User_42751212015Module1and2pagestocompetework.pdf User_42751212015Module1and2pagestocompetework_1.pdf User_42751212015Module2Homework(CIS330).docx [INSERT TITLE HERE] 1 Running head: [INSERT TITLE HERE] [INSERT TITLE HERE] Student Name Allied American University Author Note This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME]. Directions: Please complete each of the following exercises. Please read the instructions carefully. For all “short programming assignments,” include source code files in your submission. 1. Short programming assignment. Combine the malloc2D function of program 3.16 with the adjacency matrix code of program 3.18 to write a program that allows the user to first enter the count of vertices, and then enter the graph edges. The program should then output the graph with lines of the form: There is an edge between 0 and 3. 2. Short programming assignment. Modify your program for question 2.1 so that after the adjacency matrix is created, it is then converted to an adjacency list, and the output is generated from the list. 3. Short programming assignment. Modify program 4.7 from the text, overloading the == operator to work for this ADT using a friend function. 4. Is the ADT given in program 4.7 a first-class ADT? Explain your answer. 5. Suppose you are given the source code for a C++ class, and asked if the class shown is an ADT. On what factors would your decision be based? 6. How does using strings instead of simple types like integers alter the O-notation of operations? User_42751212015Module1Homework(CIS330)Corrected (1).docx [INSERT TITLE HERE] 1 Running head: [INSERT TITLE HERE] [INSERT TITLE HERE] Student Name Allied American University Author Note This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME]. Directions: Please refer to your textbook to complete the following exercises.1. Refer to page 12 of your text to respond to the following:Show the contents of the id array after each union operation when you use the quick find algorithm (Program I.I) to solve the connectivity problem for the sequence 0-2, 1-4, 2-5, 3-6, 0-4, 6-0, and 1-3. Also give the number of times the program accesses the id array for each input pair.2. Refer to page 12 of your text to respond to the following:Show the contents of the id array after each union operation when you use the quick union algorithm (Program I.I) to solve the connectivity problem for the sequence 0-2, 1-4, 2-5, 3-6, 0-4, 6-0, and 1-3. Also give the number of times the program accesses the id array for each input pair.3. Refer to figures 1.7 and 1.8 on pages 16 and 17 of the text. Give the contents of the id array after each union operation for the weighted quick union algorithm running on the examples corresponding to figures 1.7 and 1.84. For what value is N is 10N lg N>2N2 ...

1. User_42751212015Module1and2pagestocompetework.pdf
User_42751212015Module1and2pagestocompetework_1.pdf
User_42751212015Module2Homework(CIS330).docx
[INSERT TITLE HERE] 1
Running head: [INSERT TITLE HERE]

2. [INSERT TITLE HERE]
Student Name
Allied American University
Author Note
This paper was prepared for [INSERT COURSE NAME],
[INSERT COURSE ASSIGNMENT] taught by [INSERT
INSTRUCTOR’S NAME].
Directions: Please complete each of the following exercises.
Please read the instructions carefully.
For all “short programming assignments,” include source code
files in your submission.
1. Short programming assignment. Combine the malloc2D
function of program 3.16 with the adjacency matrix code of
program 3.18 to write a program that allows the user to first
enter the count of vertices, and then enter the graph edges. The
program should then output the graph with lines of the form:
There is an edge between 0 and 3.

3. 2. Short programming assignment. Modify your program for
question 2.1 so that after the adjacency matrix is created, it is
then converted to an adjacency list, and the output is generated
from the list.
3. Short programming assignment. Modify program 4.7 from
the text, overloading the == operator to work for this ADT
using a friend function.
4. Is the ADT given in program 4.7 a first-class ADT?
Explain your answer.
5. Suppose you are given the source code for a C++ class,
and asked if the class shown is an ADT. On what factors would
your decision be based?
6. How does using strings instead of simple types like
integers alter the O-notation of operations?
User_42751212015Module1Homework(CIS330)Corrected
(1).docx
[INSERT TITLE HERE] 1
Running head: [INSERT TITLE HERE]
[INSERT TITLE HERE]
Student Name
Allied American University

4. Author Note
This paper was prepared for [INSERT COURSE NAME],
[INSERT COURSE ASSIGNMENT] taught by [INSERT
INSTRUCTOR’S NAME].
Directions: Please refer to your textbook to complete the
following exercises.1. Refer to page 12 of your text to respond
to the following:Show the contents of the id array after each
union operation when you use the quick find algorithm
(Program I.I) to solve the connectivity problem for the sequence
0-2, 1-4, 2-5, 3-6, 0-4, 6-0, and 1-3. Also give the number of
times the program accesses the id array for each input pair.2.
Refer to page 12 of your text to respond to the following:Show
the contents of the id array after each union operation when you
use the quick union algorithm (Program I.I) to solve the
connectivity problem for the sequence 0-2, 1-4, 2-5, 3-6, 0-4, 6-
0, and 1-3. Also give the number of times the program accesses
the id array for each input pair.3. Refer to figures 1.7 and 1.8
on pages 16 and 17 of the text. Give the contents of the id array
after each union operation for the weighted quick union
algorithm running on the examples corresponding to figures 1.7
and 1.84. For what value is N is 10N lg N>2N2?
5. Prove that O(1) is the same as O(2)
6. You are given the information that the time complexity of
one problem is N log N and that the time complexity of another
problem is N3. What does this statement imply about the
relative performance of specific algorithms that solve the
problems?

