Grader Use Only:
#1
CMSC132
Fall 2005
Final Exam Key
First Name: _______________________
Last Name: _______________________
#2
(7)
#3
(8)
#4
(13)
#5
(9)
#6
(16)
#7
(9)
#8
(7)
#9
(8)
#10
(8)
Student ID: _______________________
Total
Section time ___________
Honors
TA: _____________________
I pledge on my honor that I have not given or received any unauthorized assistance on this
examination.
Your signature: _____________________________________________________________
General Rules (Read):
a.
b.
c.
d.
e.
This exam is closed book and closed notes.
If you have a question, please raise your hand.
Total point value is 100 points.
Answer True/False questions by circling the T or F at the end of the question.
Answer multiple-choice questions by circling the letter (e.g., a, b) at the front of each
choice.
f. Answer essay questions concisely using 1 or 2 sentences. Longer answers are not necessary
and are discouraged.
g. WRITE NEATLY. If we cannot understand your answer, we will not grade it (i.e., 0
credit).
h. Honors section questions only count for credit for students in the honors section.
1
(15)
(100)
(8)
Problem 1 (15 pts) Software Engineering & Object-Oriented Design
a. (1 pt) The Waterfall model is reasonable for both small and large projects.
T or F
b. (1 pt) The Waterfall model, Unified model, and Rapid Prototyping are intended to be models of
what? (Hint: Provide a 3-word answer. You get 0 points for providing definitions of each model)
Software life cycle
c. (1 pt) Define data abstraction. Hiding implementation details of data
d. (8 pts) Given the following problem description, produce an object-oriented solution and answer the
questions below.
Design a software system for a bookstore that keeps an inventory of two types of books: traditional
books and books on CD. Books on CD may also contain music. The bookstore purchases books
from publishers and sets a price for each book. Customers can purchase books from the bookstore,
using either cash or a credit card. The bookstore keeps track of which books it has its inventory, and
the books purchased by each customer.
i.
What are the objects in your object-oriented solution?
Store, Book, NormalBook, CDBook, Customer (NormalBook is optional)
ii. What are the interactions between objects in your object-oriented solution?
BookstorePurchaseBook(FromPublisher), SetPrice, CustomerPurchaseBook(FromBookstore)
iii. Which objects “have” other objects? (Also list target object)
Store has Book, Store has Customer, (Customer has Book is optional)
iv. Which objects “use” other objects? (Also list target object)
Customer uses Book (is optional if Customer has book)
v. Which objects “are” other objects? (Also list target object)
NormalBook is Book, CDBook is Book (NormalBook is optional)
e. (4 pts) Given the following Java code, draw its UML class diagram.
public class Button {
RemoteControl
public String operation;
controlButton : Button[ ]
public double frequency;
*
}
dvd : DVD
public class DVD {
allOnButton : AllOnButton
public void onOff() { // … }
activateButton( String, String ) : void
public void play() { // … }
}
public class AllOnButton extends Button {
1
1
public int currentValue;
DVD
}
public class RemoteControl {
public Button[ ] controlButtons;
onOff( ) : void
public DVD dvd;
play( ) : void
public AllOnButton allOnButton;
public void activateButtonOn(String operation, String deviceName) { //... }
}
2
Button
operation : String
frequency : double
AllOnButton
currentValue : int
Problem 2 (7 pts) Algorithm Complexity
a. (3 pts) Calculate the asymptotic complexity of the code snippets below (using big-O notation) with
respect to the problem size n.
i.
for (int i=0; i<n/2; i++) {
f(n) = O(
n
)
for (int k=0; k<20; k++) {
for (int j=0; j<30; j++) {
// ...
}
}
}
ii. for (int i=n/2; i<=n; i++) {
f(n) = O( n log(n) log(n) )
for (int j=1; j<=n; j=j*2) {
for (int k=1; k<=n; k=k*2) {
// ...
}
}
}
iii. for (int i=1; i<=100; i++) {
f(n) = O(
1
)
// ...
}
b. (2 pts) List the following big-O expressions in order of asymptotic complexity (with the lowest
complexity first)
O(nlog(n))
O(1)
O(log(n))
O(2^n)
O(n)
O(1), O(log(n)), O(n), O(nlog(n)), O(2^n)
c. (2 pts) How can asymptotic complexity be analyzed for recursive algorithms?
