1. Programming Fundamentals
Lecture-8

2. Programming Fundamentals | Lecture-8
Consider this Example
Find sum of first 5 natural numbers
Programming Fundamentals | Lecture-8

3. Programming Fundamentals | Lecture-8
START
sum = 0
sum = sum + 1
(sum=0)
sum = sum + 2
(sum=1)
sum = sum + 3
(sum=3)
sum = sum + 4
(sum=6)
sum = sum + 5
(sum=10)
DISPLAY sum
(sum=15)
STOP
Programming Fundamentals | Lecture-8

4. Programming Fundamentals | Lecture-8
Consider This
What if we have to find sum of first 50 natural numbers?
Should we write down 50 processing steps?
Programming Fundamentals | Lecture-8

5. What if the numbers are not just 50, they are 1000?
Programming Fundamentals | Lecture-8

6. Programming Fundamentals | Lecture-8
Analyze the Problem
Notice that you are doing the same operation of addition again and again
The only difference is the value which is being added
If we could somehow instruct the computer to repeat certain number of operations for certain number of times, our job will be much more easier
Programming Fundamentals | Lecture-8

7. Programming Fundamentals | Lecture-8
Is this Correct?
START
sum = 0
sum = sum + _
STOP
Programming Fundamentals | Lecture-8

8. Programming Fundamentals | Lecture-8
What is Required?
Your program needs to decide after every repetition that whether further repetition is required or not?
Whether number of repetitions has reached its limit or not?
As the program needs to “decide”, it is clear that we need to use a “decision box”
What will be the basis of decision?
* Only a decision box can divide the order or flow of program into two alternative paths
Programming Fundamentals | Lecture-8

9. Programming Fundamentals | Lecture-8
How to Achieve This?
Need to keep record of number of repetitions (repetitions count)
Make use of a field whose purpose is to keep record of no. of repetitions which are done so far
That field (or repetition count) will become the basis of decision
Hence your program will be able to control the repetitions and will proceed further after the desired no. of repetitions are done
Programming Fundamentals | Lecture-8

10. Sum of 1st 5 natural numbers
START
sum = 0
count = 0
count < 5 No
Yes
count = count + 1
DISPLAY sum
sum = sum + count
STOP
Programming Fundamentals | Lecture-8

11. Programming Fundamentals | Lecture-8
How to Test This?
count = 0
sum = 0
Repetition-1
Repetition-2
Repetition-3
Repetition-4
Repetition-5
decision (count < 5)
0 < 5
1 < 5
2 < 5
3 < 5
4 < 5
count = count + 1 1 2 3 4 5
sum = sum + count 6 10 15
Programming Fundamentals | Lecture-8

12. Power of Computer Programs
Controlled Repetition
Programmers can instruct computers to do certain tasks repeatedly for certain period of time
As the complexity of problems increases, repetition may become more extensive
This way computers prove very useful by performing repeating tasks themselves without the intervention of human beings
Programming Fundamentals | Lecture-8

13. Programming Fundamentals | Lecture-8
Steps to Follow
Which instructions are needed to be repeated?
How many times the repetition is to be done?
Programming Fundamentals | Lecture-8

14. Extending that Example
Find sum of first n natural numbers
Where n can be any number
Programming Fundamentals | Lecture-8

15. Programming Fundamentals | Lecture-8
START
READ n
sum = 0
count = 0
count < n No
Yes
count = count + 1
DISPLAY sum
sum = sum + count
STOP
Programming Fundamentals | Lecture-8

16. Programming Fundamentals | Lecture-8
Another Example
Find factorial of a number
factorial(n) = 1 * 2 * …… * n
Programming Fundamentals | Lecture-8

17. Programming Fundamentals | Lecture-8
START
READ n
fact = 1
count = 0
count < n-1 No
Yes
count = count + 1
DISPLAY sum
fact = fact * (count + 1)
STOP
Programming Fundamentals | Lecture-8

18. Programming Fundamentals | Lecture-8
Testing
count = 0
fact = 1
n = 5
Repetition-1
Repetition-2
Repetition-3
Repetition-4
decision (count < 5)
0 < 5-1
1 < 5-1
2 < 5-1
3 < 5-1
count = count + 1
1 = 0 + 1
2 = 1 + 1
3 = 2 + 1
4 = 3 + 1
fact = fact * (count +1)
2 = 1 * (1 + 1)
6 = 2 * (2 + 1)
24 = 6 + (3 + 1)
120 = 24 * (4 + 1)
Programming Fundamentals | Lecture-8

