meljun cortes algorithm funda of algorithm

8/21/2019 Meljun Cortes Algorithm Funda of Algorithm

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Fundamentals of Algorithm

Design and Analysis of Algorithm

* Property of STI

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Definition of algorithm

Importance of studying algorithm

Notion of algorithm

Algorithm design and analysis process

Types of computing problems


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a step-by-step problem-solving procedure,

especially an established, recursive computational

procedure for solving a problem in a finite number

of steps

used in many activities and come in many forms

Examples: instructions for assembling kits,

recipes, steps for processing credit card

approvals, directions to a destination

a well-defined procedure to solve a problem

a fundamental area of computer science


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the study of algorithm and is more than a branch

of computer science

the core of computer, and, in all fairness, can besaid to be relevant to most business and

technology [Har92], p.6.


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Computer programs would not exist without

algorithms.

It is essential in different aspects such as

professional and personal lives.

It is useful in developing analytical skills.

Algorithms can be seen as special kinds of

solution to problems-not answered.


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Instructions: implies that there is something

capable of understanding and following the given

instructions.

Algorithm tells the computer what specific steps to

perform (in what specific order) in order to carry

out a specified task, such as calculating

employee’s paychecks or printing student’s report

cards.


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Problem: must be defined cautiously by describing

the set of instances it must work on

Algorithm: solving the same problem can be

represented with several algorithms

Input: data is read from an input source or device

Output: data is written to an output device

Computer: process the implemented algorithm

thru a computer program


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In a real world, we dealt with algorithm by giving

instructions going to a particular place or following

a recipe cook book.

The example below is an algorithm for giving

instructions in making a small sponge cake:

Method

EggSponge


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Some similarities of the recipe to algorithms used

for programming:

1. Steps 1 to 6 shows a sequence: a series of stepsperformed one after the other.

2. Step 2 shows a reference to a commonly used

task that is specified in detail elsewhere: Follow

method for Egg Sponge from step a to step d.

3. Step c shows repetition: "Beat egg white until stiff"

- something is repeated until some condition ismet.

4. Step 6 shows selection: "Ice with glace or melted

butter icing" - one of two possible actions is taken.


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An algorithm is represented using two common

techniques:

1. Flowchart

2. Pseudocode

Flowchart: a diagrammatic representation that

illustrates the sequence of operations to be

performed to get the solution of a problem.


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Pseudocode a type of structured English that is

used to specify an algorithm.


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Algorithms are procedural solutions to different

types of problem.

Algorithm design and analysis process:

emphasizes an exact, well-defined constructive

procedures that makes computer science distinct

from other disciplines.


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The diagram shows the sequence of steps that

typically goes through in designing and analyzing

an algorithm.


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Understanding the Problem

Understand the problem completely before

designing an algorithm.

Read the problems description carefully and

ask questions if you have any doubts about

the problem, do a few small examples byhand, think about special cases, and ask

questions again if needed.


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Decide on Ascertaining the Capabilities of a

Computational Device

Once you completely understand a problem,

you need to establish the capabilities of the

computational device the algorithm is

intended for.

Sequential algorithms all instructions are

executed one after another, one operation at

a time

Parallel algorithms all instructions are

executed concurrently


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Decide on Choosing between Exact and

Approximate Problem Solving

Exact algorithm: algorithms used to find exact

solutions

Approximation algorithm: algorithms used tofind approximate solutions


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Decide on Deciding on Appropriate Data

Structures

As with all problems in computer science,

there is more than one solution to which data

structure should be used.

Algorithms Data Structures = Programs


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Algorithm Design Techniques

general approach to solving problems

algorithmically that is applicable to a variety of

problems from different areas of computing


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Methods of Specifying an Algorithm

Pseudocode

Flowchart


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Proving an lgorithm’s Correctness

Proving the correctness of an algorithm is

similar to proving a mathematical theorem.

Once an algorithm has been specified, you

have to prove its correctness.

That is, you have to prove that the algorithm

yields a required result for every legitimate

input in a finite amount of time.


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Analyzing an Algorithm

Qualities to be considered in analyzing an

algorithm:

• Correctness

• Efficiency

–Time efficiency: indicates how fastthe algorithms run

–Space efficiency: indicates how much

extra memory the algorithm needs.

• Simplicity

• Generality


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Coding an Algorithm

Algorithms are created to be implemented as

computer programs

A running program provides an additional

opportunity in allowing practical analysis of

the underlying algorithm.

Time efficiency: indicates how fast the

algorithms run

Space efficiency: indicates how much extra

memory the algorithm needs.


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The following are the different types of problems

encountered in designing and analyzing

algorithms:

Sorting

Searching

String processing

Graph problems

Combinatorial problems

Geometrical problems

Numerical problems


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The following are the different types of problems

encountered in designing and analyzing

algorithms:

Sorting: requires to rearrange the items

of a given list in ascending or descending

order.

Searching: deals with finding a given

value called the key in a given list or set.

String processing: deals with non-

numerical that intensifies the interest ofresearchers and computing practitioners

in string-handling algorithms.


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Continuation:

Graph problems: deal with objects and

their connections like determining

whether all of the locations are

connected, visiting all of the locations

that can be reached from a given

location, or finding the shortest path fromone location to another.

Combinatorial problems: most difficult

problems in computing that ask

(explicitly or implicitly) to find acombination of an object such as

permutation, combination or a subset

that satisfies certain constraints and has

some desired property.


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Continuation:

Geometrical problems: deal with

geometric objects such as points, lines

and polygons that can be applied to

computer graphics and robotics.

Numerical problems: involve

mathematical objects of continuous

nature such as solving equations, system

equations, computing definite integrals,

evaluating functions etc


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Algorithm representation: Draw a flowchart and a

pseudocode based on the given problems below.

1. According to Plato, a man should marry a woman

whose age is half his age plus seven years. Draw

a flowchart and write pseudocode that will ask a

man’s age as input and outputs the ideal age of

his wife.

2. Given integer variables num1 and num2 and a

character variable ch, input the values for num1,

num2, and ch (the value of ch can be ‘a’, ‘s’, ‘m’

or ‘d’). Compute the output based on the ff:

if ch = ’a’ perform addition;

if ch = ‘s’ perform subtraction;if ch = ‘m’ perform multiplication; and

if ch = ‘d’ perform division.

3. Enter 10 integer values from 1 to 200. Find how

many of these values fall in the range 1-50, 51-100, 101-150 and 151-200.


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Research for the following topics:

Definition of data structure

Different types of data structure

Types of Linear data structure

Types of Graph data structure

Types of Trees data structure

Note: The research work should be in a printed

copy compiled in a folder with a title page.

meljun cortes algorithm funda of algorithm

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