Using recurrence relations
Problem 3 (8 pts) Data Structures and Recursion
a. (1 pt) Elements in a map have exactly 1 successor.
T or F
b. (1 pt) A base case is optional for some recursive problems.
T or F
c. (6 pts) Given the following Java class definition for a binary tree, write a recursive method named
numLeafNodes that determines the number of leaf nodes in the binary tree. Remember that
leaf nodes are nodes with no children. Assume “left” and “right” have the value “null” if no
subtree is present. You may use helper functions.
Class Node {
Object myValue;
Node left;
Node right; }
Class Tree {
Node root;
// root node in tree
int numLeafNodes( ) {
// return number of leaf nodes in tree
return countLeaf( root );
}
int countLeaf(Node n) {
if (n == null) return 0;
int L = countLeaf(n.left);
int R = countLeaf(n.right);
if (n.left == null) && (n.right == null)) return 1;
return L+R; }
3
Problem 4 (13 pts) Graph Algorithms
a.
b.
c.
d.
(1 pt) Every cycle is a path.
(1 pt) Every graph has a unique minimum spanning tree.
(1 pt) You can implement a Depth First Traversal using a Queue.
(10 pts) Consider the following graph.
T or F
T or F
T or F
10
10
4
S
B
D
2
2
1
3
A
6
C
6
E
8
7
i.
(2 pts) List the set of nodes visited (in the order first visited) while performing a Depth First
Search starting at B.
B,A,C,E,D or B,C,E,D,A or B,D,A,C,E or B,D,C,E,A or BCEAD
(C,E,D always immediately after A unless already visited,
E,D always after C unless already visited)
ii. (2 pts) List the set of nodes visited (in the order first visited) while performing a Breadth
First Search starting at B.
B,A,C,D,E or B,A,D,C,E or B,C,A,D,E or B,C,D,A,E
(E is always last)
iii. (2 pts) List the first edge rejected by Kruskal’s minimal spanning tree algorithm (you can
treat all edges as undirected edges for this problem)
(A,C) or (D,E)
iv. (4 pts) Show the entries in the following table after adding the first 3 nodes (S & 2 other
nodes) when applying Djikstra’s single source shortest path algorithm starting at S.
S
LowestCost
0
Predecessor none
A
B
C
D
E
2
10
8
10
16
S
S
A
S
C
4
Problem 5 (9 pts) Compression and Huffman Codes
a. (1 pt) The compression factor associated with the Huffman encoding
is affected by how 0’s and 1’s are assigned to a Huffman tree.
b. (4 pts) Consider the following Huffman tree.
H
T
0
1
M
K
Z
0
0
1
1
0
1
i. (2 pts) Decode the sequence “1001000”
ii. (2 pts) Encode the string “MTZ”
KMH
0100111
c. (4 pts) Create a Huffman tree for the following nodes
A
B
B
C
D
C
A
D
5
T or F
Problem 6 (16 pts) Multithreading and Synchronization
a.
b.
c.
d.
(1 pt) Excessive use of synchronization mechanisms can reduce performance.
T or F
(1 pt) A Java object can be assigned two locks.
T or F
(1 pt) A program with data races will produce different results each time it is run.
T or F
(9 pts) Given the following diagram of states a thread can assume, draw all possible transitions
between states, and list one possible cause for each transition.
notify, notifyAll,
IO complete, sleep
expired,
join complete
runnable
start
yield,
time
slice
scheduler
new
running
blocked
IO, sleep,
wait, join
terminate
dead
e. (4 pts) Consider the following code for a multithreaded Cashier class:
public class Cashier {
private static MyQueue clientQueue = new MyQueue( ); // same Queue for all cashiers
…
public void doWork() { // work on register, then work with client if one is in the Queue
int queueLength;
workOnRegister( );
// do some work without client
queueLength = clientQueue.size();
if (queueLength > 0) {
Object client = clientQueue.dequeue();
workWithClient( client );
}
}
}
6
// do some work with client
i.
(1 pts) Why are data races possible if two Cashier objects invoke doWork( )
simultaneously?