19. Programming Fundamentals | Lecture-8
Try this Yourself
Find 220
Hint: Multiply 2 by itself, 19 times
Find xy
x and y can be any numbers
Xy is basically equivalent to x multiplied by itself y-1 times
Programming Fundamentals | Lecture-8

20. Programming Fundamentals | Lecture-9
Another Example
Find sum of first 5 even numbers
There are two ways to do this
Make use of count OR
Use a special field instead of count
What about sum of first ‘n’ even numbers
Programming Fundamentals | Lecture-9

21. Sum of first 5 even numbers
START
sum = 0
count = 0
count < 5 No
Yes
count = count + 1
DISPLAY sum
sum = sum + count + count
STOP
Programming Fundamentals | Lecture-9

22. Programming Fundamentals | Lecture-9
Alternative
START
sum = 0
even = 0
count = 0
count < 5 No
Yes
count = count + 1
even = even + 2
DISPLAY sum
STOP
sum = sum + even
Programming Fundamentals | Lecture-9

23. Programming Fundamentals | Lecture-9
Another Example
Find sum of first n odd numbers
Similarly, two ways to do it
Programming Fundamentals | Lecture-9

24. Sum of first n odd numbers
START
sum = 0
count = 0
count < n No
Yes
sum = sum + count + count + 1
DISPLAY sum
count = count + 1
STOP
Programming Fundamentals | Lecture-9

25. Programming Fundamentals | Lecture-9
Alternative
START
sum = 0
odd = -1
count = 0
count < 5 No
Yes
count = count + 1
odd = odd + 2
DISPLAY sum
STOP
sum = sum + odd
Programming Fundamentals | Lecture-9

26. Programming Fundamentals | Lecture-9
Consider This
Display first n even numbers
How it is different from the earlier example?
If we don’t need to use the result of previous calculation, we don’t need to save it
Programming Fundamentals | Lecture-9

27. Display first n even numbers
START
even = 0
count = 0
count < 5 No
Yes
count = count + 1
even = even + 2
STOP
DISPLAY even
Programming Fundamentals | Lecture-9

28. Programming Fundamentals | Lecture-9
Another Example
Display “multiplication table” of a number up to 10
Do we need to save the result of calculation in every repetition?
Let’s see the solution
Programming Fundamentals | Lecture-9

29. Programming Fundamentals | Lecture-9
Table of a number up to 10
START
READ num
count = 0
count < 10 No
Yes
count = count + 1
DISPLAY num * count
STOP
Programming Fundamentals | Lecture-9

30. Programming Fundamentals | Lecture-9
Another Example
Find sum of 5 natural numbers starting from 26
Programming Fundamentals | Lecture-9

31. Programming Fundamentals | Lecture-9
START
sum = 0
count = 0
count < 5 No
Yes
count = count + 1
DISPLAY sum
sum = sum + count + 25
STOP
Programming Fundamentals | Lecture-9

32. Programming Fundamentals | Lecture-9
Testing
count = 0
sum = 0
Repetition-1
Repetition-2
Repetition-3
Repetition-4
Repetition-5
decision (count < 5)
0 < 5
1 < 5
2 < 5
3 < 5
4 < 5
count = count + 1
1 = 0 + 1
2 = 1 + 1
3 = 2 + 1
4 = 3 + 1
5 = 4 + 1
sum = sum + count +25
26 =
0 + (1 + 25)
53 =
26 + (2 + 25)
81 =
53 + (3 + 25)
110 =
81 + (4 + 25)
140 =
110 + (5 + 25)
Programming Fundamentals | Lecture-9

33. Tasks (to be done by next lecture)
Find the sum of square of first n numbers
Find first 5 multiples of a number
Hint: Multiply the number from 1 to 5

34. Programming Fundamentals | Lecture-9
A Challenging Task
Display the following series for first n numbers in this series ……
Programming Fundamentals | Lecture-9

35. Programming Fundamentals | Lecture-9
BE PREPARED
FOR
QUIZ IN
NEXT LECTURE
Programming Fundamentals | Lecture-9