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COSC 2123 Algorithm Design & Complexity Analysis
创建日期：2024-08-05 14:55:19
标签： COSC 2123
Algorithm Design & Complexity Analysis

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Algorithms and Analysis

COSC 2123/1285

Assignment 2: Algorithm Design & Complexity Analysis

Assessment Type Individual Assignment. Submit online via Canvas → Assignments

→ Assignment 2. Clarifications/updates/FAQs can be

found in Canvas Announcements and Discussion → Assignment

2 Queries.

IMPORTANT NOTES

? If you are asked to develop/design an algorithm, you need to describe it in

plain English first, say a paragraph, and then provide an unambiguous pseudo

code, unless specified otherwise. The description must include enough details to

understand how the algorithm runs and what the complexity is roughly. All algorithm

descriptions and pseudo codes required in this assignment are at most half

a page in length.

? Standard array operations such as sorting, linear search, binary search, sum,

max/min elements, as well as algorithms discussed in the pre-recorded lectures

can be used straight away (but make sure to include the input and output if you

are using them as a library). However, if some modification is needed, you have to

provide a full description. 

? Marks are given based on correctness, conciseness (with page limits), and clarity

of your answers. If the marker thinks that the answer is completely not understandable,

a zero mark might be given. If correct, ambiguous solutions may still

receive a deduction of 0.5 mark for the lack of clarity.

? Page limits apply to ALL problems in this assignment. Over-length answers may

attract mark deduction (0.5 per question). We do this to (1) make sure you develop

a concise solution and (2) to keep the reading/marking time under control. Please

do NOT include the problem statements in your submission because this

may increase Turnitin’s similarity scores significantly.

? All stories are fictitious and just for fun. Please do not take them seriously.

? In the submission (your PDF file), you will be required to certify that the submitted

solution represents your own work only by agreeing to the following statement:

I certify that this is all my own original work. If I took any parts from

elsewhere, then they were non-essential parts of the assignment, and they

are clearly attributed in my submission. I will show that I agree to this

honour code by typing “Yes":

2

1 Part I: Fundamental

Problem 1 (8 marks, 1 page). Saving the niece.

One day, your niece comes to visit you with a worried look on her face. It turns out

that her teacher just gave a very tricky problem as part of their VCE Algorithmics Unit 3.

She has spent 3 days working on it without any success. As a loving (and very capable)

uncle/aunt, you must help her out. Here is the problem.

Consider the algorithm mystery() whose input is an integer array A of size n.

Algorithm mystery(A[0...(n?1)])

return mysteryRecursive(A[0...(n?1)]);

Algorithm mysteryRecursive(A[`... r])

a) [2 marks] What does the algorithm compute? Justify your answer.

b) [1 mark] What is the algorithmic paradigm the algorithm belongs to?

c) [1 marks] Write the recurrence relation (formula + base condition) for C(n), which

counts the number of array elements comparisons.

d) [3 marks] Solve the recurrence relation by the backward substitution method to

obtain an explicit formula for C(n) in n.

e) [1 mark] Write the complexity class that C(n) belongs to using the Big-Θ notation.

3

Transaction ti Size si Fee fi

1 1 4

2 3 9

3 2 6

4 4 11

5 5 13

Table 1: A toy example of five transactions with their corresponding sizes and fees.

Problem 2 (8 marks, 1 page). Profit maximisation in block mining - version 1.

As the Bitcoin price has quadrupled in the past one year (9/2020-9/2021), you have

made a decision of becoming a miner to earn some profit. You find out that in Bitcoin

blockchain and the like, miners are responsible for constructing blocks and if successful

(being the first to solve a puzzle), will receive not only a base reward but also transaction

fees included in the transactions in the block. While the base reward is fixed and out

of control of the miners, the transaction fees are not. You quickly figure out that one

way for the miners to maximise their profit is to select the set of transactions that sum

up to the highest fee. 

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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 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