5. User_42751212015Module1Homework(CIS330).docx
1
Running head: [INSERT TITLE HERE]
Introduction to Algorithm Analysis
Candice R. James
Allied American University
Author Note
This paper was prepared for Algorithm Design and
Analysis, Module One Homework, taught by Biswajit Panja.
Directions: Please complete each of the following exercises.
Please read the instructions carefully.
For all “short programming assignments,” include source code
files in your submission.
1. The following questions refer to the connectivity problem.
a. Explain the difference between the quick-find algorithm
and the quick-union algorithm.
Quick find :is an algorithm that places emphasis on finding out
if two nodes are connected or not.

6. We can use a typical array to represent a set of nodes and their
connections to each other.
{1,2,3,4,5};
Indexes of the array are the nodes and the values of the array
are the connections. When the value of one index equals that of
another node’s value, then the two nodes are connected.
Quick Find approach has a very fast method to check
connectivity. To check the connectivity, you just need to access
the array twice. However, union is extremely slow. Since
whenever you do union, you have to go through all the array,
you will end up with O(N) runtime.
The quick find has 3 methods. They are:
constructor: prepares the set as an array
connected: checks if two nodes are connected or not
union: connects two nodes
Quick Union:
Quick union improves greatly in union operation. Instead of
going through entire array during union, you attach one node’s
root to another’s root.
b. How can maintaining the “weight” of each subtree improve
the quick-union algorithm?
During a union operation, the data structure correctly adjusts
the size of the root of the merged trees. Therefore, after any
union operation, all the tree roots have the correct sizes.
While you are correct that during path compression in the find
step that the sizes aren't updated, there is no reason that the data
structure would change sizes here. Path compression just
reduces the length of the paths from nodes in some tree up to
the root of the tree. It doesn't change the number of nodes
stored in that tree. Accordingly, the size information at the root
of the tree undergoing path compression does not need to
change. Although some internal subtrees might lose some
children as they are reparented higher up in the tree, this is
irrelevant because the union/find structure only needs to

7. maintain size information at the roots of its trees, not at internal
nodes.
Overall, this means that the data structure does correctly store
size information. There is no adverse impact on runtime, nor is
there a need to correct anything.
c. What is path compression and why is it useful?
Generally heuristics by rank and path compression are used to
achieve fast disjoint-set data structure operations. Somehow, I
find heuristics by weight and path compression more sensible
2. For each of the following connectivity problem data sets,
explain whether it describes actual, random, or perverse data.
a. The data is the list 0-1, 1-2, 2-3, 3-4, ..., 99-100.
Data in the above set is perverse.
Because list contains values that are floating point numbers.
So we cannot predict the actual value.
b. The data is generated by rolling a hundred-sided die.
Data in the above set is random.
We get a number in range(1-100)
Because every number in the set has same probability to occur.
c. The data is an encoding of links in a country’s railway
system.
Data in the above set is Actual because exact value can be
encoded by using some mechanism or algorithm
3. The following refer to O-notation.
a. Suppose f(n) = n2 + 10n + 5. Explain what is meant when
we say f(n) is O(n2).
Big O notation describes the limiting behavior of a function
when the argument tends towards a particular value or infinity,
usually in terms of simpler functions. It is a member of a larger
family of notations that is called Landau notation, Bachmann–
Landau notation (after Edmund Landau and Paul
Bachmann),[1][2] or asymptotic notation. In computer science,
big O notation is used to classify algorithms[3][4] by how they

8. respond (e.g., in their processing time or working space
requirements) to changes in input size. In analytic number
theory, it is used to estimate the "error committed" while
replacing the asymptotic size, or asymptotic mean size, of an
arithmetical function, by the value, or mean value, it takes at a
large finite argument. A famous example is the problem of
estimating the remainder term in the prime number theorem.
Big O notation characterizes functions according to their growth
rates: different functions with the same growth rate may be
represented using the same O notation. The letter O is used
because the growth rate of a function is also referred to as order
of the function. A description of a function in terms of big O
notation usually only provides an upper bound on the growth
rate of the function. Associated with big O notation are several
related notations, using the symbols o, ?, ?, and ?, to describe
other kinds of bounds on asymptotic growth rates.
b. What is an asymptotic expression?
an asymptotic expansion, asymptotic series or Poincaré
expansion (after Henri Poincaré) is a formal series of functions
which has the property that truncating the series after a finite
number of terms provides an approximation to a given function
as the argument of the function tends towards a particular, often
infinite, point.
The most common type of asymptotic expansion is a power
series in either positive or negative powers. Methods of
generating such expansions include the Euler–Maclaurin
summation formula and integral transforms such as the Laplace
and Mellin transforms. Repeated integration by parts will often
lead to an asymptotic expansion.
Since a convergent Taylor series fits the definition of
asymptotic expansion as well, the phrase "asymptotic series"
usually implies a non-convergent series. Despite non-
convergence, the asymptotic expansion is useful when truncated
to a finite number of terms. Typically, the best approximation is
given when the series is truncated at the smallest term. This

