) time and computes p for a given user.

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MATH 239 QF5203 INFR08010 IT114105 FIT2093 ECON3124 ECON1195 MATH 337 STAT 3006 COMP202 COMP3130 MATH3609 COMP 250 CS6140 IEEE ELE00041I FIN40090 CIV 5899 MATH3066 IGNMENT MATH 2009 STAT3405 HIST 101 MATH 3281 CEGE0042 ICT532 LAB 7 LAB 5 MCO455 CSIT214 Q4 IFB104 A1 ECO220Y5Y DA5020 CMPSC473 FIN9007 DSCI553 MSCI534 COMP3308 CSE-112 CMPT 310 EE104 F 2C P20 ALY2010 BUSM060 STA258 ECO00030M R BIOSTAT 274 COS6012-B FIT3155 CMPUT 340 EC421 INFS4205 ECOM135 NATS 1740 COMP809 MBE 6005 STA465 CSSE2310 CIVL2700 DATA4700 CMPSC 473 ISE 529 CS5044 MAST30020 COMP2207 ENGG1001 COMP0046 FIT3165 STAT GR5241 MECH0007 vATHK1001 ANALYTIC ATHK1001 MATH352001 HW3 S1 BMAN 24662 COMP 636 Stat-461 STAT 302 STAT 2132 STAR534 ENG4137 CMP3752M CS3103 BISM3222 STA 135 ME155A IIMT3601 ECON3371 ECON 3371 HW4 FINA 5840 DT211C CTEC3902 MAT005 MATH2148 S261F Econ 332 MATH3734 MIS41270 7CCMFM13 SYST 664 CIS434 CENG10014 MT4111 MT4527 ECMM424 CMT219 Math 136 MATH 3120 COMP10002 MAST20009 MATH0058 BEEM117 ISYE 6420 MGMTMFE 405 25579 1ECE 273 M122 COMP4434 1ELEC ELEC5620M STAT0010 BFF2401 MXB361 MATH3811 CS330 CMT307 FIT1033 CptS 583 UP 431 MATH6005 AF5343 CS2435 ECOM30002 ES50061 CS 2506 ECMT6002 CODE 00099F MT4539 ESSAY ICM317 MATH1231 MFIT5010 BMA547 MATH334 CIVL2201 MATH39032 T-04 CIVE97119 EMESTER CAB302 CAB301 59PM STAT802 ISYS3412 RM3 COSC 2123 AcF 311 MATH2022 1FINAL 4CCS1PHC ICM 142 ENVS3023 Math 4023 I1 ACSE8 FIN B385F CS-275 STA 4109-01 A31021 EE140 MT1 EE124 ECO-6004B Inf2-IADS CS126 IS2184 UL18 MATH5092 ECOM009 COMP 6211 ELEC202 MKT3019 IAB230 FIT5046 584-S21 COMP3210 CO250 A29401 MATH 136 MGT6174 ECMT6007 DATA2001 MAT 443 MATH10222 PHDE0071 ELE00123M COSC1295 MAT00045H MATH32032 1004GRC MAS223 COMP10001 DATA3404 CIVL2110 STAT2008 FNCE10002 EEE6431 COM6515 COMP9120 NBS8185 ECTE942 ECON 405 MATH314301 STAT 2011 COMPSCI 350 COMP20007 CMPSC-132 ECON5002 STA 35 MTH6108 FIT5147 MTH6150 100C FINA 5260 DESC9115 ECON4998 NBS8257 GMM ECON 6070 BSA2 ECE599 STATS 102B STA120 INFS601 BFC3241 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 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