CSE 3101E Design and Analysis of Algorithms

Prof. J. Elder

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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

Lecture 1. What is this course about?

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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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– Knowledge: An up to date grasp of fundamental problems and solutions

– Ability: Principles and techniques that can be adapted to solve new problems

The future belongs to the computer scientist/engineer who has

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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

Input Size

Tim

e

Classifying Functionsf(i) = n(n)

Recurrence Relations

T(n) = a T(n/b) + f(n)Summations

∑i=1 f(i).

Time Complexityt(n) = (n2)

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Iterative Algorithms Loop Invariants

i-1 i

ii0 T+1

<preCond> codeA loop <loop-invariant> exit when <exit Cond> codeBcodeC<postCond>

9 km

5 km

Code Relay RaceOne step at a time

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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

5 3

4

2 84523

16575

32644

85982

Useful Learning Techniques

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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.

Be Creative

•Ask questions.

• Why is it done this way and not that way?

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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

Rudich www.discretemath.com

End