problem solving concept by meetendra sir(unit 5)

8/10/2019 Problem Solving Concept by Meetendra Sir(Unit 5)

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Problem Solving Concepts

UNIT-5

1

Meetendra Singh Chahar

Astt. Professor

R.B.S.M.T.C, Agra

MEETENDRA SINGH CHAHAR


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INTRODUCTION

A problem obstructs and hinders the progress or movementin achieving of an objective.

The nature of the problem depends on the situation.

In problem solving each individual may have his or her ownunique way.

2MEETENDRA SINGH CHAHAR


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PROBLEM DEFINITION

Problem definition is the first and most important step indetermining information needs.

Information needs of software can be determined by:

1. Studying the existing system2. Using questionnaires

3. Stating the tentative information needs

4. Suggesting interpretation of information needs with

users.



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PROBLEM SOLVING TECHNIQUES

For solving a problem there are many techniques available,some of popular techniques are:

1. Trail & Error Method

2. Brain Storming Method3. Divide & Conquer Method



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1. TRAIL & ERROR METHOD

This is an iterative method.

It is based on the idea of successive approximation.

Starting with initial approximation to the root.

It is the most natural technique because in this sequenceof steps is repeated over and over again.



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2. BRAINSTORMING METHOD

Brainstorming is a group activity designed to increase thequantity of fresh ideas.

or

Brainstorming is a group method for obtaining new ideas andbusiness solutions.

The groups are organized for sitting together and stimulategreater creativity by exchange of mutual experiences andparticipating in the discussions.

The brainstorming ideas are canalized to a particular

segment of product line or services.



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Method of Conducting Brainstorming Sessions

The group should be informed of the broad areas of thesubject or area of discussions.

The group should consist of people drawn from differentstreams of knowledge such as marketing, production, qualitycontrol, planning, finance, costing, stores, handling, taxationand the like. The group also should consist of differentlevels of officers, supervisors from the organization.

The brainstorming session should be held in a good placewith ambience. So, that the group comes open with their

ideas.

To be continued



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The member should have no inhibitions about their status inthe organization or department where they serve. The

session should be frank and be fun. The brainstormingsessions are held where no individual or group dominate thediscussions and no boss-subordinate relationships.

Day dreaming or wild ideas to be encouraged.

There should not be any negative comments or criticismsagainst any particular individuals or groups or departments.

The ideas of one can be improved by others but norepetition of ideas. Each individual may be given a chance tothree ideas and these ideas being recorded on a flip chart

or black board. All the ideas are recorded on the flip charteven if one idea is not practical or ill-logical.



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3. DIVIDE & CONQUER METHOD

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Steps in Divide and Conquer Algorithm

Divide Step: In this step of the algorithm, the input ispartitioned into p 1 parts, each of size strictly less than n,the size of the original instance. The most common value ofp is 2, although other small constants greater than 2 arenot uncommon.

Conquer Step:This step consists of performing p recursive

call(s) if the problem size is greater than some pre-definedthreshold n0 . This threshold is derived by mathematicalanalysis of the algorithm. Once it is found, it can beincreased by any constant amount without affecting thetime complexity of the algorithm.

Combine Step: In this step, the solutions to the p recursivecall(s) are combined to obtain the desired output. Thecombine step in a divide-and-conquer algorithm may consistof merging, sorting, searching, finding the maximum orminimum, matrix addition, etc.

MEETENDRA SINGH CHAHAR 9


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Divide-and-conquer algorithm consists of

following major phases:1. Breaking the problem into several sub-problems that

are similar to the original problem but smaller in size.

2. Solve the sub-problem recursively (successively and

independently), and then,3. Combine these solutions to sub-problems to create a

solution to the original problem.



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A Problem of Sizen (Instance)

Subproblem 1 ofSize n/2

Subproblem 2 ofSize n/2

A Solution toSubproblem 1

A Solution toSubproblem 2

A Solution to theOriginal Problem

Divide-and-Conquer StrategyMEETENDRA SINGH CHAHAR


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STEPS IN PROBLEM SOLVING

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There are mainly three steps to solving a problem-

1. Defining the Problem

2. Analyze the Problem

3. Explore Solution



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1. DEFINING THE PROBLEM

When a problem is to be solved, two question arise,1. What to do ?

