The document outlines problem-solving algorithms and flowcharts, describing their construction using standardized symbols and connections. It provides examples of decision structures, nested ifs, and loops within algorithms, explaining how to calculate grades, areas, and bonus payments. Various pseudocode examples clarify the algorithmic logic for each scenario, enhancing understanding of flowcharting and algorithm design.

1. Problem Solving
ALGORITHMS AND FLOWCHARTS

2. Flowchart
 Flowchart is a pictorial representation of an algorithm
 Uses symbols (boxes of different shapes) that have
standardized meanings to denote different types
of instructions
 Actual instructions are written within the boxes
 Boxes are connected by solid lines having arrow marks
to indicate the exact sequence in which the instructions
are to be executed
 Process of drawing a flowchart for an algorithm is called
flowcharting

3. Basic Flowchart Symbols
Terminal Processing
Decision
Input/Output
Flow lines Connectors

4. FLOWCHART
 Example 2: Draw flowchart to add two numbers

5. Pseudocode
STAR
T
Input
Lft
Lcm Lft x 30
STOP
Flowchart
Print
Lcm
 Step 1: Start
 Step 2: Input
Lft
 Step 3: Lcm Lft x
30
 Step 4: Print Lcm
 Step 5: End

6. DECISION STRUCTURES
Y N
Is
condition
true
Process 1 Process 2
Conditional/Decision programing – a structure which requires a
decision for any lines of code to be executed.

7. Decision Structure: Pseudocode
 IF–THEN–ELSE STRUCTURE
 The structure is as follows:
IF condition is TRUE THEN
Process step(s) 1
ELSE
Process step(s) 2
END IF

8. 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
Print A Print B

9. Decision Structure flowchart
Is I = 10?
No
Yes
(a) A two-way branch decision. (b) A three-way branch decision.
A > B
A = B
A < B Compare
A & B

10. PSEUDOCODE & ALGORITHM
 Example 3: Write an algorithm and draw
flowchart to determine a student’s final grade
and indicate whether it is passing or failing if its
below 50. The final grade is calculated as the
average of four marks.

11. PSEUDOCODE & ALGORITHM
ALGORITHM:
 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”

12. PSEUDOCODE & ALGORITHM
Pseudo code:
Step 1:
Step 2:
Step 3:
Input M1,M2,M3,M4
GRADE (M1+M2+M3+M4)/4
if (GRADE < 50) then
Print “FAIL”
else
Print “PASS”
endif

13. EXAMPLE
Input M1,M2,M3,M4
Step 1:
Step 2:
Step 3:
GRADE (M1+M2+M3+M4)/4
if (GRADE <50) then
Print “FAIL”
else
Print “PASS”
endif
STAR
T
Input
M1,M2,M3,M4
GRADE (M1+M2+M3+M4)/4
IS
GRADE<5
0
PRINT
“FAIL
”
STOP
Y
N
PRINT
“FAIL”
PRINT
“PASS”

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

15. MAX VALUE1
STOP
Y N
START
Input
VALUE1,VALUE
2
MAX VALUE2
is
VALUE1>VALUE2
Print
“The largest value is”,
MAX

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

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

18. 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

19. LOOP LOGIC STRUCTURE

20. Example
 A student appears in an examination, which consists of
total 10 subjects, each subject having maximum
marks of 100.
 The roll number of the student, his/her name, and the
marks obtained by him/her in various subjects are
supplied as input data.
 Draw a flowchart for the algorithm to calculate the
percentage marks obtained by the student in this
examination and then to print it along with his/her roll
number and name.

