Description
Question 1.
(a) Construct the BST that results when the following integers are inserted in the order given:
50, 20, 40, 55, 45, 30 10, 15, 35, 60, 5, 25
(b) Perform preorder, inorder, and postorder traversals of the BST above.
(c) Construct the BST that results when the following integers are deleted from the BST in
the order given:
60, 30, 20
(d) Perform preorder, inorder, and postorder traversals of the BST in item (c) above.
Question 2.
For each of the following questions start with the AVL tree shown below.
Show the AVL tree that results from performing the following
operations.
To be clear, in addition to preserving the BST property,
you will need to preserve the AVL property of the tree by
rebalancing it after each insertion and each deletion operation.
(a) Add 75 and then 65
(b) Add 75, 23, and then 32
(c) remove 15 and then 35
(d) remove 25 and then 30
20
15
10
35
25
30
55
70
Question 3.
Sort the following list of numbers by hand.
13, 11, 4, 40, 7, 34, 25, 17, 50, 17, 14
For each item (a), (b), and (c) below, show the list’s contents each time it’s elements are
rearranged as well as showing all the steps you followed according to each sorting algorithm.
(a) insersion sort
(b) selection sort
(c) heapsort
(d) mergesort
Use Bottom-Up (Nonrecursive) Merge-Sort (Page 543) to sort the list in place. Here
is an example of in place mergesort animation: Merge sort
To facilitate grading, your work should be
arranged to look like Figure 12.1.b on page
533 but upside down and with boxes replaced by square brackets, as shown at
right.
[85][24][63][45][17][31][96][50]
[24 85][45 63][17 31][50 96]
[24 45 63 85][17 31 50 96]
[17 24 31 45 50 63 85 96]
(e) quicksort Select the pivot to be the last
element in in the list.
To facilitate grading, your work should be
arranged to look like Figure 12.14 Page 554
using square brackets and text instead of
boxes and arrows, as shown at right.
Apply the same process to the left partition
and then to the right partition.
Requirements
pivot = 50 at index 7
[85 24 63 45 17 31 96 50]
pivot = 50, L=0, R=6, swap
[31 24 63 45 17 85 96 50]
pivot = 50, L=1, R=4, no swap
[31 24 63 45 17 85 96 50]
pivot = 50, L=2, R=4, swap
[31 24 17 45 63 85 96 50]
pivot = 50, L=3, R=3, no swap
[31 24 17 45 63 85 96 50]
pivot = 50, L=4, R=3, exit loop
[31 24 17 45 63 85 96 50]
Swap pivot=50 and 63 at L=4
[31 24 17 45] [63] [85 96 50]
1. Each of methods above must sort the list in place, using no other auxiliary arrays,
lists, etc.
2. In each case count the number of assignments and comparisons.
Assignment 4, COMP 352 page 2 of 9
Question 4.
Consider the graph shown below:
1
2
3
4
5
6 0
7 8 9
1. Give the adjacency matrix representing this graph.
2. Give the adjacency lists representing this graph.
3. Show the breadth-first search trees for the graph starting at node 0.
4. Show the depth-first search trees for the the graph starting at node 0.
Assignment 4, COMP 352 page 3 of 9
Question 5.
Consider the graph shown below:
A
B
D H
C
F
E
G
4
6
2
1
3
1
1
5
1 1
2
3
1
2
1
1. Applying Kruskal’s algorithm, find a minimal spanning tree for the graph.
Use a table that includes column headers shown below (and possibly other columns
of your choice) to show the progress of the algorithm at each step.
Step Edge Considered Cost Accepted/Rejected
2. Applying Prim’s algorithm, find a minimal spanning tree for the graph.
Use a table that includes the following columns (and possibly other columns of your
choice) to show the progress of the algorithm at each step.
Vertex Visited? Cost Predecessor
Assignment 4, COMP 352 page 4 of 9
Question 6.
Consider the graph shown below.
A
C
D
B
F E
G
H
I
J
22
14
20
10
7
40
31
5 7
11
12
42
17
9
(a) Find depth-first and breadth-first topological orderings for the graph.
(b) Applying Dijkstra’s algorithm, find the shortest distance from node A to every other
node in the graph.
Use a table that includes the following columns (and possibly other columns of your
choice) to show the progress of the algorithm at each step.
Vertex Visited? Cost Predecessor
Assignment 4, COMP 352 page 5 of 9
Programming Questions (50 marks)
In this assignment you will implement a map using a hash table, handling collisions via separate
chaining and exploring the map’s performance using hash table load factors. (The ratio λ = n/N
is called the load factor of the hash table, where N is the hash table capacity, and n is the number
of elements stored in it.)
Class Entry
Write a class Entry to represent <Key, Value> entry pairs in the hash map. This will be a
non-generic implementation. Specifically, Key is of type integer, while Value can be any type of
your choice. Your class must include the following methods:
A constructor that generates a new Entry object using a random integer (key). The
value component of the <Key, Value> pair may be supplied as a parameter or it may be
generated randomly, depending on you choice of the Value type.
