11 Unit 1 Problem Solving Techniques

4.1 Unit 1:
Programming and Computational Thinking (PCT-1)
XI
Computer Science (083)
Board : CBSE
Courtesy CBSE

4.1 Unit I
Programming and Computational
Thinking (PCT-1)
(80 Theory + 70 Practical)
Praveen M Jigajinni
Prepared by
Courtesy CBSE
DCSc & Engg, PGDCA,ADCA,MCA.MSc(IT),Mtech(IT),MPhil (Comp. Sci)
Department of Computer Science, Sainik School Amaravathinagar
Cell No: 9431453730 Email – praveenkumarjigajinni@gmail.com

 able to define problem;
 able to define algorithm;
 write algorithms for simple problems;
 explain properties of an algorithm;
 the meaning of flowchart;
 explain the need of flow chart;
 explain different symbols used in flow chart;
 draw flow chart for simple problems; and
convert a flow chart into an algorithm and
vice versa.
ALGORITHM AND FLOW CHART
OBJECTIVES

Intelligence is one of the key
characteristics which differentiate a human
being from other living creatures on the
earth. Basic intelligence covers day to day
problem solving and making strategies to
handle different situations which keep
arising in day to day life.
INTRODUCTION

One person goes Bank to withdraw money.
After knowing the balance in his account,
he/she decides to withdraw the entire
amount from his account but he/she has to
leave minimum balance in his account.
INTRODUCTION

Here deciding about how much amount
he/she may withdraw from the account is
one of the example of the basic
intelligence. During the process of solving
any problem, one tries to find the
necessary steps to be taken in a sequence.
INTRODUCTION

What is Algorithm?
Algorithm can be defined as: “A sequ
ence of activities to be processed for getti
ng desired output from a given input.”

What is Algorithm?
Webopedia defines an algorithm as:
“A formula or set of steps for solving a
particularproblem. To be an algorithm, a set
of rules must be unambiguous and have a cl
ear stopping point”.

MUHAMMAD IBN MUSA AL-KHWARIZMI
Muḥammad ibn Mūsā al-
Khwārizmī (Persian: ‫محمد‬‫بن‬‫موسى‬
‫;خوارزمی‬ c. 780 – c. 850),
Formerly Latinized as Algoritmi, was
a Persian scholar who produced
works in mathematics, astronomy,
& geography under the patronage
of the Caliph Al-Ma'mun of
the Abbasid Caliphate.
Around 820 AD he was appointed as the astronomer
and head of the library of the House of
Wisdom in Baghdad.

PROPERTIES OF ALGORITHM
Donald Ervin Knuth has given a list of five
properties for an algorithm, these
properties are:
1) FINITENESS
2) DEFINITENESS
3) INPUT
4) OUTPUT
5) EFFECTIVENESS

1) FINITENESS:
An algorithm must always terminate
after a finite number of steps. It
means after every step one reach
closer to solution of the problem and
after a finite number of steps
algorithm reaches to an end point.

2) DEFINITENESS
Each step of an algorithm must be
precisely defined. It is done by well
thought actions to be performed at
each step of the algorithm. Also the
actions are defined unambiguously for
each activity in the algorithm.

3) INPUT
Any operation you perform need
some beginning value/quantities
associated with different activities in
the operation. So the value/quantities
are given to the algorithm before it
begins.

4) OUTPUT:
One always expects output/result
(expected value/quantities) in terms of output
from an algorithm. The result may be obtained
at different stages of the algorithm. If some
result is from the intermediate stage of the
operation then it is known as intermediate
result and result obtained at the end of
algorithm is known as end result. The output
is expected value/quantities always have a
specified relation to the inputs.

5) EFFECTIVENESS:
Algorithms to be developed/written
using basic operations. Actually operations
should be basic, so that even they can in
principle be done exactly and in a finite
amount of time by a person, by using paper
and pencil only.

Any algorithm should have all these five
properties otherwise it will not fulfil the
basic objective of solving a problem in finite
time. As you have seen in previous
examples, every step of an algorithm puts
you closer to the solution

ADVANTAGES OF ALGORITHM
The use of algorithms provides a number of
advantages. One of these advantages is in
the development of the procedure itself,
which involves identification of the
processes, major decision points, and
variables necessary to solve the problem.
Developing an algorithm allows and even
forces examination of the solution process
in a rational manner.

