ALGORITHMS AND FLOWCHARTS

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

Flowchart Symbols
Basic
Oval
Parallelogram
Rectangle
Diamond
Hybrid
Name Symbol Use in Flowchart
Denotes the beginning or end of the program
Denotes an input operation
Denotes an output operation
Denotes a decision (or branch) to be made.
The program should continue along one of
two routes. (e.g. IF/THEN/ELSE)
Denotes a process to be carried out
e.g. addition, subtraction, division etc.
Flow line Denotes the direction of logic flow in the program

Example
PRINT
“PASS”
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
START
Input
M1,M2,M3,M4
GRADE(M1+M2+M3+M4)/4
IS
GRADE<5
0
PRINT
“FAIL”
STOP
Y
N

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
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
Flowchart

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  L x W
Print
A
STOP

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

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
 Algorithm:
 Step 1: Input a, b, c
 Step 2: d  sqrt ( )
 Step 3: x1  (–b + d) / (2 x a)
 Step 4: x2  (–b – d) / (2 x a)
 Step 5: Print x1, x2
START
Input
a, b, c
d  sqrt(b x b – 4 x a x c)
Print
x1 ,x2
STOP
x1 (–b + d) / (2 x a)
X2  (–b – d) / (2 x a)
4
b b a c
   

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
is
A>B
Print
B
Print
A
Y N

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
print A
else
print B
endif
is
A>B
Print
B
Print
A
Y N

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 6
 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 6
MAX  VALUE1
Print
“The largest value is”,
MAX
STOP
Y N
START
Input
VALUE1,VALUE2
MAX  VALUE2
is
VALUE1>VALUE2

LOOPS
 Computers are particularly well suited to
applications in which operations are
repeated many times.
 If the same task is repeated over and over
again a loop can be used to reduce
program size and complexity

Example 7: Write an algorithm and
draw a flowchart to calculate 24 .
 Algorithm:
 Step 1: Base  2
 Step 2: Product  Base
 Step 3: Product  Product * Base
 Step 6: Print Product

Flowchart
START
Product  Base
Print
Product
STOP
Product  Product * Base
Base2

 Question: What happens if you want to
calculate 2 to the power of 1000?
 Answer: Use a LOOP (repeated execution
of the same set of instructions)

Example 8:
 Write an algorithm and draw a flowchart to
calculate 24 using a loop approach? Verify
your result by a trace table.

Algorithm:
Step 1: Base  2
Step 2: Power  4
Step 3: Product  Base
Step 4: Counter  1
Step 5: While Counter < Power
Repeat Step 5 through step 7
Step 6: Product  Product * Base
Step 7: Counter  Counter +1
Step 8: Print Product

START
Product  Base
Counter  1
Print
Product
STOP
Y
is
Counter < Power
Counter  Counter + 1
N
Base  2
Power 4

TRACING
BASE POWER PRODUCT COUNTER COUNTER < POWER
STEP 1: 2 ? ? ? ?
STEP 2: 2 4 ? ? ?
STEP 3: 2 4 2 ? ?
STEP 4: 2 4 2 1 T
STEP 5: 2 4 2 1 T
STEP 6: 2 4 2x2=4 1 T
STEP 7: 2 4 4 1+1=2 T
STEP 5: 2 4 4 2 T
STEP 6: 2 4 4x2=8 2 T
STEP 7: 2 4 8 2+1=3 T
STEP 5: 2 4 8 3 T
STEP 6: 2 4 8x2=16 3 T
STEP 7: 2 4 16 3+1=4 F
STEP 5: 2 4 16 4 F
STEP 8: print 16.
Step 1: Base  2
Step 2: Power  4
Step 3: Product  Base
Step 4: Counter  1
Step 5: While Counter < Power
Repeat Step 5 through
step 7
Step 6: Product  Product *
Base
Step 7: Counter  Counter +1
Step 8: Print Product

 Example 10: Write down an algorithm and
draw a flowchart to find and print the
largest of three numbers. Read numbers
one by one. Verify your result by a trace
table. (Use 5, 7, 3 as the numbers read)

