lecture 101 aug 2014 upload

8/10/2019 Lecture 101 Aug 2014 Upload

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QEEE DSA05

DATA STRUCTURES ANDALGORITHMSG VENKATESH AND MADHAVAN MUKUND

LECTURE 1, 1 AUGUST 2014


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Understanding Algorithms

Correctness

E"ciency

Asymptotic complexity, O( ) notation

Modelling

Graphs, data structures, decomposing the problem

Techniques

Divide and conquer, greedy, dynamic programming


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Expectations

Background in programming

Any language (C, C++, Java, Python)

Basic data structures

Arrays, lists


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Topics to be covered

Asymptotic complexity, basic searching and sorting(2 lectures)

Divide and conquer (3 lectures)

Basics of graphs and graph algorithms (4 lectures)

Greedy algorithms (1 lecture)

Trees (1 lecture)

Dynamic Programming (3 lectures)


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Evaluation

Programming assignments (4-5)

Online judge

http://www.iarcs.org.in/qeee-dsa05/index.php

Log in and create an account for yourself

Enter your name and institution accurately!

Quizzes, paper and pen (2)

Objective (multiple choice, unique answer )
http://www.iarcs.org.in/qeee-dsa05/index.php


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Example 1: Air travel

Barbet Airlines serves several cities in India

Some cities are connected by direct flights

Want to compute all pairs of cities A,B such that A

and B are connected by a sequence of flights


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Throw away the map and record the network

This is a grapha collection of nodes and edges


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Can distort the picture without changing meaning


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Can distort the picture without changing meaning


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Connected destinations

Compute pathsin the graph

How do we represent the graph so that we canmanipulate it using a computer program?

Suitable data structure

How do we design an e"cient algorithm for this

data representation?


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Efficiency?

N cities, F direct flights

Computing paths depends on N and F

What is this dependency?

How large a value of N and F can we handle?

Online booking requires response in seconds


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Variations

Flights have arrival and departure times

Only some connections are feasible

Should not have to wait overnight

or more than 4 hours

How to compute feasible pathswith constraints?


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Example 2: Xerox Shop

Campus Xerox has several photocopiers

Tomorrow is the deadline for BTech projects and

there is a rush of reports to be printed

How to schedule the pending jobs most

e$ectively?


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Xerox Shop

The number of pages for each job is known

Each customer has been promised delivery by a

deadline

Campus Xerox o$ers discount if deadline is not

met

How to sequentially allocate the jobs to

photocopiers to maximize revenue?


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Xerox Shop

Brute force

Try all possible allocations

Choose one that is optimum

Number of possibilities is exponential!

Even with 30 jobs, it would take hours to compute

an optimal schedule


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Xerox Shop

Decompose the problem

Choose a job to schedule first, and the machine

on which it will run, according to some strategy

Now, recursively solve the problem for N-1 jobs


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Xerox Shop

Greedy approach

Fix the choice of next job once and for all

Never go back and try another sequence

How to choose the next job?

Shortest processing time?

Earliest deadline?

How to show that this strategy is optimal?


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Variations

Some photocopiers are old and slow, some are

new and fast

Time for a job depends on choice of machine

Cost of ink and paper varies across machines

Net revenue for a job depends on choice of

machine


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Example 3: Document

similarity

Given two documents, how similar are they?

Plagiarism detection

Checking changes between versions of code

Answering web search queries more e$ectively


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Document similarity

What is a good measure of similarity?

Edit distance

How many changes does one have to make to get

from one document to another?

What types of changes are allowed?

Add or remove a letter

Replace one letter by another


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Document similarity Edit Distance

Minimum number of edit operations to transformone document to another

How do we compute it?

Brute force: try all sequences and choose the bestone

Delete all of first document, add all of seconddocument

Impossibly ine"cient!


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Decomposing the problem

Make the first character in both documents the

same

Explore all possible edit operations that makethis possible

Recursively fix the rest of the documents

Naive recursion is ine"cient

Same subproblem solved recursively many times


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Naive recursion can be

inefficientFibonacci numbers:

F(n) = F(n-1) + F(n-2), F(1) = 1, F(2) = 1

Sequence is 1,1,2,3,5,8,13,21,.

Computing recursively

F(7) = F(6) + F(5) = (F(5) + F(4)) + (F(4)+F(3)) =

(F(4)+F(3)+F(3)+F(2)) + (F(3)+F(2)+F(2)+F(1)) =


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Dynamic Programming

Making recursive computations e"

cient

Ensure that subproblems are computed only once

How do we store and look up answers to already

solved subproblems?


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Variations

Interested only in the meaning of the document

Focus on words

Documents are near if they overlap on many words

Order in which words occur may not matter

Useful for topic based web search

Can have dictionary of similar words