Identification of the processes and decision
points reduces the task into a series of
smaller steps of more manageable size.
Problems that would be difficult or
impossible to solve wholesale can be
approached as a series of small, solvable
sub problems. The required specification
aids in the identification and reduction of
subconscious biases. By using an algorithm,
decision-making becomes a more rational
process.

In additional to making the process more
rational, use of an algorithm will make the
process more efficient and more consistent.
Efficiency is an inherent result of the
analysis and specification process.
Consistency comes from both the use of the
same specified process and increased skill in
applying the process. An algorithm serves
as a mnemonic device and helps ensure
that variables or parts of the problem are
not ignored.

Presenting the solution process as an
algorithm allows more precise
communication. Finally, separation of the
procedure steps facilitates division of labor
and development of expertise.
A final benefit of the use of an algorithm
comes from the improvement it makes
possible. If the problem solver does not
know what was done, he or she will not
know what was done wrong.

As time goes by and results are compared
with goals, the existence of a specified
solution process allows identification of
weaknesses and errors in the process.
Reduction of a task to a specified set of
steps or algorithm is an important part of
analysis, control, and evaluation.

DISADVANTAGES OF ALGORITHM
One disadvantage of algorithms is that they
always terminate, which means there are
some computational procedures—occasionally
even useful ones—which are not algorithms.
Furthermore, all computational procedures,
whether they terminate or not, can only give
computable results, so you cannot, for
example, design a program which determines a
busy beaver number more quickly than could
be done by actually running the associated
types of Turing machines.

ALGORITHM EXAMPLES
Let us take one simple day-to-day example
by writing algorithm for making, “Maggi
Noodles‟ as a food.
Step 1: Start
Step 2: Take pan with water
Step 3: Put pan on the burner
Step 4: Switch on the gas/burner
Step 5: Put magi and masala
Step 6: Give two minutes to boil
Step 7: Take off the pan
Step 8: Take out the magi with the help of
fork/spoon
Step 9: Put the maggi on the plate and serve it
Step 10: Stop.

ALGORITHM EXAMPLES
Write an algorithm to print “Good Morning‟
Step 1: Start
Step 2: Print “Good Morning‟
Step 3: Stop

ALGORITHM EXAMPLES
Write an algorithm to find area of a rectangle.
Step 1: Start
Step 2: Take length and breadth and
store them as L and B?
Step 3: Multiply by L and B and store it
in area
Step 4: Print area
Step 5: Stop

ALGORITHM EXAMPLES
Write an algorithm to check whether he is
eligible to vote? (more than or equal to 18
years old).
Step 1: Start
Step 2: Take age and store it in age
Step 3: Check age value, if age >= 18 then go
to step 4 else step 5
Step 4: Print “Eligible to vote” and go to
step 6
Step 5: Print “Not eligible to vote”
Step 6: Stop

ALGORITHM EXAMPLES
Write an algorithm to check whether given
number is +ve, -ve or zero.
Step 1: Start
Step 2: Take any number and store it in n.
Step 3: Check n value, if n > 0 then go to
step 5 else go to step 4
Step 4: Check n value, if n < 0 then go to
step 6 else go to step 7

ALGORITHM EXAMPLES
Write an algorithm to check whether given
number is +ve, -ve or zero.
Step 5: Print “Given number is +ve”and go
to step 8
Step 6: Print “Given number is -ve” and go
to step 8
Step 7: Print “Given number is zero”
Step 8: Stop

The flowchart is a diagram which visually pre
sents the flow of data through processing
systems. This means by seeing a flow chart o
ne can know the operations performed and
the sequence of these operations in a syste
m. Algorithms are nothing but sequence of
steps for solving problems. So a flow chart ca
n be used for representing an algorithm. A
flowchart, will describe the operations
(and in what sequence) are required
to solve a given problem.
FLOWCHART

A flowchart is a type of diagram that
represents an algorithm, workflow or
process. The flowchart shows the steps as
boxes of various kinds, and their order by
connecting the boxes with arrows. This
diagrammatic representation illustrates a
solution model to a given problem.
Flowcharts are used in analyzing, designing,
documenting or managing a process or
program in various fields.
FLOWCHART

BUILDING BLOCKS
OF
FLOW CHART
OR
COMMON SYMBOLS
OF
FLOW CHART

The American National Standards
Institute (ANSI) set standards for flowcharts
and their symbols in the
1960s. The International Organization for
Standardization(ISO) adopted the ANSI
symbols in 1970. The current standard was
revised in 1985. Generally, flowcharts flow
from top to bottom and left to right.
BUILDING BLOCKS OF FLOW CHART

ANSI/ISO
Shape
Name Description
Flowline
(Arrowhead)
Shows the process's order of
operation. A line coming from
one symbol and pointing at
another. Arrowheads are
added if the flow is not the
standard top-to-bottom, left-
to right.

