CS223 AlgorithmsD-Term 2013

Instructor: Mohamed Eltabakh

WPI, CS

Introduction

Slide 1

Lecture Outline

• Introduction and Definitions

• Example Problems

• Course Logistics

Slide 2

Definition

• An algorithm is a finite sequence of step by step, discrete, unambiguous instructions for solving a particular problem

– Receives input data– Produces output data– Each instruction can be carried out in a finite

amount of time in a deterministic way

Slide 3

Definition

• In simple terms, an algorithm is a series of instructions to solve a problem (complete a task)

• We focus on Deterministic Algorithms– Under the same input it must produce the

same output

Algorithminput output

Well defined sequence of computer instructions

Slide 4

Two Key Properties

• Correctness– An algorithm is correct if under all valid inputs, it produces

the correct output

• Efficiency– Same problem can have many ways (algorithms) to solve it– Which one is more efficient?– Efficiency means:

• How long will it take?

• How much storage will it need?

Time CPU # of instructions

StorageSpace Memory

Slide 5

CS223 AlgorithmsD-Term 2013

Representative Problems

Slide 6

Problem Family I: Sorting

– Input• A list of unsorted values

– Output• The corresponding sorted list

B R U T E F O R C E

B C E E F O R R T U

The algorithm must know how to compare values (<, =, or >)

Slide 7

Problem Family II: Searching– Input

• A list of values L, and a key (single value) K

– Output• The position in L that contain K (if exists)

B R U T E F O R C E

Search for 33?

Search for C?

Will it make a difference if the list is sorted ???

Slide 8

Problem Family III: Trees– Input

• A tree of values

– Different problems• Traverse the tree and list the values

• Search for a value in the tree

• Deletion from or insertion into the tree

Can you notice a certain order in this tree?

Binary Tree Binary Search Tree

Left smaller thanRight greater than

Slide 9

Problem Family IV: Graphs– Input

• A graph of values G

– Different problems• Traverse the graph• Searching for a value in the graph• Shortest path from one node to another

What is the shortest path from F to B?

What is the shortest path from F to all other nodes?

Find a minimum spanning tree?

Slide 10

Problem Family V: String Processing

– Input• One or multiple strings

– Different problems• Search for one string in another

• Edit distance between strings

• String alignment

Search for sentence “algorithms are fun”

Find the smallest difference between this document and another document

Slide 11

Too Many Others

Protein networks

DNA sequence alignment

Matrix multiplication

Scheduling problem

Greatest Common Divisor (GCD)

Nearest neighbor (closest gas station to me)

Slide 12

Algorithm Design Phases

-- What are the inputs?-- What are the outputs?-- What is the functionality?

-- Correctness?

-- Efficiency?

Must give the correct answer under all valid inputs

Analyze your algorithm * How fast is it? * Does it consume much resources (CPU, memory, disk, etc…)

-- Choose a language to implement your algorithm (E.g., C, Java, Perl, etc…)

-- Correct implementation !!!

-- Test you algorithm -- Try different inputs-- Check special and corner cases

Slide 13

Course Outline (What You Will Learn)

• Algorithmic Strategies and Methodologies – Tree and graph traversal, Greedy Algorithms, Dynamic

Programming, Divide and Conquer

• Problem Types/Families– Sorting, Searching, Graph and Tree Algorithms, Scheduling and

Optimization, String Processing

• Algorithms on Different Data Structures– Arrays, Trees, Queues, Graphs, Strings, Hash Tables, Linked Lists

• Analysis and Evaluation– Coding and running algorithms, – Analytical analysis using big-O notation

Slide 14

CS223 AlgorithmsD-Term 2013

Course Logistics

Slide 15

Textbook

• Required Introduction to Algorithms

T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein.

Third Edition, MIT Press, 2009. ISBN 978-0-262-03384-8.

URL: Book Website

Slide 16

Available in bookstore Several copies on reserve in library

Course Logistics

• Website: http://web.cs.wpi.edu/~cs2223/d13

• Electronic WPI system: blackboard.wpi.edu

• Lectures– MTRF (2:00pm - 2:50pm)

• Grading– All assignments are

done individually

Slide 17

Tentative Scheduling

• Tentative scheduling for assignments, exams, and quizzes– Visit the website: http://web.cs.wpi.edu/~cs2223/d13

• Late Submission Policy– One-day late 10% off the max grade – Two-day late 20% off the max grade– Three-day late 30% off the max grade– Beyond that no late submission is accepted

Slide 18

Course Management

• Two systems will be maintained

– Web Page: http://web.cs.wpi.edu/~cs2223/d13

– Electronic WPI system: blackboard.wpi.edu

• Homework/Project submissions

– Either at the beginning of class on the due date

– Or electronically on blackboard.wpi.edu (Recommended)

• Viewing Grades

– On blackboard.wpi.edu

Slide 19

Office Hours

• Posted on the course web page

• Covers most days of the week

• Make use of them– they are there for YOU !

• Feel free to send me email or stop by my office

Slide 20

Programming Language

• In assignments, use a language of your choice– Most students use either Java, C, or Python

• In lectures, I will use pseudocode closer to Java or C

Slide 21

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