An override for class Object’s compression function public int hashCode(), using any of
the strategies covered in section 10.2.1 (Hash Functions, page 411).
Abstract Class AbsHashMap
This abstract class models a hash table without providing any concrete representation of the
underlying data structure of a table of “buckets.” (See pages 410 and 417.)
The class must include a constructor that accepts the initial capacity for the hash table as a
parameter, and uses the function h(k) = k mod N as the hash (compression) function.
The class must include the following abstract methods
size() Returns the number of entries in the map
isEmpty() Returns a Boolean indicating whether the map is empty
get(k) Returns the value v associated with key k, if such an entry exists; otherwise return
null.
Put(k,v) if the map does not have an entry with key k, then adds entry (k,v) to it and
returns null; else replaces with v the existing value of the entry with key equal to k
and returns the old value.
remove(k) Removes from the map the entry with key equal to k, and returns its value; if the
map has no such entry, then it returns null.
Assignment 4, COMP 352 page 6 of 9
Class MyHashMap
Write a concrete class named MyHashMap that implements AbsHashMap. The class must
use separate chaining to resolve key collisions. You may use Java’s ArrayList as the buckets to
store the entries.
For the purpose of output presentation in this assignment, equip the class to print the following
information each time the method put(k,v) is invoked:
the size of the table,
the number of elements in the table after the method has finished processing (k,v) entry,
the number of keys that resulted in a collision
the number of items in the bucket storing v
Additionally,
each invocation of get(k), put(k,v), and remove(k) should print the time used to run
the method. If any put(k,v) takes an excessive amount of time, handle this with a suitable
exception.
Class HashMapDriver
This class should include the following static void methods:
1. void validate() must perform the following:
(a) Create a local Java.util ArrayList (say, data) of 50 random <Key, Value> pairs.
(b) Create a MyHashMap object using 100 as the initial capacity (N) of the hash map.
Heads-up: you should never use a non-prime hash table size
in practice, but do this for the purposes of this experiment.
(c) Add all 50 entries from the data array to the map, using the put(k,v) method, of
course.
(d) Run get(k) on each of the 50 elements in data.
(e) Run remove(k) on the first 25 keys, followed by get(k) on each of the 50 keys.
(f) Ensure that your hash map functions correctly.
Assignment 4, COMP 352 page 7 of 9
2. void experiment interpret() must perform the following:
(a) Create a hash map of initial capacity 100
(b) Create a local Java.util ArrayList (say, data) of 150 random <Key, Value> pairs.
(c) For n ∈ {25, 50, 75, 100, 125, 150}
Describe (by inspection or graphing) how the time to run put(k,v) increases as
the load factor of the hash table increases, and provide reason to justify your
observation.
If your put(k,v) method takes an excessive amount of time, describe why this is
happening and why it happens at the value it happens at.
Note
Feel free to include other methods of your own and choice if you feel they would facilitate
your tasks in this assignment. Justify inclusion of such methods.
Deliverables
A written specification of each of the classes you implemented, providing any information
about design decisions.
A written report with the trial run of validate(), and answers to questions in item (c) of
experiment interpret().
Well-formatted and documented Java source code
Assignment 4, COMP 352 page 8 of 9
Answers to Theory Questions
For all questions, including the programming questions, the parts that require written answers,
pseudo-code, graphs, etc., you can express your answers into any number of files of any format,
including image files, plain text, hand-writing, Word, Excel, PowerPoint, etc.
However, no matter what program you are using, you must convert each and every file into a
PDF before submitting. This is to ensure the markers and you have exact same view of your
work regardless of the original file formats.
Whether or not you are in a team, you must each submit a copy of your written answers.
Solutions to Programming Question
Developing your programming work using a Java IDE such as NetBeans, Eclipse, etc., you are
required to submit the project folder(s) created by your Java IDE, together with any input files
used and output files produced by your program(s).
If you are in a team, you must to submit only ONE copy of your program project folders(s) and
input/output files.
What and How to Submit
1. Letting the # character denote the assignment number, create a folder as follows:
(a) If your working individually, name your folder A# studentID, where studentID denotes your student ID. Then, copy the PDF files you prepared for the theory questions
together with your project folder(s) and input/output files to the A# studentID folder.
(b) If you are working in a team, name your folder A# studentID1 studentID2, where
studentID1 denotes the ID number of the student who is responsible for submitting
the programming solutions for both of you, and studentID2 denotes the ID number
of the other team member. Then, the student whose ID number is studentID1 must
follow item (a), as if she/he completed the programming question individually. The
other team member must also follow item (a) above, but she/he must NOT include
the team’s programming solutions.
2. Compress the folder you created in (1) into a zip file with the same name as that of the
folder being compressed.
3. Upload the compressed file you created in item (2) to Moodle.
1.1 Last but not Least
To receive credit for your programming solutions, you must demo your program to your
marker, who will schedule the date and time for the demo for you (please refer to the course
outline for full details). If working in a team, both members of the team must be present
during the demo. Please notice that failing to demo your programming solution will result
in zero mark regardless of your submission.
