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Exam 2
EE 322C - University of Texas at Austin - Summer 2009
Name ____________________________________
Test taking instructions. No calculators, laptops or other assisting devices are allowed. Write your
answers on these sheets. Wherever code is required, write JAVA statements in the blank areas
provided, or by modifying the given code in place. You are not required to follow the coding style
guidelines when writing code on the exam, but be as neat as possible. If you are unsure of the meaning
of a specific test question, then write down your assumptions and proceed to answer the question on
that basis. If you see a typo or syntax error, fix it, circle it, and if you are right you will get a bonus
point for each one fixed. In your programming solutions on this test you may use any of the
classes/methods that you know from the library, or collections.
Questions about the exam questions will not be answered during the test.
For the binary tree related questions on this exam you may assume that this generic class has been
defined for your use and is included. When the term Btnode is used on the exam it is referring to
this generic class.
class Btnode<T>
{
/* this generic class models a node of a binary tree */
/* here are the private data members of the binary tree node */
private T element;
private Btnode<T> left;
private Btnode<T> right;
/* the constructor given an Object,left child,and right child. */
Btnode(T theElement, Btnode<T> lt, Btnode<T> rt )
{
element = theElement;
left
= lt;
right
= rt;
}
/* here are the public get/set methods for the data members */
public T getElement( ){ return element;}
public Btnode<T> getLeft( ) {return left;}
public Btnode<T> getRight( ){return right;}
public void setElement( T x ){element = x;}
public void setLeft( Btnode<T> t ) {left = t;}
public void setRight( Btnode<T> t ){right = t;}
}
Page 2
Question 0 - Terminology. [19 pts.] Answer each of the following questions; choose
the best answer from the numbered list below. Answers can be reused.
A. ____A binary operation which takes two given sets and yields a set made up of all the items that are in
either set or both sets (without duplicates)
B. ____A collection of key-value pairs that associate a key with a value.
C. ____A hierarchical structure that place elements in nodes along branches that originate from a root.
D. ____A tree structure in which each node can have at most two children, and in which a unique path
exists from the root to every other node.
E. ____A type of tree in which the key value of each node is less than every key value in its right subtree,
and greater than every key value in its left subtree.
F. ____ A type of binary tree in which the height of each node’s subtrees differs by no more than one.
G. ____A graph in which each edge is directed from one vertex to another (or the same) vertex
H. ____A graph in which every vertex is directly connected to every other vertex
I. ____A graph in which each edge carries a value
J. ____A sequential structure that is divided into table elements. The address of an identifier X in the
structure is gotten by computing some arithmetic function
K. ____This occurs when 2 different identifiers are hashed into the same location
L. ____ A method for finding the shortest path from one vertex to another in a weighted digraph
M. ____ A type of Java program that runs inside of a web browser
N. ____ A document layout language for web pages
O. ____ The method that is called every time the surface of an applet window is redrawn
P. ____ A signal to the program that something has happened in the user interface
Q. ____ The method that is called when a printable character is pressed and released
R. ____ The type of object that event notifications are sent to
S. ____ a systematic approach to implementing a trial and error strategy in the search for a solution to a
problem
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
2-3-4 tree
applet
AVL tree
backtracking
binary tree
binary search tree
black box testing
breadth first search
collision
complete
depth
depth first search
Dijkstra’s algorithm
digraph
event
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
functional
full
graph
hash table
heap
HTML
Infix
keyTyped
leaf
listener
map
matrix
overflow
paint
partially filled array
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
Prim’s algorithm
queue
RGB
root
set
set difference
set intersection
set union
stack
synchronization
ttree
42) weighted graph
43) White box
Page 3
Question 1 - Multiple Choice. [2 pts. each - 12 pts total] For each of the following
subparts, circle the best or all correct answers as indicated.
A. Which of the following sorting algorithms have a worst case performance that is better than O(n*n)?
i) selectionsort
ii) bubblesort
iii) insertionsort
iv) mergesort
v) heapsort
vi) quicksort
vii) radix (bin) sort
B. Which tree below corresponds to the vector v created by the code below?
int arr[ 8 ] = {3, 12, 15, 4, 67, 6, 55, 9};
Vector <Integer> v = new Vector <Integer> (8);
for (int i=0; i< 8; i++) { v.addElement(arr[i]); }
(i)
(ii)
12
3
15
3
67
4
6
12
15
55
9
67
4
6
55
9
(iv)
(iii)
