1. Teaching Computing to GCSE
Session 7
Theory: Sorting Algorithms
Practical: Testing

2. Specification Content
OCR
Standard sorting algorithms:
Bubble sort
Merge sort
Insertion sort
AQA
Understand and explain how the merge sort algorithm works.
Understand and explain how the bubble sort algorithm works.
Compare and contrast merge sort and bubble sort algorithms.
Edexcel
Understand how standard algorithms (bubble sort, merge sort) work.

3. Sorting Algorithms
We use sorting algorithms to sort lists of unordered values.
There are many different sorting algorithms, these include:
Bubble Sort
Merge Sort
Insertion Sort

4. Activity 1
This activity will demonstrate a fun way of teaching sorting algorithms.

5. Bubble Sort Tracing (1)
In exams students may be asked to demonstrate their understanding of the bubble sort algorithm by tracing it. One method of tracing is to show the state of the list after each swap.
Original List 2 3 1 5 6 4
Swap 1
Swap 2
Swap 3
Swap 4

6. Bubble Sort Tracing (2)
Another way to trace the bubble sort algorithm is to show the state of the list after each complete pass.
Original List 2 3 1 5 6 4
Pass 1
Pass 2
Pass 3

7. Activity 2a
Complete this table to show the state of the list after each swap using the bubble sort algorithm:
Original List 56 32 49 24
Swap 1
Swap 2
Swap 3
Swap 4
Swap 5

8. Activity 2b
Complete this table to show the state of the list after each pass using the bubble sort algorithm:
Original List 78 46 13 27
Pass 1
Pass 2
Pass 3

9. Merge Sort Tracing
In exams students may be asked to demonstrate their understanding of the merge sort algorithm by tracing it.
Original List 3 2 7 5 1 8 6 4
Stage 1
Stage 2
Stage 3
Stage 4

10. Activity 3
Complete this table to show the state of the list after each stage of the merge sort algorithm:
Original List 56 44 76 21 14 82 65 71
Stage 1
Stage 2
Stage 3
Stage 4

11. Insertion Sort Tracing
In exams students may be asked to demonstrate their understanding of the insertion sort algorithm by tracing it.
Sorted
Unsorted
Stage 1
23, 56, 87, 18, 29
Stage 2 23
56, 87, 18, 29
Stage 3
23, 56
87, 18, 29
Stage 4
23, 56, 87
18, 29
Stage 5
18, 23, 56, 87 29
Stage 6
18, 23, 29, 56, 87

12. Activity 4
Complete this table to show the state of the list (56, 44, 76, 21, 14) after each stage of the insertion sort algorithm:
Sorted
Unsorted
Stage 1
Stage 2
Stage 3
Stage 4
Stage 5
Stage 6

13. Comparison
Students need to understand the benefits and drawbacks of each sorting algorithm.
Algorithm
Benefits / Drawbacks
Bubble Sort
Simple to implement but very inefficient.
Merge Sort
An efficient algorithm for sorting both large and small lists.
Insertion Sort
Relatively efficient when used with small lists, but not with larger lists.