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COMP3600/6466 Algorithms Assignment
创建日期：2024-04-15 17:39:33
标签： COMP3600
Algorithms Assignment

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COMP3600/6466 Algorithms Assignment 1

COMP3600/6466 — Algorithms
Assignment 1
Due: Friday, 20 August 2020 23:59 Canberra Time
Grace Period Ends: Saturday, 21 August 2020 13:00 Canberra Time
Late Penalty: 100%
IMPORTANT NOTES (PLEASE READ BEFORE WORKING ON THE SOLUTION):
? Please submit your assignment as a single .pdf file, named A1-[studentID].pdf, via Wattle before the due date.
? We provide 13 hours grace period. This means, there will be no penalty if you submit before the grace period
ends. However, we will NOT accept assignment submission beyond this time (i.e., late penalty after the grace
period ends is 100%).
– You can update your assignment until the grace period ends.
? Assignment marking:
– The total mark you can get in this assignment is 90 points.
– This assignment will contribute 20% to your overall mark.
– In each question, you need to provide a convincing argument (including mathematical derivation) that
supports your answer. The argument is worth 80% of the marks, while the solution alone is 20%.
? Discussion with your colleagues are allowed and encouraged. However, you need to work on the assignment
on your own AND write the names you discussed this assignment with.
In all the questions below, you can assume that all n are positive integers, while all f (n) and g(n) are asymptotically
positive functions —that is, a function whose value is positive for all sufficiently large n.
[15 pts] Part A
For each statement below, please identify if the statement is Always True, Sometimes True, or False and provide your
reasoning. Each question is worth 5 points.
1. f (n) + o( f (n)) = Θ( f (n))
2. f (n) = ?(g(n)) implies g(n) = ?( f (n))
3. f (n) + g(n) = ?(min( f (n), g(n)))
[35 pts] Part B
4. [15 pts] Please rank the following function by increasing order of growth and explain your answer
? f1(n) = dlog(n)e!
? f2(n) = log(n!)
? f3(n) = nlog n
? f4(n) = n2
? f5(n) = 2
√
2 log(n)
5. [20 pts] Ms Tree was given the following algorithm to be implemented and analyse.
Can you please help Ms Tree by answering the following questions:
(a) [5 pts] Given a tree T with n nodes, what does the algorithm AFunction compute?
1
COMP3600/6466 Algorithms Assignment 1
Algorithm 1 AFunction(A binary tree T )
1: if T == ? then
2: Return 0
3: if T .root.le f tChild == ? AND T .root.rightChild == ? then
4: Return 1
5: Return AFunction(T .root.le f tChild) + AFunction(T .root.rightChild)
(b) [7.5 pts] Please provide the total running time T (n) for AFunction in the form of a recurrence function,
when given a tree T with n nodes as input.
(c) [7.5pt] Please solve the above recurrence using substitution method when the tree is a complete binary
tree —that is, a binary tree where all non-leaf nodes have two children and all leaves are at the same level.
Please frame the solution as a tight asymptotic bound (i.e., Θ).
[40 pts] Part C
6. [15 pts] In a galaxy far far away, the Planet Htrae is fighting a health crisis over the spread of a new highly
contagious disease, called DV. The Senate of Planet Htrae is discussing the standard medical procedure to be
adopted to keep its residents safe. For discussion, the health officials of Htrae proposes three different health
measure plans, as described below.
All the proposed health measure plans allow an infected person to be identified and contained (such that the
person can no longer infect another person) within a day. However, during that one day, the infected person
may have spread the disease to others. The rate of spreading and fatality for the different health measure plan
are as follows.
Plan-1. Under this strategy, each infected person can infect at most 12 other people within a day, while the
fatality rate among the infected is 10%.
Plan-2. Under this strategy, each infected person can spread the virus to at most 5 other people within a day.
Under this plan, the fatality rate among the infected remains 10%.