2. How to do ?

This phase answer the first question.

Here, the programmer has to defined the taskprecisely(correctly) and check for completeness.

There should not be any ambiguity(confusion).

The imprecisely or arbitrarily defined problem may result in

wrong analysis and design.

To be continued



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Different programmers may program this problem as peer

their understanding. The problem definition skill is directly proportional to the

depth of understanding of the programmer.

In the problem definition phase, the programmer has toreflect all the possibilities that need decision-making.



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2. ANALYZE THE PROBLEM

This is the programmers talent-testing phase.

A good analysis may result in good designing and coding.

In this phase, the programmer has to answer the secondquestion, How to do?

This is the initial investigation of the problem.

The programmer has to declare the computationalstrategies to analyze the defined problem with the help ofavailable tools.

Programming techniques like sequence, selection and

iteration can be used to develop the logic for analysis.

To be continued



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The primary operations that are performed on data are

arithmetic, logical and relational. The mostly used database operations are searching, sorting,

inserting, merging, etc.

Once we analyze the problem, the next phase is to designthe program.



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3. EXPLORE SOLUTION

When programmer complete the analysis then he/she willexplore (or design) the different solution of the problemand the best or optimum solution is chooses by thedevelopment team.

Once the problem is defined and the idea of how to solve it

is developed, the programmer can begin designing algorithm. Before starting designing, the problem must be refined

step-wise. This is known as the top-down design.

It is a strategy where the problem is divided into ahierarchical structure.

To be continued



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A separate sub-program may be designed for each module.

The top-down approach provides a method of handling theinherent logical complexity.

This allows the programmer to build solution in a step-wisemanner.



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Steps of using a Computer as a Problem-Solving Tool

Develop an Algorithm and a Flowchart.

Write the program in a computer language. (i.e. C, C++, etc.)

Enter the program into the computer.

Test and debug the program.

Run the program, input data and get the results from thecomputer.



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ALGORITHMS An algorithmis any well-defined computational procedure

that takes some value, or set of values, as input

andproduces some value, or set of values, as output.

An algorithm is thus a sequence of computational stepsthat transform the input into the output.

or An algorithm is a sequence of unambiguous instructions for

solving a problem.

Obtaining a required output for any valid input in afinite amount of time.

Procedural solutions to problems.

To be continued



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Computer is capable of understanding and following theinstructions given.

An input specifies an instance of the problem, the algorithm

solves.

Problem

Algorithm

ComputerInput Output

Notion of AlgorithmMEETENDRA SINGH CHAHAR


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The word algorithm comes from the name of the 9thcentury Persian Muslim mathematician Abu Abdullah

Muhammad ibn Musa Al Khwarizmi. An algorithm is an effective method for solving a problem

using a finite sequence of instructions.

The computational complexity and efficient implementation

of the algorithm are important in computing and thisdepends on suitable data structure.

Each algorithm is a list of well-defined instructions forcompleting a task.



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Format of an Algorithm

Input: Step 1:

Step 2:

Step 3:

..

..

..

Step n:

Output:



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Characteristics of an Algorithm

Finiteness:Terminates after a finite number of steps. Definiteness:Rigorously and unambiguously specified.

Input:Valid inputs are clearly specified.

Output:Can be proved to produce the correct output given

a valid input. Effectiveness:Steps are sufficiently simple and basic.



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Advantages of an Algorithm

Provides step by step procedure to understand easily.

Algorithm is easy to write.

Solves those problems which are complex and not solve bysimple methods.

Algorithm in general, can be directly coded in aprogramming language.



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Example- Addition of two numbers.

AlgorithmStep 1: START

Step 2: Initialize x, y and z

Step 3: Read x, y

Step 4: Calculate z = x + y

Step 5: Print Sum of two numbers, z

Step 6: STOP



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FLOWCHARTS

A flowchart is a graphical representation of an algorithm.or

A flowchart is a diagram that is prepared by theprogrammer which represents the sequence of stepsinvolved in solving a problem.

It is an aid to solve a complex problem easily andefficiently.

It is also used to correct and debug a program flow afterthe coding part is completed.

To be continued



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It is one of the best tool for testing and maintaining asoftware.