9. way of optimally truncating an asymptotic expansion is known
as superasymptotics.[1] The error is then typically of the form
where ? is the expansion parameter. The error is thus beyond all
orders in the expansion parameter. It is possible to improve on
the superasymptotic error, e.g. by employing resummation
methods such as Borel resummation to the divergent tail. Such
methods are often referred to as hyperasymptotic
approximations
4. Solve the recurrence
CN = CN/2 + N, C1 = 0
when N is a power of 2.
C2 = -2C1 / 3
C_n+3 = [ C_n – (n+2)(n+5)*C_n+2 ] / [ 3(n+2)(n+3) ]
For the first independent solution, let C0 = 0.
For the second, let C1 = 0.
We get
y1 = C0 * [ 1 + 1/18 * x^3 – 1/36 * x^4 + 7/540 * x^5 + … ]
y2 = C1 * [x – 2/3 * x^2 + 10/27 * x^3 – 17/108 * x^4 +
101/1620 * x^5 + …
5. Consider a sales record book with 1000 pages, one for each
customer, in no particular order. Below are algorithms for
looking up a customer’s record in the book. For each algorithm,
describe the best case, the average case, and the worst case.
a. Start from the first page and work towards the back.
best case: the record to be looked up appears in the very first
page of the record book.(eg page 1)
average case: the record to be looked up appears somewhere in
the middle of the record book.(eg between 400-600)
worst case: the record to be looked up appears on the last page
of the record book.(eg 1000th page)
b. Use dice to generate a number from 1 to 1000, look on that
page; repeat as needed.
best case: the record to be looked up is represented by the very

10. first throw of the dice.
average case: the record to be looked up is represented by the
dice after a few throws.
worst case: the record to be looked up is never ever represented
by the dice or represented after several hundred throws.
User_42751212015Module2Homework(CIS330).docx
[INSERT TITLE HERE] 1
Running head: [INSERT TITLE HERE]
[INSERT TITLE HERE]
Student Name
Allied American University
Author Note
This paper was prepared for [INSERT COURSE NAME],
[INSERT COURSE ASSIGNMENT] taught by [INSERT
INSTRUCTOR’S NAME].
Directions: Please complete each of the following exercises.
Please read the instructions carefully.

11. For all “short programming assignments,” include source code
files in your submission.
1. Short programming assignment. Combine the malloc2D
function of program 3.16 with the adjacency matrix code of
program 3.18 to write a program that allows the user to first
enter the count of vertices, and then enter the graph edges. The
program should then output the graph with lines of the form:
There is an edge between 0 and 3.
2. Short programming assignment. Modify your program for
question 2.1 so that after the adjacency matrix is created, it is
then converted to an adjacency list, and the output is generated
from the list.
3. Short programming assignment. Modify program 4.7 from
the text, overloading the == operator to work for this ADT
using a friend function.
4. Is the ADT given in program 4.7 a first-class ADT?
Explain your answer.
5. Suppose you are given the source code for a C++ class,
and asked if the class shown is an ADT. On what factors would
your decision be based?
6. How does using strings instead of simple types like
integers alter the O-notation of operations?
User_42751212015Module1Homework(CIS330)Corrected
(1).docx
[INSERT TITLE HERE] 1
Running head: [INSERT TITLE HERE]

12. [INSERT TITLE HERE]
Student Name
Allied American University
Author Note
This paper was prepared for [INSERT COURSE NAME],
[INSERT COURSE ASSIGNMENT] taught by [INSERT
INSTRUCTOR’S NAME].
Directions: Please refer to your textbook to complete the
following exercises.1. Refer to page 12 of your text to respond
to the following:Show the contents of the id array after each
union operation when you use the quick find algorithm
(Program I.I) to solve the connectivity problem for the sequence
0-2, 1-4, 2-5, 3-6, 0-4, 6-0, and 1-3. Also give the number of
times the program accesses the id array for each input pair.2.
Refer to page 12 of your text to respond to the following:Show
the contents of the id array after each union operation when you
use the quick union algorithm (Program I.I) to solve the
connectivity problem for the sequence 0-2, 1-4, 2-5, 3-6, 0-4, 6-
0, and 1-3. Also give the number of times the program accesses
the id array for each input pair.3. Refer to figures 1.7 and 1.8

13. on pages 16 and 17 of the text. Give the contents of the id array
after each union operation for the weighted quick union
algorithm running on the examples corresponding to figures 1.7
and 1.84. For what value is N is 10N lg N>2N2?
5. Prove that O(1) is the same as O(2)
6. You are given the information that the time complexity of
one problem is N log N and that the time complexity of another
problem is N3. What does this statement imply about the
relative performance of specific algorithms that solve the
problems?