Plan-3. Under this strategy, each infected person can spread the virus to at most 5 other people within a day.
However, the fatality rate among the infected is only 0.1%.
Since Htrae is governed by technocrats and the population of Htrae is huge, the government asked the health
officials to provide asymptotic analysis with respect to fatality rate on the different plans above. To this end,
please help the health officials by answering the following questions.
Suppose the number of people infected at the end of day-0 is 1. Then,
(a) [6 pts] Please define the tight asymptotic bound (i.e., Θ) on the number of fatalities due to DV under each
plan, as the days progress.
(b) [3 pts] Are there any clear winner on which plan should be applied to minimize the number of fatalities,
based on asymptotic bound and their equivalence classes on the growth in the number of fatalities?
(c) [3 pts] Are there any clear winner on which plan should be applied to minimize the number of fatalities,
based on actual growth in the number of fatalities under the different plans?
(d) [3 pts] Based on the results of (a)-(c), please elaborate when would analysis on asymptotic bound of the
growth of a function be sufficient, and when would such an analysis be insufficient?
7. [25 pts] To welcome new students to the UNA university, each student receives a voucher of $d, which can
be used to purchase stationery and snacks. To reduce queueing time, UNA has packaged n different stationery
packs and n different snack packs, so that students just need to pick exactly one of the stationery packs and
exactly one of the snack packs. You can assume that every student has the full option (i.e., n stationery and n
snack packs). Now, of course, different packs may have different prices. Given this scenario, many students
would like to purchase the pair of stationery and snack packs with the total cost under $d but is as close as
2
COMP3600/6466 Algorithms Assignment 1
possible to $d. Please help these students by answering the following questions.
(a) [10 pts] Mr SP said that a Θ(n2) algorithm can find the desired pair of stationery and snack packs. Is
he correct? If he is, please provide the algorithm along with the analysis. Otherwise, please provide an
explanation why such an algorithm is not possible.
(b) [15 pts] Mr SP2 said that actually, a O(n log n) algorithm can find the desired pair of stationery and snack
packs. Is he correct? If he is, please provide the algorithm along with the analysis. Otherwise, please
provide an explanation why such an algorithm is not possible.
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EARN 5 FE 825 IERG 5130 STAT 8178 EE161 ADS2 G54FUZ CS326 113B ECN 226 QBUS6860 ELEC3202 COMP9334 MGT11B MET CS 777 STA238 00099F Python SMM306 CMT206 EC116 SP MAST90084 CS480/680 BCPM0091 CMPT 300 ECON2209 FY20 STAT 432 CVEN9625 MATH1712 CMP9771M CMP3750M CIS 325 AI506 MAT344H1S MGT7180 PSTAT 160B CSYS5010 1D STAT 453/558 ME152B STA304H1F CSCI-128 ME428 CO3002 FINE 7640 COMP3234 ECSE 223 EE497 – 3D MATH5905 ECS648U ENG5009 MATH10242 EC665 A CPI221 ISOM5220 MACE40402 MGT B456F COMP9315 AFM 113 STAT 778 CS 564 MA231 CS 230 CS 124 COMP5511 CSC317 ITEC1010 ELEC207 INFT 3019 7CCMFM06 EE 161 5G ECLT5810 MATH 7349 CS526 O2 COMP90054 ELE00063M ACCT5034 ARC1015 CSCI 40 CSCI E40 FIN 524B CS 462 389COM CMT309 MFIN703 COMP4250 STA304 STA304H1S STA 1003 FIN 448 BUFN 732 CS520 CVEN3701 ECMT6006 PHAS0100 CSIT314 MDIA 5028 CSCI 2134 MAT 451 CMPT 459 STAT 457 INFO20003 COMP4141 IELE8066 F540 ECM9 CSE 6321 FIN 430 MATH3911 BFC5916 COMP1011 EEE 6209 STATS 240 CW3 COMP206 COMP1003 4331W ISE 530 CMPT 295 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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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