2. Algorithms and Problem Solving in Java.pptx

Algorithms
&
Problem
Solving 1
9/11/2018 BY: AMBROSE NJERU [BSC, MSC COMPUTER SCIENCE

Learn about problem solving skills
Explore the algorithmic approach for problem
solving
Learn about algorithm development
Become aware of problem solving process
Objectives
2

Programming is a process of problem solving.
Problem solving techniques involve:
Analyzing the problem.
Outlining the problem requirements.
Designing steps (algorithm) to solve the
problem
Algorithm:
Step-by-step problem-solving process with
solution achieved in finite amount of time.
A procedure for solving a problem in terms
of the actions to execute and the order in
which these actions execute. 3
Problem Solving

A useful point of view concerning
computers and computer programs in
problem solving is:
A computer is a tool that can be used to
implement a plan for solving a problem.
A computer program is a set of instructions
for a computer. These instructions describe
the steps that the computer must follow to
implement a plan.
An algorithm is a plan for solving a
problem.
A person must design an algorithm.
A person must translate an algorithm
into a computer program. 4
Problem Solving

A computer cannot solve a problem on its
own. One has to provide step by step
solutions of the problem to the computer.
The task of problem solving is not that of
the computer. It is the programmer who
has to write down the solution to the
problem in terms of simple operations
which the computer can understand and
execute.
In order to solve a problem by the
computer, one has to pass though certain
stages or steps and this are:
5
Problem Solving Process

1.Understanding the problem:
 Involves understanding the problem to be solved
in
totally.
 Before the next stage or step, one should be
absolutely
sure about the objectives of the given problem.
2.Analyzing the problem:
Involves at looking different ways of solving the
problem and evaluating each of them, after
understanding thoroughly the problem to be
solved.
The idea here is to search an appropriate solution
to the problem under consideration. The end
6

3.Developing the solution:
 Here the overview of the sequence of
operations that was the result of analysis stage
is expanded to form a detailed step by step
solution to the problem under consideration.
4. Coding and Implementation:
 The last stage of the problem solving is the
conversion of the detailed sequence of operations
in to a language that the computer can
understand.
 Each step is converted to its equivalent
instruction or instructions in the computer
language that has been chosen for the
implementation.
7

The idea behind the computer program.
Stays the same independent of:
Which kind of hardware it is running on
Which programming language it is written in
Solves a well-specified problem in a general
way.
Is specified by:
Describing the set of instances (input) it
must work on.
Describing the desired properties of the
output.
8
What ’s in an
Algorithm?

 Before a computer can perform a task, it
must have an algorithm that tells it what
to do.
Informally: “An algorithm is a set of
steps that
define how a task is performed.”
Formally: “An algorithm is an ordered
set of unambiguous executable steps,
defining a terminating process.”
 Ordered set of steps: structure!
Executable steps: doable!
Unambiguous steps: follow the
directions! 9
What ’s in an
Algorithm?

 Correct: Always returns the desired output
for all legal instances of the problem.
 Unambiguous: Not open to more than one
presentation.
 Precise: Marked by exactness and
accuracy of expression or detail.
 Efficient: Achieving maximum productivity
with minimum wasted effort or expense. Can
be measured in terms of time and space. Time
tends to be more important.
10
Properties of Algorithms

Finiteness: An algorithm must terminate in a
finite
number of steps.
Effectiveness: Each step must be effective, in
the sense that it should be primitive easily
convert able into program statement) can be
performed exactly in a finite amount of time.
Generality: The algorithm must be
complete in itself so that it can be used to
solve problems of a specific type for any
input data.
Input/output: Each algorithm must take zero,
one or more quantities as input data produce
11
Properties of Algorithms

Every problem solution starts with a plan.
That plan is called an algorithm.
 The development of an algorithm (a plan)
is a key
step in solving a problem.
 Once we have an algorithm, we can translate
it into a computer program in some
programming language.
 Algorithm development process consists
of five major steps:
Algorithm Development Process
12

Step 1: Obtain a description of the problem.
 This step starts with the developer
(someone who finds a way to solve the
problem) creating an algorithm that will
solve the client's problem.
 The client (someone who wants to find a
solution to a problem) is responsible for
creating a description of the problem.
During problem description, its common to
find one or more of the following types of
defects:
 The description relies on unstated
assumptions,
13

During problem description, its common to
find one or more of the following types of
defects:
 The description relies on unstated
assumptions,
 The description is ambiguous,
 The description is incomplete, or
 The description has internal contradictions.
 These defects are seldom due to carelessness
by the client but it’s developer's responsibility
to identify defects in the description of a
problem, and to work with the client to
remedy those defects.
14

Step 2: Analyze the problem.
 The purpose of this step is to determine both
the starting and ending points for solving the
problem.
When determining the starting point, we
should
start by seeking answers to the following
questions:
What data are available?
Where is that data?
What formulas pertain to the problem?
What rules exist for working with the data?
15

When determining the ending point, we need
to describe the characteristics of a solution. In
other words, how will we know when we're
done? Asking the following questions often
helps to determine the ending point:
What new facts will we have?
What items will have changed?
What changes will have been made to
those items?
What things will no longer exist?
16

Step 3: Develop a high-level algorithm.
 An algorithm is a plan for solving a
problem, but
plans come in several levels of detail.
It's usually better to start with a high-
level algorithm that includes the
major part of a solution, but leaves the
details until later.
An everyday example to demonstrate a
high-level algorithm would be:
 Problem: I need a send a birthday card to my
brother, Mark.
 Analysis: I don't have a card. I prefer to buy
30

 High-level algorithm:
Go to a store that sells greeting
cards Select a card
Purchase a
card Mail the
card
 This algorithm is satisfactory for daily use,
but it lacks details that would have to be
added if it were
for a computer to carry out the solution.
These details include answers to
questions such as:
 "Which store will I visit?"
 "How will I get there; walk, take a bus, 18