Because they access the same shared clientQueue object
ii. (3 pts) Change the doWork() method so that multiple Cashier objects can safely invoke the
doWork( ) method simultaneously. Maximize the amount of parallelism exploited by
ensuring multiple Cashiers can invoke workOnRegister( ) and workWithClient( )
simultaneously.
public void doWork() { // work on register, then work with client if one is in the Queue
int queueLength;
// your code here…
workOnRegister( );
// do some work without client
Object client = null;
synchronize(clientQueue) {
queueLength = clientQueue.size();
if (queueLength > 0) {
client = clientQueue.dequeue();
}
}
if (client != null)
workWithClient( client );
// do some work with client
}
Problem 7 (9 pts) Advanced Tree Data Structures
a. (2 pt) What is the property that an AVL tree must maintain so that the tree is balanced?
The height of left and right subtrees differ by at most 1
b. (1 pt) In a Red-black tree no leaf is twice as far from root as another leaf.
T or F
c. (2 pt) Consider the following binary search tree and then draw the tree that will result from
doing a single right rotation around node 7.
5
7
5
2
7
2
8
6
6
8
d. (2 pts) Draw the 2-3 tree that will result from inserting the value 4 in the following tree.
8 28
4
15
33 43
7
e. (2 pts) Draw a standard trie to represent the strings in the set {boy, bat, bad}
b
a
d
o
t
y
Problem 8 (7 pts) Java Language Features
a. (2 pt) What is a shallow copy?
A copy of an object with the same value in each field
b. (1 pt) The default clone method creates a shallow copy of the object.
T or F
c. (2pt) What is a checked exception?
Errors typical program should handle, used for operations prone to error
d. (2 pts) Given the following Java code fragment using java.util.regex:
Pattern p = Pattern.compile(“[a-z]+”);
Matcher m = p.matcher(“12abc ab12c”);
while (m.find()) { System.out.print(m.group() + “\n”); }
What will be printed out when the code is executed? abc ab c (each on new line)
Problem 9 (8 pts) Sorting, & Algorithm Strategies
a. (1 pt) What is the worst case complexity of sorting using quicksort?
O(n2)
b. (2 pt) What can cause worst case behavior for quicksort?
Picking min or max value in list for pivot (e.g., sorted list if always picking 1st element as pivot)
c. (1 pt) What is the average case complexity of sorting using bucket sort?
d. (2 pt) Why may we want to use a stable sort?
O(n)
Sorting each component in a radix sort
e. (1 pt) Which algorithm strategy allows us to efficiently compute the minimal spanning tree of a
graph?
Greedy
f.
(1 pt) Which algorithm strategy allows us to efficiently compute the shortest path between two
nodes in a graph?
Dynamic programming (+greedy optional, greedy alone is incorrect)
8
Problem 10 (8 pts) Design Patterns
a. (2 pt) Why do programmers use design patterns?
Benefit from design of experienced programmers
b. (4 pts) Based on the information provided by the following interface and classes implement a
class called ComputerDecorator which implements the decorator design pattern.
public interface Computer {
public int cost();
}
public class Laptop implements Computer { public int cost() { return 500; } }
/* Class using the decorator you are expected to write */
public class withDVDUnit extends ComputerDecorator {
public int cost() {return c.cost() + 100; }
}
public class ComputerDecorator implements Computer {
private Computer c;
public ComputerDecorator( Computer c ) { this.c = c; }
public int cost( ) { return c.cost( ); }
}
c. (2 pt) Use the withDVDUnit decorator to create a Laptop computer with DVDUnit that costs
600.
Computer myDVDLaptop = new withDVDUnit ( new Laptop( ) ) ;
Problems for Honors Section (8 pts)
a. (2 pts) What is Catch or Declare?
Java compiler requires: catch and handle exception in method, OR declare method can throw
exception, force calling function to catch or declare exception in turn
b. (2 pts) Explain how multithreaded Java code can improve performance even for a computer with
a single processor
Perform useful work in other threads when thread is waiting (e.g., for disk, network)
c. (2 pts) Given the following Java code fragment using java.util.regex:
Pattern p = Pattern.compile(“[a-z][0-9]+”);
Matcher m = p.matcher(“12abc ab12c”);
while (m.find()) { System.out.print(m.group() + “\n”); }
What will be printed out when the code is executed? 12c
d. (2 pts) Why is it difficult to make a deep copy of a graph?
Nodes in a graph can have references to any other node in a graph, will need to make copies of nodes
and make sure nodes in copy refer to other copied nodes rather than the original nodes
9