1. Queen Mary University of London
The Bubble Sort Dance
Paul Curzon
Queen Mary University of London
CAS London

2. Aims We are going to explore the way computers sort data
We will also see how dances and programs have a lot in common

3. Code = Dance Choreographing a dance is very similar to writing code.
You have to come up with the right steps in the right order.
Once you have created a dance anyone can follow the instructions without having to invent the dance anew.
The dancers follow the steps of the dance just like a computer follows the steps of a program
Programmers choreograph the way data dances round a computer memory.

4. Sort Algorithms
A sort algorithm takes a series of things and puts it into order eg
[5, 7, 2, 99, 4] -> [2, 4, 5, 7, 99]
[“cat”, “hat”, “ant”] -> [“ant”, “cat”, “hat”]
Often used as a way of making things easier to find (eg putting your music collection in alphabetical order so you can find tracks).

5. The Sorting Dance
We are going to choreograph a sort algorithm as though it were a dance.
We need 5 volunteers to be our dancers
They each get a different number on their back
They start by standing in a line.

6. The sorting dance (1)
The following is the basic steps that make up the dance
Pass hat to first dancer
Dancer with hat and next dancer step forward
if dancer with hat > next dancer
Dancer with hat swaps places with next dancer
else
Dancer with hat passes it to next dancer
The pair step back in to the line

7. The sorting dance (2) We need to do that for each pair, down the line:
Pass hat to first dancer
Repeat 4 times {
Dancer with hat and next dancer step forward
if dancer with hat > next dancer
Dancer with hat swaps places with next dancer
else
Dancer with hat passes them to next dancer
The pair step back in to the line }

8. The sorting dance (3)
Doing one pass isn’t enough we need to do it over and over again
Repeat 4 times {
Pass hat to first dancer
Dancer with hat and next dancer step forward
if dancer with hat > next dancer
Dancer with hat swaps places with next dancer
else
Dancer with hat passes them to next dancer
The pair step back in to the line }

9. How many passes
How many passes do we need to do to guarantee the dancers are in sorted order?
We have to be sure it works even if everyone starts in the worst possible positions.

10. How many passes
On the first pass, the biggest value has ended up in the right place
It went with the hat where ever it started.
On the next pass the next biggest is in the right place…and so on
When the second last one is in the right place there is no where else for the last dancer to go so it is right too.
So if there are 5 dancers we will need 4 passes or more generally n dancers needs n-1 passes

11. Can we do better? This is quite a simple version of bubble sort
It is possible to come up with an improved version that involves less steps
so the dance is much shorter
Can you work out how?

12. Doing better still What happens if the array is already sorted?
Over and over again we do comparisons, lots of wasted dance steps never changing anything

13. Doing better still Observation
If we do a whole pass and nothing changes then it never will - the array is sorted
So we can shorten the dance further by keeping track of whether we swap anything on a pass and stopping at the end of any pass where none swapped.
Now we have a dance that will be a different length depending on where the numbers are at the start.

14. Summary We have seen one simple way to sort data.
We have also seen how writing programs is similar to choreographing a dance.
Both need lots of creativity.

15. More on the fun side of computer science from:
Twitter: @cs4fn
With support from Google, BCS, Dept for Education, the Mayor of London and the BBC