Algorithmsandflowcharts1

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
Input
M1,M2,M3,M4
Step 3: if (GRADE <50) then
Print “FAIL”
else
GRADE←(M1+M2+M3+M4)/4 Print “PASS”
endif
N IS Y
GRADE<5
0

PRINT PRINT
“PASS” “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 START

 Step 1: Input Lft
Input

 Step 2: Lcm ← Lft x 30 Lft

 Step 3: Print Lcm 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 START

 Step 1: Input W,L Input
W, L
 Step 2: A ← L x W
 Step 3: Print A 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:
Input
 Step 1: Input a, b, c a, b, c
 Step 2: d ← sqrt ( b × b − 4 × a × c )
 Step 3: x1 ← (–b + d) / (2 x a) d ← sqrt(b x b – 4 x a x c)
 Step 4: x2 ← (–b – d) / (2 x a)
x1 ←(–b + d) / (2 x a)
 Step 5: Print x1, x2
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 N
is
A>B

Print Print
A 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
print A is
A>B
else
print B Print
A
Print
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 N
VALUE1>VALUE2

MAX ← VALUE1 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
 Write and algorithm and draw a flowchart
to
a) read an employee name (NAME),
overtime hours worked (OVERTIME),
hours absent (ABSENT) and
b) determine the bonus payment
(PAYMENT).

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

>40 hours $50
>30 but ≤ 40 hours $40
>20 but ≤ 30 hours $30
$20
>10 but ≤ 20 hours
$10
≤ 10 hours

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?

Algorithmsandflowcharts1

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