A flowchart is sometimes called as a logic diagramin aprogramming parlance.

Its diagrammatic representation can give a step-by-stepsolution to a given problem.

It provides not only a detailed view of a program flow butalso used as a blueprint of the software project that showsthe general plan, architecture and essential details of theproposed software structure.



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Flowchart Symbols

In constructing flowcharts, standard symbols are used.

The American National Standard Institute(ANSI) symbolsare normally used.

Some important flowchart symbols are given here:



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Symbols Name(Attribute) Description

Process An operation or action step.

Terminator A start or stop point in a process.

Decision A question or branch in the process.

Delay A waiting period.

Data(I/O)Indicates data inputs and outputs toand from a process.

Alternate

Process

An alternate to the normal process

step.

Flow LineIndicates the direction of flow formaterials and/or information

Flowchart SymbolsMEETENDRA SINGH CHAHAR


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PredefinedProcess

A formally defined sub-process

Document A document or report

Multi-DocumentSame as Document, except, well,multiple documents

PreparationA preparation or set-up processstep

Display A machine display

Manual Input Manually input into a system

Stored DataA general data storage flowchartsymbol



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Punched Tape An old computer punched tape input

Merge (Storage) Merge multiple processes into one.

Extract(Measurement)

Extract(split process) or morecommonly a measurement

Magnetic Disk(Database) A database

Direct AccessStorage

Storage on a hard disk

Internal Storage Data stored in memory

SequentialAccess Storage

An old reel of tape



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PSEUDO CODE Pseudo code is an artificial and informal language that helps

programmers to develop algorithms.

Pseudo code is a text-based detail (algorithmic) designtool.

It is a compact and informal high-level description of a

computer programming algorithm that uses the structuralconventions of a programming language, but is intended forhuman reading rather than machine reading.

Pseudo code typically omits details that are not essentialfor human understanding of the algorithm, such as variable

declaration, etc.

To be continued



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The purpose of using pseudo code is that it is easier for

humans to understand than conventional programminglanguage code.

It is commonly used in textbooks and scientific publicationsthat are documenting various algorithms and also in planningof computer program development, for sketching out the

structure of the program before the actual coding takesplace.



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Conventions for Pseudo Code

Pseudo code should be clear and easy to understand.

Give a valid name for the pseudo code procedure.

Use the line numbers for each line of code.

Use proper indentation for every statement in a blockstructure.

For a flow control statements use if-else. Always end an if

statement with an end-if. Both if-else and end-if should bealigned vertically in same line.

For example,

if(condition expression)

statements

else statements

end-if

To be continuedMEETENDRA SINGH CHAHAR


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Use = or operator for assignment statements.

For example

i = j or i j

Array elements can be represented by specifying the arrayname followed by the index in square brackets.

For ex., A[i] indicates the ith element of the array A.



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Loops in pseudo code

For looping or iteration use for or while statements.Always end a for loop with end-for and a while with end-while.

The conditional expression of for or while can be written.

We can separate two or more conditions with an and.



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Example- Finding maximum no.

Algorithm: arrayMax(a[1...n], n)Step 1: max = a[1]

Step 2: For i = 2 to n do

Step 3: If a[i] > max, then

Step 4: max = a[i]

Step 5: Endif

Step 6: Endfor

Step 7: Return max



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TIME COMPLEXITY

Time Complexity of an algorithm is the amount of computertime it needs to run to completion.

This is the sum of compile time and run time.

Some of the reasons for studying time complexity are:

1. We may be interested to know in advance that whetheran algorithm/program will provide a satisfactory realtime response.

2. There may be several possible solutions with differenttime requirements.

To be continued



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We can found complexity of any algorithm using followingnotation:

Big-Oh notation:Big-Oh is the formal method ofexpressing the upper bound of an algorithms runningtime. It is the measure of the longest amount of time itcould possibly take for the algorithm to complete. Moreformally, for non-negative functions, f(n) and g(n), ifthere exists an integer n

0

and a constant c > 0 such thatfor all integers n > n0

f(n) c.g(n)

Then f(n) is Big-Oh of g(n). This is denoted as

f(n) O(g(n))


problem solving concept by meetendra sir(unit 5)

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