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- CSE 222/505 – Homework 2

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Q1:

Give running times of each of the algorithms in proper notations. Explain your answers.

1.

2.

Q2:

1. What does the function do?

2. Give the best-case and worst-case running times of the algorithm in Ɵ notation.

Explain your answer.

Q3:

Prove that the running time of an algorithm is Ɵ(g(n)) if and only if its worst-case running

time is O(g(n)) and its best-case running time is Ω(g(n)).

Q4:

1. Express insertion sort as a recursive procedure.

2. Write a recurrence for the worst-case running time of the procedure. Explain your

answer.

3. Solve the recurrence. Give detailed answer.

Q5:

Indicate giving detailed explanation whether f(n) = O(g(n)), f(n) = Ω(g(n)) or f(n) = Ɵ(g(n)) for

the following:

1. 𝑓(𝑛) = 𝑛

0.1

, 𝑔(𝑛) = (log 𝑛)

10

2. 𝑓(𝑛) = 𝑛!, 𝑔(𝑛) = 2

𝑛

3. 𝑓(𝑛) = (log 𝑛)

log𝑛

, 𝑔(𝑛) = 2

(log2 𝑛)

2

Q6:

Rearrange your Homework 1 code using Array, Array List, and Linked List structures. Analyze

and compare their performances. Add detailed information about your test and

performance analysis method. Also, write detailed analysis results in your report.

RESTRICTIONS:

– Can be only one main class in project

– Don’t use any other third part library

GENERAL RULES:

– For any question firstly use course news forum in moodle, and then the contact TA.

– You can submit assignment one day late and will be evaluated over twenty percent (%20).

– Register github student pack and create private project and upload your projects into github.

– Your appeals are considered over your github project process.

TECHNICAL RULES:

– Use given CSE222-VM to develop and test your homeworks (your code must be working on

CSE222-VM), CSE222-VM download link will be given on Moodle.

– Implement clean code standarts in your code;

o Classes, methods and variables names must be meaningful and related with the

functionality.

o Your functions and classes must be simple, general, reusable and focus on one topic.

o Use standart java code name conventions.

REPORT RULES:

– Add all javadoc documentations for classes, methods, variables …etc. All explanation must be

meaningful and understandable.

– You should submit your homework code, javadoc and report to Moodle in a

studentid_hw#.tar.gz file.

– Use the given homework format including selected parts:

–

Detailed system requirements

The Project usecase diagrams (extra points)

Class diagrams

Other diagrams

Problem solutions approach x

Test cases x

Running command and results x

GRADING :

– No OOP design : -100

– No interface : -95

– No method overriding : -95

– No error handling : -50

– No inheritance : -95

– No polymorphism : -95

– No javadoc documentation : -50

– No report : -90

– Disobey restrictions : -100

– Cheating : -200

– Your solution is evaluated over 100 as your performance.

– Important! For Q1, Q2, Q3, Q4 and Q5, answers without rational explanations will

get 0 points.

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