CSE 3101E Design and Analysis of Algorithms
Prof. J. Elder
Textbooks
• Required Text:
– Cormen, T.H., Leiserson, C.E., Rivest, R.L. & Stein, C. (2001).
Introduction to Algorithms, 2nd Ed. Cambridge, Mass: MIT
Press.
• Available in the York University Bookstore
• Also available from www.amazon.ca for $68.01
• Optional Text:
– Edmonds, J. How to Think about Algorithms. New York, NY:
Cambridge University Press.
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Assignments
• You will learn best if you try to tackle each problem by yourself
initially.
• You are encouraged to discuss the problems and work in groups to
overcome roadblocks.
• You are encouraged to team up with a partner and write up a single
assignment report (maximum 2 per group).
• Make the reports as concise and organized as possible. Marks may
be taken off for excess verbosity or lack of clarity.
• Late assignments are not excepted (except for medical emergencies
– please see syllabus).
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Teaching Assistant
• Eduardo Corral Soto
• Eduardo will be marking all
assignments.
• Please direct any questions
regarding the marking of
assignments to Eduardo.
• If you believe there was an
error in marking your
assignment, please bring it to
Eduardo’s attention promptly
(within a week).
• Office hour: Mon 9:30-10:30
(Location TBA)
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Please ask questions!
Help me know what people
are not understanding!
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On the slides
• These slides:
– are available from the website
www.elderlab.yorku.ca/~elder/teaching/cse3101
– may change up to the last minute as I polish the lecture.
– Include slides originally created by J. Edmonds: Thanks Jeff!
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Lectures
• I will teach the first 18 lectures
• Jeff Edmonds will teach the last 3 lectures on dynamic
programming
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Lecture 1. What is this course about?
Course Content
• A list of algorithms.
– Learn their code.
– Trace them until you are convinced that they work.
– Implement them.
– Worry about details.
class InsertionSortAlgorithm extends SortAlgorithm
{
void sort(int a[]) throws Exception {
for (int i = 1; i < a.length; i++) {
int j = i;
int B = a[i];
while ((j > 0) && (a[j-1] > B)) {
a[j] = a[j-1];
j--; }
a[j] = B;
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}}
Innovation
Abraham Lincoln
Thomas Edison
Steve Wozniak and Steve Jobs
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The future belongs to the computer scientist/engineer who has
– Knowledge: An up to date grasp of fundamental problems
and solutions
– Ability: Principles and techniques that can be adapted to
solve new problems
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Course Content
• A survey of algorithmic design techniques.
• Abstract thinking.
• How to develop new algorithms for any problem that
may arise.
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A survey of fundamental ideas
and algorithmic design
techniques
For example . . .
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Mathematical Tools
Recurrence Relations
Summations
∑i=1 f(i).
T(n) = a T(n/b) + f(n)
Classifying Functions
f(i) = nQ(n)
Time
Time Complexity
t(n) = Q(n2)
Input Size
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Iterative Algorithms
Loop Invariants
<preCond>
codeA
loop
<loop-invariant>
exit when <exit Cond>
codeB
codeC
<postCond>
Code
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5 km
i-1
i
9 km
One step
at a time
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Relay Race
Recursive Algorithms
?
?
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Graph Search Algorithms
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Network Flows
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Greedy Algorithms
Example: Making Change
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Dynamic Programing
4
5
3
2
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8
9
5
8
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4
6
2
3
5
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1
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2
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Useful Learning Techniques
Read Ahead
You are expected to read the lecture notes before the
lecture.
This will facilitate more productive discussion during class.
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Explaining
• We are going to test you on
your ability to explain the
material.
• One good way to study is to
explain the material over and
over again to yourself or to
each other.
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Be Creative
•Ask questions.
• Why is it done this way and not that way?
Guesses and Counter Examples
• Guess at potential algorithms for solving a problem.
•
Look for input instances for which your algorithm gives
the wrong answer.
• Treat it as a game between these two players.
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Refinement:
The best solution comes from a process of
repeatedly refining and inventing alternative
solutions
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Rudich www.discretemath.com
End