Algorithm Lecture1

8/1/2019 Algorithm Lecture1

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Algorithms


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Algorithm

Basic idea or logic behind computer programs. Step by step procedure for performing a task in a finite amount of

time. Procedure of manipulating data. A set of finite unambiguous instructions that take input and give

desired output Set of rule for carrying out some calculations either manually or

usually by a machine. Any well defined computational procedure that takes some value

or a set of values as input and produces some value or a set ofvalue a output

Sequence of computations that transform input to output Algorithms can be viewed as a tool for solving a well specified

computational problem. The statement of the problem specifiesin general terms the desired input/output relation. The algorithmdescribes a specific computational procedure for achieving that

desired I/O relation.


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Pictorial Representation


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Features of an Algorithm

An algorithm has the five important features:finiteness

terminates after a finite number of steps

definiteness

Precise/complete definition of each stepinput (zero or more)

Valid inputs are clearly defined

output (one or more) Can be proved to produce the correct output given a valid

input

effectiveness Steps are sufficiently simple and basic


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What is Algorithmics?

Study of Algorithms A problem may have many algorithms as solutions Priorities+ Limitations require that we choose one amongst

them It may happen that none of the available algorithms satisfy the

requirement thus we have to devise a new algorithm Algorithmics is a science that lets us evaluate the effect of

various external factors on the available algorithm so that wean choose the one that best suits out particularcircumstances. It is also a science that tells us how to design

a new algorithm External factors: Storage requirement, Speed


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PARAMETERS FOR SELECTION

OF AN ALGORITHM

Type of Available Computing Equipment

Nature of Problem

Speed of Execution Storage Requirement

Programming Effort

Good choice can save both money and time,and can successfully solve the problem


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Problem Solving


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Algorithm Development Algorithm

Algorithm Design (informal problem statement)Formalize ProblemRepeat

Devise Algo

Analyze correctness Analyze Efficiency Refine

Until Algorithm Good EnoughReturn Algorithm

Specify Input

Specify Output

Specify what processing required

Write steps to accomplish that


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Important Points

Non-ambiguity

Range of inputs

The same algorithm can be represented indifferent ways

Several algorithms for solving the same problem

Most algorithms are intended to be implementedas computer programs.


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Expressing algorithms

There is a need to specify /express sequence of stepscomprising an Algorithm.

The only requirement is that the specification must provide aprecise description of the computational procedure to befollowed.

Algorithms can be expressed in many kinds of notation:

Natural languages

Pseudocode

Flowcharts

Programming Languages

Natural language expressions of algorithms tend to beambiguous, and are rarely used for formal complex ortechnical algorithms.


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How to specify algorithms?

Pseudocode, flowcharts are more structured ways toexpress algorithms that avoid many of the ambiguitiescommon in natural language statements, whileremaining independent of a particular implementationlanguage.

Programming languages are primarily intended forexpressing algorithms in a form that can be executed bya computer.

Typically algorithms are described as pseudo code

because it gives the liberty of expressing in a mannerthat is most clear & concise. May come across phrases of English at places. Since we are not confining ourselves to programming

language therefore essential parts of the algorithm will

not be obscured by unimportant programming details


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Psuedo Code Conventions

No need of well structured language Use of English for simplicity & clarity Use of mathematical language & symbols where appropriate Indentation indicates block structures.

Delimiters are not used. No variable declaration All variables used are implicitly local unless specified

otherwise. Return statement used to mark end of algorithm to return a

value if required. Assignment operator used is = or


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Phrases for writing algorithm

Phrases such as mentioned below are used tolink sequences of steps if required:-

ifthen__________________

else___________________________


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Repeat

_________

_________

_________

_________

until


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while _______________

do__________

_____While


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Representations of Algorithms

High-level description

Prose to describe an algorithm, ignoring theimplementation details.

Formal description

Detailed

Lowest level description


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Example

Algorithm to find the largest number in an (unsorted) list of numbers.

High-level description (somewhat ambiguous)Assume the first item is largest.Look at each of the remaining items in the list and if it is largerthan the largest item so far, make a note of it.

The last noted item is the largest in the list when the process iscomplete.

Formal descriptionInput: A non-empty list of numbers L.

Output: The largestnumber in the list L.largest L0for eachitemin the list L

1, do

if the item> largest, thenlargest the item

returnlargest


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Flowchart

A flowchart is a common type of diagram, thatrepresents an algorithm, showing the steps as boxes ofvarious kinds, and their order by connecting these witharrows.

This diagrammatic representation can give a step-by-step solution to a given problem.

Data is represented in these boxes, and arrowsconnecting them represent flow / direction of flow ofdata.

Flowcharts are used in analyzing, designing,documenting or managing a process or program invarious fields.


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Flowchart Symbols

Start/Stop (End) Symbol

Read/Write (Input/Output) Symbol

The Operation (Process) Symbol

Lines and Arrow

Connector, New page

Decision


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Examples


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Replying to a friends letter

Algorithm

Read friends letter

Decide what to write

Write letter in reply

START

END

Decide what towrite

Readfriends

letter

Write letterin reply


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Algorithm Lecture1

Documents

Transcript of Algorithm Lecture1