INTRODUCTION TO ALGORITHMS - Programming … 2.pdf · This sequence of steps is called an algorithm ... steps and some steps may involve decision making, repetition. ... an algorithm

INTRODUCTION TO ALGORITHMS

Logic

Logic is a tool to develop reasonable conclusions based on a given set of data. Logic is free of emotion and deals very specifically with information in its purest form.

1. Informal logic is the mode used in everyday reasoning and argument analysis.

2. Formal logic deal with deductive reasoning and the validity of the inferences produced.

Steps involved solving a particular problem:� Analyze the problem.� Identify the Inputs� Identify the Outputs� Identify the Process� Write the steps in english to solve the problem.� Draw a control flow diagram to link these steps.� Write the program for the solution.� Execute the program with different inputs and

verify for output.

1.1. PROGRAMMINGA typical programming task can be divided into two phases:� Problem solving phaseProduce an ordered sequence of steps that describe solution of problemThis sequence of steps is called an algorithm� Implementation phaseImplement the program in some programming language

1.2. PROBLEM SOLVINGProgramming is a process of problem solvingProblem solving techniques� Analyze the problem� Outline the problem requirements� Design steps (algorithm) to solve the problem� Algorithm:o Step-by-step problem-solving processo Solution achieved in finite amount of time

1.3. ANALYZE THE PROBLEMThoroughly understand the problemUnderstand problem requirements� Does program require user interaction?� Does program manipulate data?� What will be the output?If the problem is complex, divide it into subproblems� Analyze each subproblem as above

An informal definition of an algorithm is:

Algorithm: a step-by-step method for solving a problem or doing a task.

Formal definition

• Algorithm:• An ordered set of unambiguous steps that produces a

result and terminates in a finite time.

ALGORITHM“Algorithm" is a formally defined procedure for performing some calculation. If a procedure is

formally defined, then it must be implemented using a programming language. The algorithm

gives logic of the program, that is, a step-by-step description of how to arrive at a solution.

Algorithm provides a blueprint to write a program to solve a particular problem in finite

number of steps. Algorithms are mainly used to achieve software re-use

In order to qualify as an algorithm, a sequence of instructions must process the following

characteristics:

Instructions must be precise

Instructions must be unambiguous

Not even a single instruction must be repeated infinitely

After the algorithm gets terminated, the desired result must be obtained

PROPERTIES OF ALGORITHM1. Input:- an algorithm accepts zero or more inputs2. Output:- it produces at least one output.3. Finiteness:- an algorithm terminates after a finite numbers of steps.4. Definiteness:- each step in algorithm is unambiguous. This means that the

action specified by the step cannot be interpreted (explain the meaning of) in multiple ways & can be performed without any confusion.

5. Effectiveness:- it consists of basic instructions that are realizable. This means that the instructions can be performed by using the given inputs in a finite amount of time.

DEVELOPING AN ALGORITHM1.Identify the Inputs� What data do I need?� How will I get the data?� In what format will the data be?

2. Identify the Processes� How can I manipulate data to produce meaningful results?� Data vs. Information

3. Identify the Outputs� What outputs do I need to return to the user?� What format should the output take?

4. Top-down design approach is often used.� How can I break larger problems into smaller, more manageable pieces?� First try to break the process into a number of steps, which are smaller andsimpler than that for the entire process.� The sub-algorithms can themselves be broken down into smaller portions.

KEY FEARTURES OF AN ALGORITHM

Any algorithm has a finite number of steps and some steps may involve decision making,

repetition. Broadly speaking, an algorithm exhibits three key features that can be given as:

Sequence: Sequence means that each step of the algorithm is executed in the specified order.

Decision: Decision statements are used when the outcome of the process depends on some

condition.

Repetition: Repetition which involves executing one or more steps for a number of times can be

implemented using constructs like the while, do-while and for loops. These loops executed one

or more steps until some condition is true.

Three constructs

Algorithm• Find area of a rectangle • Step 1: Input L,B

Step 2: area=L*BStep 3: Print area

Step 4: Exit• Find the area of a circle• Step 1: Input R

Step 2: area=3.14*R*RStep 3: Print area

Step 4: Exit

• Step 1: Input SP,CP Step 2: if (SP>CP) then

p=SP-CPPrint p

elsel=CP-SP

Print lendif

Step 3:Exit

• Detailed Algorithm • Step 1: Input M1,M2,M3,M4

Step 2: GRADE (M1+M2+M3+M4)/4 Step 3: if (GRADE < 50) then

Print “FAIL”else

Print “PASS”endif

Step 4:Exit

• Detailed Algorithm • Step 1: Input M1,M2,M3,M4

Step 2: GRADE (M1+M2+M3+M4)/4 Step 3: if (GRADE > 60) then

Print “Ist”elseif (GRADE > 50)and (GRADE <60) then

Print “IInd”else

Print “Fail”endif

Step 4:Exit

• Step 1: Input the value of NStep 2: Set i=1Step 3: Repeat until i<=N

Step 5: Print iStep 4: Set i=i+1

end loopStep 5: Exit

Concept of a subalgorithm

Translators

• Translators are just computer programs which accept a program written in high level or low level language and produce an equivalent machine level program as output. Translators are of three types :

• Assembler• Compiler• Interpreter

• Assembler is used for converting the code of low level language (assembly language) into machine level language.

• Compilers and interpreters are used to convert the code of high level language into machine language. The high level program is known as source program and the corresponding machine level program is known as object program. Although both compilers and interpreters perform the same task but there is a difference in their working.

• A compiler searches all the errors of a program and lists them. If the program is error free then it converts the code of program into machine code and then the program can be executed by separate commands.

• An interpreter checks the errors of a program statement by statement. After checking one statement, it converts that statement into machine code and then executes that statement. The process continues until the last statement of program occurs.

• Compiler scans the entire program once and then converts it into machine language which can then be executed by computer's processor. In short compiler translates the entire program in one go and then executes it. Interpreter on the other hand first converts high level language into an intermediate code and then executes it line by line. This intermediate code is executed by another program.

• The execution of program is faster in compiler than interpreter as in interpreter code is executed line by line.

• Compiler generates error report after translation of entire code whereas in case of interpreter once an error is encountered it is notified and no further code is scanned.

Difference between Compiler and Interpreter

Programming Languages:

• Machine Language (Low Level)• Assembly Language• High level Language

Machine Language

• The fundamental language of the computer’s processor, also called Low Level Language.

• All programs are converted into machine language before they can be executed.

• Consists of combination of 0’s and 1’s that represent high and low electrical voltage.

Assembly Language

• A low level language that is similar to machine language.

• Uses symbolic operation code to represent the machine operation code.

High Level Language

• Computer (programming) languages that are easier to learn.

• Uses English like statements.• Examples are C ++, Visual Basic, Pascal,

Fortran and …....

Design Methodologies

• Functional decomposition (Top-Down) –The whole system is characterized by

a single function, and then the function is decomposed into a set of functions in a process of stepwise refinement.

Functional decomposition

The System

Function1 Function2 Function3

Function11 Function12

. . . . . .

. . . . . .

. . . . . .

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Design Methodologies

• Functional composition (bottom-up)– You can have different components of

functions such as that from a function library

– You can compose them into a module with a more significant function.

Functional composition

The System

Function1 Function2 Function3

Function11 Function12

. . . . . .

. . . . . .

. . . . . .

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Left drawer Middle drawer Right drawer