3
3
15
12
67
4
6
15
12
55
9
4
67
6
55
9
C. Which of the following are true of sets?
i. A set with no elements in it is called an empty set
ii. Each element (ie, value) in a set is distinct
iii. The universal set is that which contains all the values of the base type
iv. The cardinality of a set denotes the number of elements in a set
v. New sets can be created by the union, intersection and difference operations
vi. The elements of a set are not ordered
D. Binary search is an ______ search algorithm for the average case.
(i) O(log2n)
(ii) O(n2)
(iii) O(n)
(iv) O(1)
Page 4
E. What is the value of the postfix expression
i)
ii)
iii)
iv)
v)
6245 + * +
10
24
25
33
none of the above
F. Given three arrays with L, M and N elements respectively, estimate the running time for the
following algorithm in terms of the number of times that the pairwise comparison step is executed:
repeat the following for i from 1 to L for array1
repeat the following for j from 1 to M for array2
repeat the following for k from 1 to N for array3
pairwise compare array1[i], array2 [j] and array3 [k] and based on the result do one the following
case 1: if array1[i] and array2 [j] are equal then { do something 1}
case 2: if array1[i] and array3 [k] are equal then { do something 2}
case 3: if array3[k] and array2 [j] are equal then { do something 3}
end repeat
end repeat
end repeat
i.
ii.
iii.
iv.
O ( log 2 (L+M+N) )
O(N3)
O(L*M*N)
None of the above
Question 2. Evaluation. (2 points each = 6 pts. total) For each of the following code segments,
write in the value of the variable x after the Java statements are executed. You may assume that the
proper import statements have already appeared.
A. ______________
Vector <Integer> alist = new Vector <Integer> (3,2);
alist.add (40);
alist.add (10);
alist.add (20);
alist.add (8);
int x = alist.get(0 ) * alist.get( 2) + alist.size( ) * alist.capacity( ) ;
B. ______________
Stack <Integer> intStack = new Stack <Integer> ( );
intStack.push (5);
intStack.push (6);
intStack.push (13 + intStack.peek ( ));
int y = intStack.peek ( ) ;
intStack.pop ( ) ;
int x = y + intStack.peek ( ) ;
C. ______________
int array [ ] = {1,2,3,4,5,6,7,8,9, 10};
Queue <Integer> s = new LinkedList <Integer> ( );
for (int i = 0; i < 10; i++) s.add (array [ i ]);
s.remove ( );
int x = s.peek ( ) + array [5];
// hint: from the ADT for queue: add is enqueue, remove is dequeue, peek is front
Page 5
Question 3. Handling exceptions [8 Points] Modify the following code to make it “bullet proof” (it
will not fail in execution). You may ask the user to re-input the needed information if needed, so as to
ensure the successful completion of the required computation in the try block.
import java.io.*;
public class Demo
{ public static void main(String args[ ])
{
Scanner input = new Scanner (System.in);
int a, n;
String s;
System.out.println ("Enter a quantity: ");
try // block of code to be monitored for exceptions
{
s = input.next( );
n = Integer.parseInt (s);
a = 356 / n;
}
catch (ArithmeticException e1) //catch arithmetic run time errors
{ System.out.println (“divide by zero attempted”);
}
catch (NumberFormatException e2)
{ //catch invalid conversions of a string to a numeric format
System.out.println (“invalid number in string”);
}
catch (IOException e3) //catch a bad input
{ System.out.println (“invalid input attempt by user”);
}
finally
{
}
System.out.println (“successfully completed with values ” + s + “ “ + n + “ “ + a);
}
}
Page 6
4. Tree questions (11 pts)
A. (2 pts) Draw the tree created by the following statements. Btnode is defined on page 1.
Btnode<Integer> root, a, b, c, d;
d = new Btnode<Integer> (6, NULL, NULL);
c = new Btnode<Integer> (9, d, NULL);
b = new Btnode<Integer> (4, NULL, c);
a = new Btnode<Integer> (12, NULL, NULL);
root = new Btnode<Integer> (10, a, b);
B. (4 pts) Trace the method count() below and describe what it does
public static <T> int count (Btnode<T> t)
{ int ctLeft, ctRight, ct;
if (t == NULL)
ct = 0;
else
{ ctLeft = count(t.getLeft());
ctRight= count(t.getRight());
boolean flag = (t.getLeft()!= NULL && t.getRight()!= NULL);
ct = ctLeft + ctRight;
if (flag) ct++;
}
return ct;
}
C. (5 pts) Consider the following binary search tree. Use the original tree below when answering each subpart (a)
through (e).
50
25
20
15
35
70
90
23
30
5
80
18
45
65
100
75
68
95
150
(a) If the value 46 is inserted into this tree, which node becomes its parent? __________________
(b) If the value 64 is inserted into this tree, which node becomes its parent? ___________________
(c) If we delete node 65, which node should be its replacement node?
___________________
(d) If we delete node 90, which node should be its replacement node?
__________________
(e) If we delete the root node 50, which node should be selected as its replacement node so that the fewest number
of changes are made to the tree? ______________________
Page 7
5. Heaps and Graphs (19 pts)
A. (3 pts) A heap can be represented by a vector. Start with the following maximum heap and list the elements after each
operation. Execute the operations sequentially, using the result of the previous operation. The initial vector values
for the heap are {50, 35, 15, 12, 3, 5}.
50
15
35
12
3
5
(a) Insert 23: The vector values are now {____________________________}.
