Page 3 SECTION 1. Algorithm Analysis [1 pt per prompt = 12 points] TO DO WELL: Before you work on this section, write down what W(N) means, and the F(N)s of sorting and searching. 1) What is the purpose of using asymptotic notation such as O, Omega and Theta instead of using the exact number of comparisons done by a sorting algorithm? i.e. why do we use O(n^2) instead of saying 2n^2 + 3n + 4 *Because we are only interested in 2) Computing the Average time complexity for a real-world problem is difficult. Explain why by referring back to the formula for computing A(n). *Why? 3) Your friend is very excited about having found a sorting algorithm that sorts in much less than W(n) =Theta(N^2)comparisons even though it corrects only one bad pair per comparison. He thinks this is the fastest sort ever and that he will get a Ph.D. tomorrow. Please teach him why he is wrong. *Answer: 4) Your friend says she can find a comparison based algorithm that searches for an element in an ordered list in much less thanW(N) = Theta(log N). Please teach her why she is wrong. *Answer: 5) Name2Divide and Conquer algorithms we studied in this class. *Name: *Name: 6) Describe 2 Space vs. Time decision cases we discussed in this class. In what ways can each be called Space vs. Time? *Example Algorithms: ________ vs.______________ *Reason: *Example Data Structures: _________vs.____________ *Reason: 7) Name 2 greedy algorithms we have learned in this class. *Algorithm for solving/finding: *Algorithm for solving/finding: SECTION 2. Sorting [2pts per prompt = 10 points] Your mean employer has five sorting programs. But they are labeled by their descriptions - no names. Read each label then say which of the following it is: Heap Sort Insertion Sort Merge Sort Quick Sort Radix Sort 1) "I am a good choice if you want consistent theta(nlogn) time and have lots of space." *Answer: This is 2) "Although I take O(n^2) time in the worst case, on the average I only use theta(nlogn) and I do not need as much space as another divide and conquer algorithm.” *Answer: This is 3) "I use theta(nlogn) time in the worst case. The data structure I use is also useful for efficiently implementing priority queues." *Answer: This is 4) "Even though my average complexity is theta(n^2), I am a good choice if you want to sort small files, or large files that are very nearly in order." *Answer: This is 5) "I am a good choice if you want to quickly sort a large number of K digit numeric IDs." *Answer: This is SECTION 3. Object-Oriented Programming [2pts per prompt = 16 points] TO DO WELL: Before you work on this section, re-read the notes from Week6 and Week7. 1) (inheritance), we placed data members of the base class in protected. Why did we do that? Answer each separately. *Why not private? *Why not public? 2) You had to overload = to make it work with slists. .

1. Page 3
SECTION 1. Algorithm Analysis [1 pt per prompt = 12 points]
TO DO WELL: Before you work on this section, write down
what W(N) means, and the F(N)s of sorting and searching.
1) What is the purpose of using asymptotic notation
such as O, Omega and Theta instead of using
the exact number of comparisons done by a sorting algorithm?
i.e. why do we use O(n^2) instead of saying 2n^2 + 3n + 4
*Because we are only interested in
2) Computing the Average time complexity for a real-world
problem is difficult.
Explain why by referring back to the formula for computing
A(n).
*Why?
3) Your friend is very excited about having found a sorting
algorithm that
sorts in much less than W(n) =Theta(N^2)comparisons even
though it corrects
only one bad pair per comparison. He thinks this is the fastest
sort ever
and that he will get a Ph.D. tomorrow.
Please teach him why he is wrong.
*Answer:
4) Your friend says she can find a comparison based algorithm

2. that searches
for an element in an ordered list in much less thanW(N) =
Theta(log N).
Please teach her why she is wrong.
*Answer:
5) Name2Divide and Conquer algorithms we studied in this
class.
*Name:
*Name:
6) Describe 2 Space vs. Time decision cases we discussed in
this class.
In what ways can each be called Space vs. Time?
*Example Algorithms: ________ vs.______________
*Reason:
*Example Data Structures: _________vs.____________
*Reason:
7) Name 2 greedy algorithms we have learned in this class.
*Algorithm for solving/finding:
*Algorithm for solving/finding:
SECTION 2. Sorting [2pts per prompt = 10 points]
Your mean employer has five sorting programs. But they are
labeled
by their descriptions - no names.
Read each label then say which of the following it is:
Heap Sort