21. Example (Algorithm)
Step 1: Start
Step 2: read the input data
Step 3: compute total marks by adding marks of each subject
Step 4: compute percentage by dividing total by 100
Step 5: write percentage, roll number and name of student
Step 6: end

22. Read input data
Add marks of all
subjects giving Total
Percentage = Total / 10
Write output data
Stop
Example Flowchart
(contd…)
Start

23. 50 students of a class appear in the examination of
above Example .
Draw a flowchart for the algorithm to calculate and print
the percentage marks obtained by each student along
with his/her roll number and name.
Flowchart

24. Example (Algorithm)
Step 1: Start
Step 2: read the input data
Step 3: compute total marks by adding marks of each subject
Step 4: compute percentage by dividing total by 100
Step 5: write percentage, roll number and name of student
Step 6: go to step 2.

25. Flowchart for the solution
of Example 4 with an
infinite (endless) process
loop.
Start
Add marks of all
subjects giving Total
Percentage = Total / 10
Write output data
Read input data
Flowchart
(contd…)

26. Example (Algorithm)
Step 1: Start
Step 2: count  0
Step 3: read the input data
Step 4: compute total marks by adding marks of each subject
Step 5: compute percentage by dividing total by 100
Step 6: write percentage, roll number and name of student
Step 7: count  count +1.
Step 8: if count = 50
stop
else
go to step 3
end if

27. Start
Read input data
Count = 0
Add marks of all subjects giving Total
Percentage = Total/10
Write output data
Add 1 to Count
No
Is Count = 50?
Yes
Flowchart (Example)
(contd…)
Stop

28. Many students of a class appear in the examination of
above Example .
Draw a flowchart for the algorithm to calculate and print
the percentage marks obtained by each student along
with his/her roll number and name.
Flowchart

29. Example (Algorithm)
Step 1: Start
Step 2: read the input data
Step 3: If Rollno = 0?
then stop
else
compute total marks by adding marks of each subject
compute percentage by dividing total by 100
print percentage, roll number & name of student
go to step 2.

30. Example (Algorithm)
Step 1: Start
Step 2: repeat
read the input data
compute total marks by adding marks of each subject
compute percentage by dividing total by 100
print percentage, roll number & name of student
until Rollno = 0

31. Flowchart
Here the process loop
is terminated by
detecting a special
non-data record.
Stop
Yes
Start
Add marks of all subjects
giving Total
Percentage = Total / 10
No
Is Rollno = 0000000?
Read input data
Write output data
(contd…)

32. PRACTICE QUESTIONS:

33. EXAMPLE
Write an algorithm and draw a flowchart
that will read the two sides of a rectangle
and calculate its area.

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

35. Pseudocode
 Step 1:
 Step 2:
 Step 3:
Input W,L
A L x W
Print A
STAR
T
Input
W,
L
A L x
W
STOP
Print A

36. EXAMPLE
 Write an algorithm and draw a flowchart that
will calculate the roots of a quadratic equation
ax2
bx c 0

Hint: d = sqrt ( b2
4ac ), and the roots
are:
x1 = (–b + d)/2a and x2 = (–b – d)/2a

37. Pseudo code:
 Input the coefficients (a, b, c) of the quadratic
equation
 Calculate d
 Calculate x1
 Calculate x2
 Print x1 and x2

38.  Algorithm:
Input a, b, c
 Step 1:
 Step 2:
 Step 3:
 Step 4:
 Step 5: Print x1, x2
d sqrt ( b b 4 a c )
x1 (–b + d) / (2 x a)
x2 (–b – d) / (2 x a)
STAR
T
Input
a, b,
c
d sqrt(b x b – 4 x a x
c)
STOP
1
x (–b + d) / (2 x
a)
X2 (–b – d) / (2 x a)
Print
x1 ,x2

39. EXAMPLE
 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).

40. 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
else if (OVERTIME–
(2/3)*ABSENT > 20) then
PAYMENT
30
else if (OVERTIME–
(2/3)*ABSENT > 10) then
PAYMENT 20
else
PAYMENT 10

41. Bonus Schedule
OVERTIME – (2/3)*ABSENT Bonus Paid
>40 hours $50
>30 but 40 hours $40
>20 but 30 hours $30
>10 but 20 hours
10 hours
$20
$10