1. IGCSE 6 Cambridge Effectiveness of algorithms Computer Science
Section 2
Effectiveness of algorithms
Unit 7
Algorithm design and problem-solving 6

2. Objectives Produce an algorithm for a given problem
Explain standard methods of solution
Comment on the effectiveness of a given solution
Use a trace table to find the value of variables at each step in an algorithm

3. Designing an algorithm
Designing an algorithm involves developing a set of instructions to solve a problem
The instructions need to work for any instance of the problem
Sometimes it helps to figure out a solution to one particular instance, and from that, understand how to solve the general problem

4. Multiplying by ten
How do you multiply an integer by 10?
Why is this easier than multiplying by 9 or by 11?
What is special about the number 10?
4623 x 10 = 46230

5. Multiplying by the number base
Decimal numbers use 10 digits 0..9
They are base 10 numbers
Binary digits use two digits 0 and 1. They are base 2 numbers
What do you get when you multiply the binary number by 2? (Remember that 2 converts to 10 in binary)
From this instance you can work out a general solution to the problem of multiplying a number by its “base”!

6. Evaluating an algorithm
When designing an algorithm, you need to consider whether it is the best solution, or even a good solution
Does it always give the correct answer?
Is it fast enough?
Is it economical in terms of resources (e.g. memory, disk space or computational power)?
Is it easy for someone to use?

7. Efficiency of an algorithm
When designing an algorithm, you need to consider whether it is the best solution, or even a good solution
An algorithm which works well for a few items may not be suitable for a large number of items!
Could you use this algorithm to add the numbers 1 to 1000?
total =
Output total

8. A better algorithm What goes in the blank decision box? total = 0
Output total
total = 0
count = 0
count = count + 1
total = total + count No
Yes

9. An even better solution
……1000 …
= …… = 1000 * 1001
Total =
n * (n + 1) / 2
Output Total
n = 1000
Output Total

10. A search algorithm
Ask a friend to think of an integer between 1 and 20
Each time they guess, tell them whether the guess was too high, too low or spot on
How many guesses did it take to get the right number?
What algorithm were they using to solve the problem?

11. See Binary video

12. The binary search algorithm
This is a very efficient algorithm for finding a particular item in a sorted array or file
Think of how you might search for a name in a telephone directory
If you’re searching for Richards, you might open the page and find Smith
Then you try a few pages back and find Patel
What next?

13. The binary search algorithm
Can be applied to guessing a number x between 1 and n
Compare x with the middle element m of the set of numbers
If x = guess, then the item is found
Otherwise, if x < m, repeat the search on the subset to the left of the middle element
Or, if x > m, repeat the search on the subset to the right of the middle element
For example, suppose your partner thought of the number 6 2 3
Guess 1 too high
Guess 4 – found it!

14. Worksheet 6
Try Tasks 1 and 2 on the worksheet

15. Extension - Sorting
Sorting is a very common operation in data processing applications
Why would you need to sort data?
There are many sorting algorithms and they vary wildly in their efficiency
The merge sort is 200 times faster than a bubble sort for sorting 10,000 items

16. The bubble sort
The bubble sort is not efficient for a large number of items, but it is a simple algorithm to follow
Each item in a list is compared to the one next to it, and if it is greater, they swap places
At the end of one pass through the list, the largest item is at the end of the list
This is repeated until the items are sorted

17. Worksheet 6
Try Task 3 on the worksheet

18. Plenary
You’ve had lots of practice at constructing and testing algorithms
You’ve learned how to use a trace table to find out what’s going on in an algorithm
You’ve learned something about the effectiveness of different solutions to problems
You’re ready for the final assessment test!