3. Insertion Sort
Merge Sort
Quick Sort
Radix Sort
1) "I am a good choice if you want consistent theta(nlogn) time
and have lots of space."
*Answer: This is
2) "Although I take O(n^2) time in the worst case, on the
average
I only use theta(nlogn) and I do not need as much space as
another divide and conquer algorithm.”
*Answer: This is
3) "I use theta(nlogn) time in the worst case. The data structure
I use is also useful for efficiently implementing priority
queues."
*Answer: This is
4) "Even though my average complexity is theta(n^2), I am a
good choice if you want to sort small files, or large files that
are very nearly in order."
*Answer: This is
5) "I am a good choice if you want to quickly sort a large
number of K digit numeric IDs."
*Answer: This is
SECTION 3. Object-Oriented Programming [2pts per prompt =
16 points]

4. TO DO WELL: Before you work on this section, re-read the
notes from Week6 and Week7.
1) (inheritance), we placed data members of the base class in
protected.
Why did we do that? Answer each separately.
*Why not private?
*Why not public?
2) You had to overload = to make it work with slists.
*We had to overload=. What’s wrong with the one provided by
C++?
*We had to overload==. What’s wrong with the one provided by
C++?
3) Why did you have to write a copy constructor for linked
lists?
Also, give twocases in which your copy constructor is
automatically invoked in relation to calling regular functions.
*What’s wrong with the one provided by C++?
*Invoked when:
*Invoked when:
4) Why is it useful to use virtual functions with inheritance and
pointers? Explain using the Animals array which contains
pointers to Dog and Cat objects with a virtual function Speak.
*The stated combinations allows
SECTION 4. Binary Search Trees (HW4)[1 pt per prompt = 5

5. points]
void BST::traverse(Vertex *V) // post order traversal
recursively
{
if (V != NULL)
{
traverse(V->Left);
traverse(V->Right);
cout << V->elem << endl;
}
}
1) Modify the above slightly (just re-order) to do the Depth
First traversalrecursively. What is this traversal called?
*Code:
*Name of the traversal: ____________ order traversal.
2) Why would we want to balance search trees?
(i.e. What is wrong with unbalanced trees?)
What were the two ways (from our notes) of having a balanced
search tree?
*Why:
*Way1:
*Way2:
SECTION 5. GRAPHS: Islands and Bridges [2pts per prompt =

6. 4 points]
800 islands are connected with many two-way bridges (i.e.
lines, not arrows).
You know the cost of maintaining each bridge.
You want to minimize the total maintenance cost by eliminating
some bridges while leaving all the islands connected.
1) What algorithm would you use to solve this problem?
(Algorithm for finding what?)
*Algorithm for finding:
2) How many bridges will you end up with if you used this
algorithm?
*Give the Formula where N = 800:
SECTION 6. ENCYPTION and BIG DATA (from Notes-14)[1
pt per blank = 4 points]
*Fill in the blanks in the following:
Encryption in essential in cybersecurity.
Using RSA, if people want to send messages to Mary, they have
to use her ______ encryption key. She uses her ______
decryption key to decode them.
_______ numbers play an important role in constructing these
keys.
The computer can use big training data to learn to identify or
classify things.
By analyzing a vast number of examples labeled with their
categories, the computer will learn to place unlabeled ones into
these categories. This area of Artificial Intelligence is called
_________ learning.
SECTION 7. MEMORY [1pt per prompt = 3 points]
1) What are garbage cells? i.e. What kind of cells are they and
why do they happen? (Recall that there are 3 kinds of cells and

7. garbage cells are just one of them)
*What are they?
*Why do they happen?
2) Which garbage collection method from the notes worked
incrementally and also prevented dangling pointers?
*Method:
SECTION 8 NP vs. P Consulting Job [2pts per prompt = 6
points]
1) Your boss says "I want you to find the shortest path that
passes through all the Mars alien bases.
The objective is to infect each base
and thus you cannot return to the same base ever again.
I want an algorithm to do it in Polynomial time."
*What would you say to him? Explain why:
2) 10 years from today, while sleeping, you find a polynomial
time algorithm for bin packing. Congratulations!! What
implication does this have on your answer to the question
above? Whatfamous question have you answered to make you
rich?
*Implication on (1):
*Question answered:
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