Download CSE 2320 Algorithms and Data Structures

CSE 2320 Algorithms and Data Structures
Introduction
Dimitrios Kosmopoulos
General info
• Dimitrios Kosmopoulos
[email protected]
• Office: ERB644 (to change)
• Hours: TuTh 12:30pm-2:30pm
• GTA: 2B announced
• web page
http://heracleia.uta.edu/~dkosmo/
General info
Textbook: R. Sedgewick, Algorithms in Java, Parts
1-5, 3rd ed., Addison-Wesley, 2003.
References:
Al Aho and Jeff Ullman, Foundations of Computer
Science,
http://infolab.stanford.edu/~ullman/focs.html
S. Baase and A. Van Gelder, Computer Algorithms:
Introduction to Design and Analysis, 3rd ed.,
Addison-Wesley, 2000.
Cormen, Leiserson, Rivest, Stein, Introduction to
Algorithms, 2nd ed., MIT Press, 2001.
J. Lewis and W. Loftus, Java Software Solutions:
Foundations of Program Design, 6th ed.,
Pearson Education, 2009.
Prerequisites
• C programming (CSE 1320)
• Java programming (CSE 1325)
(a) problem-> (b) algorithm-> (c) program-> (d) executable
So far: (b)->(c)->(d)
Here: (a)->(b)
Objectives
• To become capable of developing, applying,
and evaluating algorithmic solutions.
• Intuition about particular algorithms and data
structures that have wide applicability.
• Understanding of classic approaches to
algorithm design – decomposition, dynamic
programming, and greedy methods.
• Understanding of basic algorithm analysis
concepts by applying math skills to worst-case
and expected time using recurrences and
asymptotic notation.
• Improved programming skills - especially data
structures, recursion, and graphs.
Grading
Based on the following weights:
Exams: 65% divided evenly among 3
exams.
Programs: 15% divided evenly among
three assignments.
Homework assignments: 10%
Practice homeworks with answers, will be
available on the course web page
ABET Outcome B (Experimentation)
Assessment Project: 10%
Grading (cont.)
• Students achieving a semester grade of C
or better, but failing the experimentation
assessment (below 60%) and
documenting their circumstances will be
assigned a semester grade of I
(incomplete) and may re-attempt the
assessment in the next semester. If the
assessment is then passed, the semester
grade will be changed from I to the
achieved grade.
Policies (selection)
• Regular attendance expected
• Surprise quizzes an option, each quiz
being 2% of the semester grade taken
from the 65% allocated to exams
• Lecture notes and sample code for various
algorithms are on the course web page
http://heracleia.uta.edu/~dkosmo
• Cheating - You Are Expected To Know
University Policies
Policies (selection)
• Labs are due at 10:45 am on the
due date, not midnight. Homeworks
are due before class. After the due
time, assistance will not be
provided.
• Degree of lateness penalty
– Up to 10:45 next day 10 pts
– Up to 10:45 two days 30 pts
– Up to 10:45 three days 60 pts
• Resubmissions before the due time
are penalized 10 points each. No
resubmissions after the due time.
Lab grading
a. Output/Code 60%
b. Internal Comments 6%
c. Modularity 6%
d. Structure 6%
e. Names 6%
f. Spacing 6%
g. Generality 10%
Lab submission
• All programs must be written in Java to compile
and execute using a recent version of the JDK.
• Details for program submission will be included
with each assignment.
• You are responsible for correctly sending each
programming assignment to the GTA as an
attachment. (cc: yourself)
• No points will be awarded for programs that do
not compile. Points for b-g will not be awarded to
submissions that are not substantially complete.
Lecture structure
•
•
•
•
Abstraction
Data models
Data structures
Algorithms
Abstraction
Computer science:
The science of abstraction: creating the right
model for thinking about a problem and
devising the appropriate mechanizable
solution to solve it
Different degrees of complexity:
Digital electronic circuit
Behavior of robotic agent
Example 1
• abstraction: directed
graph
• Knowledge can be
inferred through
“formal logic”
If Fluffy is a cat then
Fluffy is an animal
Example 2
• Exams scheduling: assignment to time
slots, avoid conflict
• No student takes both exams => can have
the same time slot
• Model: graph
– Node<-course
– edge<-student in common
Example 2 (cont.)
Algorithm:
a. Find the maximum set of courses
with no common students (maximal
independent set)
b. Assign to first slot
c. Continue until no courses are left
Solution not optimal, but close to optimal, and simple
More complex representations possible (e.g. constraints in
number of student’s sequential exams)
Important concepts
• Data models: the abstractions to describe the
real world or specific problems (e.g., a
mathematical model)
• Data structures: programming language
constructs used to represent data models (e.g.,
pointers, trees)
• Algorithms: the techniques to solve problems by
manipulating data structures
• Program: the implementation of an algorithm in
a programming language
How are these related to the course?
• New data structures
• How these can be used by various
algorithms
• Typical applications
Data model- Data structure
• The data model has two aspects:
• The values that it can assume (properties) – static
aspect
• The operations that can be executed on these data
– dynamic aspect / behavior
– Can be, e.g., the boolean algebra, the algebra
of sets, or any other mathematical theory
• The data structure is the computer
language-specific implementation
Example 1
AND- gate
Data model:
Static: the values 0,1
Operation: “and” as defined in the truth table
Data structure:
variables in java: boolean x, y, z;
Operator “&&”
Example 2
• Data model List: (a1,a2,…,an)
– Values: sets of integers in specific order
– Operation: merge (a1,a2)+(a3)=(a1,a2,a3)
• Data structure
class Node
{ int a;
Node next;
Node merge(Node node1, Node node2) { …};
}
Algorithm
• A problem solving method suitable for
implementation as a computer program
• How are the algorithm related to the data
structures?
– They organize and generally use the data
structures
• Algorithms and data structures go together
Greatest Common Divider Algorithm
• The GCD of two numbers is the largest number that
divides both of them without leaving a remainder.
• The algorithm is based on the principle that the greatest
common divisor of two numbers does not change if the
smaller number is subtracted from the larger number.
• For example, 21 is the GCD of 252 and 105
(252 = 21 × 12; 105 = 21 × 5); since 252 − 105 = 147,
the GCD of 147 and 105 is also 21.
• Since the larger of the two numbers is reduced,
repeating this process gives successively smaller
numbers until one of them is zero. When that occurs, the
GCD is the remaining nonzero number.
Algorithmic problem
Specification
of input
?
Specification
of output as
function of
input
• Infinite number of input instances satisfying the
specification
• e.g., a sorted non-decreasing sequence of integers of
finite length
• -12, -5, -3, 15, 40, 56, 12454
• -19, 2
Algorithmic problem
Specification
of input
Algorithm
Specification
of output as
function of
input
• Algorithm describes the processing of the input
instances
• Many algorithms may solve the same problem in a
different way
• -12, -5, -3, 15, 40, 56, 12454
• -19, 2
What is a good algorithm?
• Efficient
– Space
– Time running
• Efficiency measured as function of input
– Number of data elements
How do we measure efficiency?
• Write a program that
implements the algorithm
• Run the program with
input of various values
and size
• Measure the time using
system routines
What are the limitations?
• The algorithm has to be implemented
• Experiments can be done on a limited set
of data
• The hardware/software configuration must
be the same
• Generic analysis methodology will be
discussed in this course