Step 4: Refine the algorithm by adding
more detail.
A high-level algorithm shows the major
steps that
need to be followed to solve a problem.
 Our goal is to develop algorithms that will lead
to computer programs, we need to consider the
capabilities of the computer and provide
enough detail so that someone else could use
your algorithm to write a computer program
that follows the steps in your algorithm.
19

In every problem, we adjust the level of detail
to
match the ability of the programmer.
Most of our programs will move from a high-
level to a detailed algorithm in a single step,
but this is not always reasonable. For larger,
more complex problems, it is common to go
through this process several times, developing
intermediate level algorithms as we go.
 This technique of gradually working from a
high- level to a detailed algorithm is often
called stepwise refinement, which is the
process for developing a detailed algorithm by
gradually adding detail to a high-level
20

Step 5: Review the algorithm.
Involves working through the algorithm step by
step to determine whether or not it will solve
the problem.
 The following questions can be asked whenever
we
review an algorithm:
 Does this algorithm solve a very specific
problem or does it solve a more general
problem? If it solves a very specific problem,
should it be generalized?
 For example, an algorithm that computes the
area of a circle having radius 5.2 meters (formula
π*5.22) solves a very specific problem, but an
21

Can this algorithm be simplified?
One formula for computing the perimeter of a
rectangle is:
length + width + length + width
A simpler formula would be:
2.0 * (length + width)
22

Is this solution similar to the solution of
another problem? How are they alike? How
are they different?
For example, consider the following two
formulae:
Rectangle area = length * width
Triangle area = 0.5 * base * height
Similarities: Each computes an area.
Each multiplies two measurements.
Differences: Different measurements are
used. The triangle formula contains 0.5.
Hypothesis: Perhaps every area formula
involves multiplying two measurements.
23

A single algorithm can be represented in
many ways:
Formulas: F = (9/5)C + 32
Words: Multiply the Celsius by 9/5 and add
32.
Flow Charts.
Pseudo-code – is an informal language that
helps programmers develop algorithms.
In each case, the algorithm stays the same;
the implementation differs!
Representation of Algorithms
24

A flow chart is a step by step diagrammatic
representation of the logic paths to solve a
given problem.
 Or a visual or graphical representation of
an
algorithm.
 The flowcharts are pictorial representation of
the methods to be used to solve a given
problem and help a great deal to analyze the
problem and plan its solution in a systematic
and orderly manner.
A flowchart when translated in to a proper
computer
Flow Charts
25

1. The flowchart shows the logic of a
problem displayed in pictorial fashion
which felicitates easier checking of an
algorithm.
2. The Flowchart is a good means of
communication to other users. It is also a
compact means of recording an algorithm
solution to a problem.
3. The flowchart allows the problem solver to
break the problem into parts. These parts
can be connected to make a master chart.
4. The flowchart is a permanent record of the
solution
Advantages of Flow Charts
26

 The following symbols are used when
drawing flowcharts as per conventions
followed by International Standard
Organization (ISO).
1. Oval: Rectangle with rounded sides is
used to
indicate either START/STOP of the
program.
2. Input and output indicators:
Parallelograms are used to represent input
and output operations. Statements like
INPUT, READ and PRINT are represented in
Flow Charts Symbols
27

3. Process Indicators: Rectangle is used to
indicate any set of processing operation such
as for storing arithmetic operations.
4. Decision Makers: The diamond is used for
indicating the step of decision making and
therefore known as decision box. Decision
boxes are used to test the conditions or ask
questions and depending upon the answers,
the appropriate actions are taken by the
computer.
Flow Charts Symbols
28

5. Flow Lines: Flow lines indicate the direction
being followed in the flowchart. Every line
must have an arrow on it to indicate the
direction.
6. On- Page connectors: Circles are used to join
the different parts of a flowchart. In a
complicated problems, a flowchart may run
in to several pages. The parts of the flowchart
on different pages are to be joined with each
other. The parts to be joined are indicated by
the circle.
Flow Charts Symbols
20

7. Off-page connectors: This connector
represents a break in the path of flowchart
which is too large to fit on a single page. It is
similar to on-page connector. The connector
symbol marks where the algorithm ends on
the first page and where it continues on the
second.
Flow Charts Symbols
30

Draw a flowchart for adding the integers from
1 to 50
and print the sum.
Start
sum = 0
n = 1
is n>50?
No
Flow Charts - Example
sum =
sum+n
n = n+1
Prin
t
Su
m
Sto
p
31

Pseudocode is like a programming language
but its rules are less stringent.
Written as a combination of English and
programming constructs.
Based on selection (if, switch) and
iteration (while, repeat) constructs in
high-level programming languages.
Pseudocode does not execute on computers.
Rather, it helps the programmer "think out" a
program before attempting to write it in a
programming language but designed using
these high level language primitives.
Pseudocode
32

Example: The sequential search
algorithm in pseudocode
Pseudocode
33

Example Algorithm
Suppose we want to find the average of three
numbers, the algorithm (pseudo code) is as
follows:
Step 1: Start
Step 2: Get the first number (e.g. 32)
Step 2: Get the second number (e.g. 27)
Step 3: Get the third number (e.g. 100)
Step 4: Add the three numbers together to
calculate the total (e.g. 159)
Step 5: Divide the total by 3 to calculate the
average (e.g. 53)
Step 6: Print the average of the three numbers.
Step 7: Stop
34

Example Algorithm
The flow chart to find the average of three
numbers, will be as follows:
35

Problem-Solving Execution Cycle
TUESDAY, SEPTEMBER 22,
2015
Computer
By: Ambrose Njeru [BSc,
Msc 3

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