ANSI/ISO
Shape
Name Description
Terminal
Indicates the beginning and ending
of a program or sub-process.
Represented as a stadium, oval or
rounded (fillet) rectangle. They
usually contain the word "Start" or
"End", or another phrase signaling
the start or end of a process, such as
"submit inquiry" or "receive
product".

ANSI/ISO
Shape
Name Description
Process
Represents a set of operations that
changes value, form, or location of
data. Represented as a rectangle

ANSI/ISO
Shape
Name Description
Decision
Shows a conditional operation that
determines which one of the two
paths the program will take. The
operation is commonly a yes/no
question or true/false test.
Represented as a diamond
(rhombus).

ANSI/ISO
Shape
Name Description
Input /
Output
Indicates the process of inputting
and outputting data, as in entering
data or displaying results.
Represented as a parallelogram

ANSI/ISO
Shape
Name Description
Annotation
(Comment)
Indicating additional
information about a step the
program. Represented as an
open rectangle with a dashed
or solid line connecting it to
the corresponding symbol in
the flowchart.

ANSI/ISO
Shape
Name Description
Predefined
Process
Functions
Shows named process
/Function which is defined
elsewhere. Represented as
a rectangle with double-
struck vertical edges.

ANSI/ISO
Shape
Name Description
On-page
Connector
Pairs of labelled connectors
replace long or confusing
lines on a flowchart page.
Represented by a small
circle with a letter inside.

ANSI/ISO
Shape
Name Description
Off-page
Connector
A labelled connector for
use when the target is on
another page. Represented
as a home plate-
shaped pentagon.

ANSI/ISO
Shape
Name Description
Storage/
Backup
Magnetic Tape used for sec
ondary storage/Backup

ANSI/ISO
Shape
Name Description
Storage/
Backup
Magnetic Disk used for sec
ondary storage/Backup

ADVANTAGES OF USING FLOWCHARTS
As we discussed flow chart is used for
representing algorithm in pictorial form.
This pictorial representation of a
solution/system is having many
advantages. These advantages are as
follows:
1. COMMUNICATION.
2. EFFECTIVE ANALYSIS.
3. DOCUMENTATION OF PROGRAM/SYSTEM.
4. EFFICIENT PROGRAM MAINTENANCE.
5. CODING OF THE PROGRAM.

1. COMMUNICATION:
A Flowchart can be used as a better way of
communication of the logic of a system and
steps involve in the solution, to all concerned
particularly to the client of system.

2. EFFECTIVE ANALYSIS:
A flowchart of a problem can be used for
effective analysis of the problem.

3.DOCUMENTATION OF PROGRAM/
SYSTEM:
Program flowcharts are a vital part of a good
program documentation. Program document is
used for various purposes like knowing the
components in the program, complexity of the
program etc.

4. EFFICIENT PROGRAM
MAINTENANCE:
Once a program is developed and becomes
operational it needs time to time maintenance.
With help of flowchart maintenance become
easier.

5. CODING OF THE PROGRAM:
Any design of solution of a problem is finally
converted into computer program. Writing code
referring the flowchart of the solution become
easy.

LIMITATIONS OF USING FLOWCHARTS
1) COMPLEXITY OF LOGIC: If program logic is
complex then flowchart of the program
becomes complicated.
2) ALTERATIONS AND MODIFICATIONS IN LOGIC:
any alterations in the program logic may require
redrawing of flowchart completely.
3) REUSE IS NOT POSSIBLE: As the flowchart
symbols cannot be typed, always reproduction
of flowchart symbols are required.

FLOWCHART EXAMPLES
Draw a flowchart to find the simple interest.
(Sequence)

FLOWCHART EXAMPLES
Draw a flowchart to find bigger number
among two numbers (selective)

FLOWCHART EXAMPLES
Draw a flow chart to find factorial of any
number.

FLOWCHART - SOLVE IT
Draw a flow chart to print the number from 1
to N.

Draw a flow chart to find biggest number
among N numbers.
FLOWCHART - SOLVE IT

11 Unit 1 Problem Solving Techniques

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