algorithm & data structures lec1(bet)

7/29/2019 Algorithm & Data Structures Lec1(BET)

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Algorithm & Data StructuresFall 2011


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My Profile

Name:Syed Muhammad Raza

Education:

MSc Wireless Communication

LTH Sweden , 2007-2009

BS Computer Information Sciences

PIEAS Pakistan , 2002-2006

Contact Information:


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Rules

Dont Mess With Me

&

I Wont Mess With You


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Course Overview

Fundamentals of AlgorithmsReview of Programming

Sorting and Searching

Stacks

Queues, Priority Queues and Circular Queues

Linked List

Trees

Hashing


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Text Book

No Text Book

&Every Text Book


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Marks Distribution

Lab 25% of 100 Marks

Theory 75% of 100 Marks

Sessional 1 = 10 Marks

Sessional 2 = 15 Marks

Final Paper = 50 Marks

Assignment = 15 Marks

Quiz = 10 Marks

Total = 100 Marks


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Lets see what you got!


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Algorithm


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Problem Solving

Problem solving is the process of transformingthe description of a problem into the solution of thatproblem by using our knowledge of the problem

domain and by relying on our ability to select anduse appropriate problem-solving strategies,techniques, and tools.


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Algorithms

An Algorithm is a step by step solution to aproblem

Why bother writing an algorithm

For your own use in the future - Don't have to

rethink the problem.

So others can solve the problem, even if theyknow very little about the principles behind how

the solution was derived.


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Examples of Algorithms

Washing machine instructions

Instructions for a ready-to-assemble piece of

furniture

A Classic: GCD - Greatest Common Divisor - The

Euclidean Algorithm


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Washing Machine Instructions

Separate clothes into white clothes and colored clothes.

For white clothes:

Set water temperature knob to HOT.

Place white laundry in tub.

For colored clothes:

Set water temperature knob to COLD

Place colored laundry in tub.

Add 1 cup of powdered laundry detergent to the tub.

Close lid and press the start button.


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Observations

There are a finite number of steps.

We are capable of doing each of the instructions.

When we have followed all of the steps, the

washing machine will wash the clothes and then

will stop.

Are all of the clothes clean ?

Do we want the washing machine to run until all

of the clothes are clean ?


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Refinement of the Definition

Our old definition:

An algorithm is a step by step solution to a problem.

Adding our observations:

An algorithm is a finite set of executable instructions that

directs a terminating activity.


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Instructions for a Ready-to-Assemble Furniture

"Align the marks on side A with the grooves on

Part F

Why are these instructions typically so hard to

follow ?

Lack of proper tools - instructions are not executable

Which side is A ? A & B look alike. Both line up with Part F

- Ambiguous instructions.


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Final Definition

An algorithm is a finite set of unambiguous,executable instructions that directs a terminatingactivity.


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History of Algorithms

The study of algorithms began as a subject in mathematics.

The search for algorithms was a significant activity of early

mathematicians.

Goal: To find a single set of instructions that could be usedto solve any problem of a particular type.


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GCD- Euclidean Algorithm

Assign M and N the value of the larger and the value of the

smaller of the two positive integer input values, respectively.

Divide M by N and call the remainder R.

If R is not 0, then assign M the value of N, assign N the valueof R and return to step 2, otherwise the greatest common

divisor is the value currently assigned to N.


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Finding GCD of 24 & 9

M N R

24 9 6

9 6 3

6 3 0

So 3 is the GCD of 24 and 9.

Do we need to know the theory that Euclid used to come up with

this algorithm in order to use it ?

What intelligence is required to find the GCD using this algorithm ?


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Idea Behind the Algorithms

Once an algorithm behind a task has been

discovered

Don't need to understand the principles.

Task is reduced to following the instructions.

Intelligence is "encoded into the algorithm"


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Algorithm Representation

Syntax and Semantics

Syntax refers to the representation itself.

Semantics refers to the concept represented.


