Cs 1114 - lecture-8
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The document discusses programming fundamentals and controlled repetition in programs. It explains how to write programs that can repeat a set of instructions a specified number of times to calculate values like the sum of the first n natural numbers or the factorial of a number n. Examples are provided to find the sum of the first 5 numbers, the factorial of 5, and raising a number to a power by repeated multiplication. Controlled repetition allows programmers to instruct computers to perform repetitive tasks without human intervention.
Cs 1114 - lecture-8
- 2. Consider this Example Find sum of first 5 natural numbers Programming Fundamentals | Lecture-8
- 3. Programming Fundamentals | Lecture-8 START STOP sum = 0 sum = sum + 2 sum = sum + 3 sum = sum + 4 sum = sum + 5 DISPLAY sum (sum=1) (sum=3) (sum=6) (sum=10) (sum=15) sum = sum + 1 (sum=0)
- 4. 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. Programming Fundamentals | Lecture-8 What if the numbers are not just 50, they are 1000?
- 6. 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. Is this Correct? Programming Fundamentals | Lecture-8 START sum = 0 sum = sum + _ STOP
- 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? Programming Fundamentals | Lecture-8
- 9. 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 1 st 5 natural numbers Programming Fundamentals | Lecture-8 START sum = 0 count = count + 1 STOP count < 5 count = 0 DISPLAY sum Yes No sum = sum + count
- 11. How to Test This? Programming Fundamentals | Lecture-8 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 1 3 6 10 15
- 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. 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 sum = 0 count = count + 1 STOP count < n count = 0 DISPLAY sum Yes No sum = sum + count READ n
- 16. Another Example Find factorial of a number factorial(n) = 1 * 2 * …… * n Programming Fundamentals | Lecture-8
- 17. Programming Fundamentals | Lecture-8 START fact = 1 count = count + 1 STOP count < n count = 0 DISPLAY sum Yes No fact = fact * count READ n
- 18. Testing Programming Fundamentals | Lecture-8 count = 0 fact = 1 n = 5 120 = 24 * 5 5 = 4 + 1 4 < 5 Repetition-5 Repetition-1 Repetition-2 Repetition-3 Repetition-4 decision (count < 5) 0 < 5 1 < 5 2 < 5 3 < 5 count = count + 1 1 = 0 + 1 2 = 1 + 1 3 = 2 + 1 4 = 3 + 1 fact = fact * count 1 = 1 * 1 2 = 2 *1 6 = 2 * 3 24 = 6 * 4
- 19. Try this Yourself Find 2 20 Hint: Multiply 2 by itself, 20 times Find x y x and y can be any numbers X y is basically equivalent to x multiplied by itself y times Programming Fundamentals | Lecture-8
- 20. Tasks (to be done by next lecture) Find the sum of square of first n natural numbers Find first 5 multiples of a number Hint: Multiply the number from 1 to 5
- 21. Programming Fundamentals | Lecture-8 BE PREPARED FOR QUIZ IN NEXT LECTURE
Editor's Notes
- #9: * Only a decision box can divide the order or flow of program into two alternative paths