Algorithms and flowcharts

ALGORITHMS AND
FLOWCHARTS
Muhammad Rizwan
rizsoft@gmail.com

ALGORITHMS AND FLOWCHARTS
A typical programming task can be divided into
two phases:
Problem solving phase
produce an ordered sequence of steps that describe
solution of problem
this sequence of steps is called an algorithm

Implementation phase
implement the program in some programming
language

Steps in Problem Solving
First produce a general algorithm (one can use
pseudocode)
Refine the algorithm successively to get step by
step detailed algorithm that is very close to a
computer language.
Pseudocode is an artificial and informal
language that helps programmers develop
algorithms. Pseudocode is very similar to
everyday English.

Pseudocode & Algorithm
Example 1: Write an algorithm to
determine a student’s final grade and
indicate whether it is passing or failing.
The final grade is calculated as the
average of four marks.

Pseudocode:
Input a set of 4 marks
Calculate their average by summing and dividing
by 4
if average is below 50
Print “FAIL”
else
Print “PASS”

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

The Flowchart
(Dictionary) A schematic representation of a sequence of
operations, as in a manufacturing process or computer
program.
(Technical) A graphical representation of the sequence
of operations in an information system or program.
Information system flowcharts show how data flows from
source documents through the computer to final
distribution to users. Program flowcharts show the
sequence of instructions in a single program or
subroutine. Different symbols are used to draw each
type of flowchart.

The Flowchart
A Flowchart
shows logic of an algorithm
emphasizes individual steps and their
interconnections
e.g. control flow from one action to the next

Example
START

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

Input
M1,M2,M3,M4

←
GRADE←(M1+M2+M3+M4)/4

N

IS
GRADE<5
0

PRINT
“PASS”

Y

PRINT
“FAIL”

STOP

Example 2
Write an algorithm and draw a flowchart to
convert the length in feet to centimeter.
Pseudocode:
Input the length in feet (Lft)
Calculate the length in cm (Lcm) by
multiplying LFT with 30
Print length in cm (LCM)

Example 2
Flowchart

Algorithm
Step 1: Input Lft
Step 2: Lcm ← Lft x 30
Step 3: Print Lcm

START

Input
Lft

Lcm ← Lft x 30

Print
Lcm

STOP

Example 3
Write an algorithm and draw a flowchart that
will read the two sides of a rectangle and
calculate its area.
Pseudocode
Input the width (W) and Length (L) of a rectangle
Calculate the area (A) by multiplying L with W
Print A

Example 3
Algorithm
Step 1: Input W,L
Step 2: A ← L x W
Step 3: Print A

START

Input
W, L

A←LxW

Print
A

STOP

Example 4
Write an algorithm and draw a flowchart that
will calculate the roots of a quadratic equation
ax 2 + bx + c = 0
Hint: d = sqrt ( b 2 − 4ac ), and the roots are:
x1 = (–b + d)/2a and x2 = (–b – d)/2a

Example 4
Pseudocode:
Input the coefficients (a, b, c) of the
quadratic equation
Calculate d
Calculate x1
Calculate x2
Print x1 and x2

Example 4
START

Algorithm:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:

Input a, b, c
d ← sqrt ( b × b − 4 × a × c )
x1 ← (–b + d) / (2 x a)
x2 ← (–b – d) / (2 x a)
Print x1, x2

Input
a, b, c

d ← sqrt(b x b – 4 x a x c)
x1 ←(–b + d) / (2 x a)
X2 ← (–b – d) / (2 x a)
Print
x1 ,x2

STOP

DECISION STRUCTURES
The expression A>B is a logical expression
it describes a condition we want to test
if A>B is true (if A is greater than B) we take
the action on left
print the value of A
if A>B is false (if A is not greater than B) we
take the action on right
print the value of B

DECISION STRUCTURES

Y

Print
A

is
A>B

N

Print
B

IF–THEN–ELSE STRUCTURE
The structure is as follows
If condition then
true alternative
else
false alternative
endif

IF–THEN–ELSE STRUCTURE
The algorithm for the flowchart is as
follows:
If A>B then
Y
N
is
print A
A>B
else
Print
Print
print B
A
B
endif

Relational Operators
Relational Operators

Operator

Description

>

Greater than

<

Less than

=

Equal to

≥

Greater than or equal to

≤

Less than or equal to

≠

Not equal to

Example 5
Write an algorithm that reads two values, determines the
largest value and prints the largest value with an
identifying message.
ALGORITHM
Step 1:
Input VALUE1, VALUE2
Step 2:
if (VALUE1 > VALUE2) then
MAX ← VALUE1
else
MAX ← VALUE2
endif
Step 3:
Print “The largest value is”, MAX

Example 5
START

Input
VALUE1,VALUE2

Y

is
VALUE1>VALUE2

MAX ← VALUE1

N

MAX ← VALUE2

Print
“The largest value is”,
MAX
STOP

NESTED IFS
One of the alternatives within an IF–
THEN–ELSE statement
may involve further IF–THEN–ELSE
statement

Example 6
Write an algorithm that reads three
numbers and prints the value of the largest
number.

Example 6
Step 1: Input N1, N2, N3
Step 2: if (N1>N2) then
if (N1>N3) then
MAX ← N1
[N1>N2, N1>N3]
else
MAX ← N3
[N3>N1>N2]
endif
else
if (N2>N3) then
MAX ← N2
[N2>N1, N2>N3]
else
MAX ← N3
[N3>N2>N1]
endif
endif
Step 3: Print “The largest number is”, MAX

Example 6
Flowchart: Draw the flowchart of the
above Algorithm.

Example 7

a)

b)

Write and algorithm and draw a flowchart
to
read an employee name (NAME),
overtime hours worked (OVERTIME),
hours absent (ABSENT) and
determine the bonus payment
(PAYMENT).

Example 7
Bonus Schedule
OVERTIME – (2/3)*ABSENT

Bonus Paid

>40 hours
>30 but ≤ 40 hours
≤ 10 hours

$50
$40
$30
$20
$10

Step 1: Input NAME,OVERTIME,ABSENT
Step 2: if (OVERTIME–(2/3)*ABSENT > 40) then
PAYMENT ← 50
else if (OVERTIME–(2/3)*ABSENT > 30) then
PAYMENT ← 40
PAYMENT ← 30
PAYMENT ←20
else
PAYMENT ← 10
endif
Step 3: Print “Bonus for”, NAME “is $”, PAYMENT

Example 7
Flowchart: Draw the flowchart of the
above algorithm?

Algorithms and flowcharts

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