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Algorithm Requirements

Requirements for an algorithm:

Input

Output

Unambiguous

Generality

Correctness

Finite

Efficiency


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Algorithm Representation

Pseudo-code

Flow chart


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Pseudo-Code

Pseudo-code is a semi-formal, English-like language with a

limited vocabulary that can be used to design and describe

algorithms.

The main purpose of a pseudo-code is to define the

procedural logic of an algorithm in a simple, easy-to-

understand manner for its readers, who may or may not be

proficient in computer programming.


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Pseudo-Code

Used in designing algorithms.

Used in communicating to users.

Used in implementing algorithms as programs.

Used in debugging logic errors in programs.

Used in documenting programs for future maintenance and

expansion purposes.


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Pseudo-Code

Must have a limited vocabulary.

Must be easy to learn.

Must produce simple, English-like narrative notation.

Must be capable of describing all algorithms, regardless of

their complexity.


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Control Structures

Sequence

Selection

Repetition


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Sequence

Series of steps or statements that are executed in the order

they are written.

Example:

Read taxable income

Read filing status

Compute income tax

Print income tax


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Selection

Defines one or two courses of action depending on the

evaluation of a condition.

A condition is an expression that is either true or false.

Example

if condition (is true)

then-part

else

else-part

end_if


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Nested Selection

if status is equal to 1

print Single

else


print Married filing jointly

else


print Married filing separately

end_if

end_if


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Repetition

Specifies a block of one or more statements that are

repeatedly executed until a condition is satisfied.

Example:

while condition

loop-body

end_while


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Conventions

Each pseudo-code statement consists of keywords that

describe operations and some appropriate, English-like

description of operands.

Each statement should be written on a separate line.

Continuation lines should be indented


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Conventions II

Sequence statements should begin with unambiguous words

(compute, set, initialize).

Selection statements then-part and else-part should be

indented.

Selection statements end with the keyword end_if.


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Convention III

Repetition statements end with end_while.

Loop-bodies are indented.

All words in a pseudo-code statement must be chosen to be

unambiguous, and as easy as possible to understand by

non-programmers.

Enclose comments between /* and */


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Example 1

If student's grade is greater than or equal to 60

Print "passed"

else

Print "failed

End_if


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Example 2

Set total to zero

Set grade counter to one

While grade counter is less than or equal to ten

Input the next grade

Add the grade into the total

End_while

Set the class average to the total divided by ten

Print the class average.


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Example 3

initialize passes to zero

initialize failures to zero

initialize student to one

while student counter is less than or equal to ten

input the next exam result

if the student passed

add one to passes

else

add one to failures


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Set asterik counter to one

Set outer while counter to one

While out counter is less than or equal to 4

set spaces counter to 1

while spaces counter is less than 4

print

increment space by one

end_while

set asterik counter to one

while asterik counter is less than or equal to odd multiple of outercounter

print *

increment asterik counter by one

end_while


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Basic Symbols

Rounded box - use it to represent anevent which occurs automatically. Suchan event will trigger a subsequent action,for example `receive telephone call, ordescribe a new state of affairs.Rectangle or box - use it to represent anevent which is controlled within the

process. Typically this will be a step oraction which is taken. In most flowchartsthis will be the most frequently usedsymbol.

Diamond - use it to represent a decisionpoint in the process. Typically, thestatement in the symbol will require a

`yes' or `no' response and branch todifferent parts of the flowchartaccordingly.

Circle - use it to represent a point atwhich the flowchart connects withanother process. The name or referencefor the other process should appear

within the symbol.


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Flowchart

A flowchart is a diagrammatic representation that illustrates

the sequence of operations to be performed to get the

solution of a problem


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Guide Lines

Flowcharts are usually drawn using some standard symbols;

however, some special symbols can also be developed when

requiredStart or end of the program. Computational steps orprocessing function of a program

Input or output operation, Decision making andbranching

Connector or joining of two parts of program

Magnetic TapeOff-page connector

Flow line

Annotation

Display


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Example

Draw a flowchart to find the largest of three numbers A,B,

and C.


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Example

Draw a flowchart to find the sum of first 50 natural

numbers.


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Imagination is more important than knowledge

Knowledge is Limited.

Imagination encircles the world

Einstein

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