CS 310: Analysis of Algorithms
Spring 2016
1
Organizational Details
Class Meeting:
1:00-3:45, Tuesday, UC249
Class Web Page:
http://www.eagle.tamut.edu/faculty/igor/CS-EE-310.htm
Instructor: Dr. Igor Aizenberg
Office: Science and Technology Building, 104C
Phone (903 334 6654)
e-mail: igor.aizenberg@tamut.edu
Office hours:
Tuesday, Thursday 4:00p – 5:00p, Wednesday 1:00a – 3:00p
2
Text Book (Optional)
T. H. Cormen, C.E. Leiserson, R. L.
Rivest and C. Stein "Introduction to
Algorithms", 3rd Edn.The MIT Press,
McGraw-Hill Book Company, 2002
ISBN 978-0-262-03384-8 (hardcover)
- ISBN 978-0-262-53305-8 (pbk)
3
Control
 Tests (open book, open notes):
Test 1:
February 23, 2016
Test 2:
March 22, 2016
Test 3:
May 3, 2016
 Homework
4
Grading
Grading Method
Homework and preparation:
Test 1:
Test 2:
Test 3:
25%
25%
25%
25%
Grading Scale:
90%+  A
80%+  B
70%+  C
60%+  D
less than 60%  F
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Algorithm

What is an algorithm?
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Algorithm in General
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An algorithm is a finite set of welldefined instructions for accomplishing
some task which, given an initial state,
will terminate in a defined end-state.
To develop any algorithm, it is
necessary to know, how the
corresponding problem can be solved.
7
Algorithm in Computer Science

An algorithm is any well-defined
computational procedure that takes
some value, or set of values, as input
and produces some value, or set of
values, as output. An algorithm is a
sequence of computational steps
(instructions) that transform the input
into the output.
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Algorithm in Computer Science



An algorithm is a tool for solving a
well-specified computational problem.
The statement of the problem specifies
in general terms the desired
input/output relationship.
The algorithm describes a specific
computational procedure for achieving
that relationship.
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Solving Computational
Problem


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Problem setting
Design of an algorithm
Analysis of the algorithm (proof of its
correctness, analysis of its efficiency,
comparison to other algorithms solving the
same problem)
Software implementation of the algorithm
Solving the problem
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So, what is this course
about?
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Solving Interesting Problems
1.
2.
3.
4.
Design of algorithms (Methods and tools).
Correctness of algorithms
•
Buggy algorithms are worthless!
Efficiency of algorithms
•
Complexity, simplicity, running time, space needed, …
Examples of efficient algorithm design
•
Fast algorithms in signal processing
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Three Kinds of Problems: 1
Decision problems
Given input, does it have a certain
property?


Is an integer prime?
Is a graph planar? (Can be drawn on a
plane without overlapping edges?)
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Three Kinds of Problems: 2
Functional problems
Given input, compute the unique solution.



Compute the product of two matrices
Sort an array
Take the Fourier transform of a signal
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Three Kinds of Problems: 3
Search problems
Given input, compute any one of a set of
solutions.




Find the factors of an integer
Find shortest path between two points in a graph
Find the longest path between two points in a graph
Find a record, which is marked by a certain key or
contains a certain value of some data in a database
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Properties of Algorithms: 1

Time efficiency


As a function of its input size, how long does
it take?
Space efficiency

As a function of its input size, how much
additional space does it use?
Most interested in asymptotic efficiency:
worst-case & average-case
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Properties of Algorithms: 2

Simplicity

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Informal notion
Easier to code correctly
Lower constant factors in efficiency
(probably)
Easier to explain
Easier to prove the correctness
More mathematically “elegant”
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Basic Types of Algorithms

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Linear algorithm consists of a sequence of
unconditional straightforward steps.
Loop is a group of steps that are repeated
until some condition will not be satisfied.
Nested Loop is a loop containing another
loop (loops).
Branching algorithm consists of a number of
subsequences that can be taken depending
on some condition (conditions).
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Modern computer technologies

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Hardware (including pipelining and
superscalar architecture)
Graphical User Interfaces (GUI)
Object-oriented programming
Networking (local-area and wide-area)
ALGORITHMS
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Algorithms Representation:
Flowchart
 Data input
 Operations (Arithmetic) and Assignments
Yes
No
 Logical block (Branching)
 Data output
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