Algorithm
 Step 1: Input N1
 Step 2: Max  N1
 Step 4: If (N2>Max) then
Max = N2
endif
 Step 6: If (N3>Max) then
Max = N3
endif
 Step 7: Print “The largest number is:”,Max

Flowchart &
Tracing
START
INPUT
N1
MAXN1
INPUT
N2
N2>MAX
MAXN2
INPUT
N3
MAXN3
Print
“Largest
Number is”,
MAX
STOP
N3>MAX
N
Y
N
Y
N1 N2 N3 Max N2>Max N3>Max
Step1: 5 ? ? ? ? ?
Step 2: 5 ? ? 5 ? ?
Step 3: 5 7 ? 5 T ?
Step 4: 5 7 ? 7 T ?
Step 5: 5 7 3 7 F F
Step 6: 5 7 3 7 F F
Step 8: Print  Largest Number is 7

 Example 11: Write down an algorithm and
draw a flowchart to find and print the
largest of N (N can be any number)
numbers. Read numbers one by one.
Verify your result by a trace table.
(Assume N to be 5 and the following set to
be the numbers {1 4 2 6 8 })

Algorithm:
 Step 1: Input N
 Step 2: Input X
 Step 3: Max  Current
 Step 4: Counter 1
 Step 5: While (Counter < N)
Repeat steps 5 through 8
 Step 6: Counter  Counter + 1
 Step 7: Input X
 Step 8: If (X > Max) then
Max  X
endif
 Step 9: Print Max

N X Max Cou
nter
Count
er < N
Next >
Max
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Step 8
Step 5
Step 6
Step 7
Step 8
Step 5
Step 6
Step 7
Step 8
Step 5
Step 6
Step 7
Step 8
Step 5
Step 9
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
1
1
1
1
1
1
4
4
4
4
2
2
2
2
6
6
6
6
8
8
8
1
1
1
1
1
4
4
4
4
4
4
4
4
6
6
6
6
8
8
8
output
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
T
T
T
T
T
T
T
T
T
T
T
T
T
T
F
F
F
F
T
F
F
F
F
F
F
T
T
F
F
T
T
F
START
Input
N, X
Max  X
Print
Max
STOP
Y
Counter < N
N
Counter 1
Counter  Counter +1
Input
X
X>Max
Y
N
Max  X
1
2
3
4
5
6
7
8
9
Tracing
How many times will steps 4, 6, and 7 be executed?

Do Loops
 It is convenient to introduce a special type
of loop that is headed by a special
macroinstructions.
 This terminology comes from FORTRAN ,
although many programming languages
have this type of loop.

 For example :
BASIC
DO K=1 to N
{body of loop}
END;
 FORTRAN
Do n K=1 , N
{body of loop}
n CONTIOUE

 Example : A company has 80
employees give a flowchart that
 finds the average salary and the number
of employees earning above the average
salary. Observe that the salaries are read
into an array, SALARY. Next, the average
salary, AVG, is calculated.
 Then each salary , SALARY(K), is
compared with AVG to obtain the number
NUM of salaries grater than AVG.

 Prob. 1. Write an algorithm and draw a flowchart to
print the square of all numbers from 1 to10.
print the SUM of numbers from LOW to HIGH. Test
with LOW=3 and HIGH=9.
print all numbers between LOW and HIGH that are
divisible by NUMBER.
 Prob. 4. Draw a flowchart for a program that reads
10 numbers from the user and prints out their sum,
and their product.

count and print all numbers from LOW to HIGH by
steps of STEP. Test with LOW=0 and HIGH=100 and
STEP=5.
print the multiplication table for 6's. i.e.
---- 1  6 = 6
---- 2  6 = 12
…
---- 12  6 = 72
 Prob. 7. Write an algorithm and draw a flowchart that
will find and print the product of 3 numbers.


 Prob. 8. Write an algorithm and draw a
flowchart that will find and print
 The factorial of NUMBER is FACTORIAL.
 Test the flowchart for NUMBER=5.

ALGORITHMS AND FLOWCHARTS

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