# REM 100- Midterm Exam Guide - Comprehensive Notes for the exam ( 19 pages long!)

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REM 100

MIDTERM EXAM

STUDY GUIDE

Name: - Vinay Lalwani

Student ID: - 301319204

Tutorial Section: - D102

Day and Time: - Monday, 12:30-1:20

The one environmental problem that affects me is overpopulation. Being from a

country which has population on the boom, I can relate to the effects of

overpopulation which range from not only scarcity of basic supplements like food

and water but also to their governing. Governing over such a large population and

making sure basic rights are granted to all is a very tough task to achieve and thus

I think overpopulation is one of the most important issues of the date.

Overpopulation is not an issue that can be dealt with overnight and thus it would

take a huge effort on the governments of all countries to educate the people on

the effects of overpopulation and of having massive families and n number of kids

in one family. As for how it is being resolved, in China, to take as an example, the

government has introduced a new law which states that a family can have only up

to two kids, after which if they want to have another kid, they must pay a fee to

the government. Such an strict law on one hand can be criticised to be ruthless

and harsh but on the other hand it does help bring control over the rapid

overgrowth of population in the country and hence even though it may seem

harsh, it ends up being quite an effective alternative.

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Answers to Homework 1

p. 13 1.2–3 “What is the smallest value of nsuch that an algorithm whose running time is 100n2runs

faster than an algorithm whose running time is 2non the same machine?”

Solution:

Find the smallest n > 0 such that 100n2< 2n.

Use a calculator and do a “binary search”. I tried n=10, 20, 15, . . ..

n100n22n

10 104∼103

13 1.69 ·1048.2 ·103

14 1.96 ·1041.64 ·104

15 2.25 ·1043.28 ·104

20 4·104∼106

At n=15 you will ﬁnd that 2nexceeds 100n2.

p. 21 2.1–3 “Consider the searching problem:

Input: A sequence of nnumbers A=ha1, a2, . . . , aniand a value v.

Output: An index isuch that v=A[i]or the special value nil if vdoes not appear in A.

Write pseudocode for linear search, which scans through the sequence, looking for v.”

Solution:

Linear-Search(A, v)

1. i←1

2. while i < length[A]and A[i]6=v

3. do i←i+1

4. if A[i]6=v

5. then i←nil

We are not concerned with correctness in this course, but if you have thought of an

invariant for Linear-Search you may want to compare it against the following.

v6∈ A[1 . . . i −1]or v=A[i]

p. 27 2.2–1 “Express the function n3/1000 −100n2−100n +3in terms of Θ-notation.”

Solution:

n3/1000 −100n2−100n +3=Θ(n3)

p. 27 2.2–3 “Consider linear search again (see Exercise 2.1–3). How many elements of the input sequence

need to be checked on the average, assuming that the element being searched for is equally

likely to be any element in the array? How about in the worst case? What are the

1

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