(b) Delete (pop) an element from the heap: The vector values are now {__________________}.
B. (3 pts) Start with following tree and "heapify" it to create a maximum heap. Draw the resulting tree.
25
33
35
18
3
22
1
55
29
98
C. (3 pts) Start with following tree and heapify it to create a minimum heap. Draw the resulting tree.
75
30
55
15
40
20
90
45
35
10
Page 8
D. (3 pts) Show the minimum cost path from node B to node E in the following digraph G.
A
1
B
2
5
2
C
3
D
7
1
E
1
E..(3 pts) Draw the node list and adjacency matrix representation for the following digraph G.
A
1
B
2
5
2
C
3
D
7
1
E
1
F (4 pts) Draw the minimal spanning tree for the following graph G.
Minimum spanning tree
Network of Hubs
1
A
BA
50
2
5
A
25
2
46
B
C
25
3 23
DC
25
7
67
F
35
55
E
32
C
25
1
D
46
B
E
23
D
35
F
55
G
E
G
32
98
H
H
Minimum amount of cable = 241
Page 9
6. Hash Tables (6 pts) The following hash table is used to store integer values. Assume that we
use the following hashing function to store values in the table.
h(x) = x % tableSize (tableSize is equal to the size of the hash table below - which is 20)
Show the resultant hash table after inserting the values: 12, 11, 2, 5, 7, 10, 21, 121, 23, 33, 71, 90, 52 in
that order. Use the linear probing technique for collision resolution. That is, if the initial hash location
yields a collision then probe forward until an empty slot can be found. The table is used in a circular
manner for that purpose.
Index
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Value
Page 10
7. Maps (6 points)
Complete the program below whose purpose is to count and record the number of occurrences of each
character found in a given text file (“in.txt”). You are to use the hash map m to store the number of
occurrences of each character. You can use the default hashcode method for Character. After all
characters in the file are processed, output a table to the screen that contains 2 columns with each
character in column 1 and its total number of occurrences in column 2. Note: all legal characters are to
be counted. Tip: read() returns a -1 if EOF is encountered.
import java.io.*;
public class CountingChars
{ public static void main(String[ ] args) throws IOException
{
Map <Character, Integer> m = new HashMap <Character, Integer> ( );
FileReader infile = new FileReader("in.txt");
BufferedReader in = new BufferedReader(infile);
// process all the characters in the file, one at a time
char c = (char) in.read( ); // read the first char from the file
while (
)
{
c = (char) in.read(); // read the next char in the file
}
// output the table of (char, count) pairs
}
}
Page 11
Question 8 [13 points total]. There are 2 parts to this question in which you are to design a system
using a new data type to support Big Integer Arithmetic for the following application.
Problem:
In the year 2050, in order to build the new version of Intergalactic Mapquest, you will need to keep
track of large mileage values between interplanetary objects. For example, you will need to record
that it is 3,647,200,000 miles from the center of our solar system to Pluto, and that it is
4,692,556,800,000,000 miles from our solar system to the Orion system. You will need to be able to
add and subtract these large mileage values so that we can plan a starship travel route and compute
the amount of fuel that will be needed. Unfortunately, in order to be backwards compatible with
previous versions of the Mapquest product suite you will still be using the Java language for
development; which sadly still uses a 32 bit representation for its int data type. So, you will need to
design a BigInt data type for your purposes.
As seen in the figure below, you will represent a BigInt value by a list of nodes with int data values
in each node. Each node stores a block of up to 3 consecutive digits. You will need to keep
references to the beginning and end of the list as well. You will only need to represent positive
BigInt values. For example, the number 9,145,632,884 would have the following BigInt
representation.
9
first
145
632
884
last
Operations: You will need operations for inputting and outputting a BigInt, as well as, operations for
adding and subtracting a pair of BigInts.
1. Input is done in blocks of 3 digit ints, left to right, separated by spaces. As each new block is
entered, a node is added to the end of the list. The first block may have less than 3 digits.
2. Output is done by a forward traversal of the list, from left to right, separating each 3-digit block
by a comma.
3. Addition adds the associated groupings of two given BigInts from right to left, handling any
carry digits from group to group as needed, and creates a new BigInt as the result.
4. Subtraction is only legal when taking a smaller BigInt value from a larger BigInt value – that is,
no negative answers are allowed. In the legal case, subtraction processes the groupings from
right to left, handling any borrowing that is required from group to group as needed, and creates
a new BigInt as a result.
Page 12
A. [7 pts] Draw a UML class diagram for the new Intergalatic Mapquest system which uses the BigInt
ADT. You must also include the class for representing a BigInt node, which will be contained inside
the BigInt class.
B. [6 points] As part of your design you will need to select and justify any underlying data structures
needed to implement the BigInt ADT. You should choose the most appropriate collection from the
Collections framework classes to represent a BigInt. Write your justification (why you selected the
implementation data structure) in terms of the suitability to support the necessary operations, and any
performance considerations. Describe your choices and justification here.