1. Mergesort: The power of divide and conquer
Paul Curzon
Queen Mary University of London
CAS London
With support from
Google,
Dept for Education
the Mayor of London

2. Aims www.teachinglondoncomputing.org
Give you deeper understanding of core topics
Merge sort
Divide and Conquer
Efficiency of algorithms
Computational thinking
Give you practical ways to teach computing in a fun, thought provoking way
away from computers, focus on concepts
Linked activity sheets and booklets can be downloaded from our website:

3. Sort Algorithms www.teachinglondoncomputing.org
A sort algorithm takes an array of data and puts it into order (either ascending order or descending 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 in a telephone directory)
There are many sort algorithms some more efficient than others

4. Divide and Conquer Sorting
Suppose you have a long array that you want to sort.
Divide and conquer says:
split it into smaller arrays
sort those smaller arrays (in the same way)
combine the sorted arrays to give the sorted large array.
There are two approaches
split is easy but combining them at the end needs work
split takes time but combining them at the end is easy

5. 1 Mergesort To mergesort an array: split the array in half
mergesort those smaller arrays
merge the two sorted arrays
Note it does option 1
- split is easy but combining them at the end needs work
We will act it out
Each new call of merge sort will be done by a new person 1

6. 1 The Merge Algorithm Merge is the key to this as it does all the work
To Merge two sorted piles
Repeat until both piles empty
Compare the top value of each pile
Take the smallest 1

7. How much work?
How many comparisons do we need to do to guarantee it is sorted?
What is the worst situation we could be in?
What is the best? 1

8. 1 How much work? Each time we recurse we go back a row of people
Each run of merge (so each person) does approximately one comparison for every piece of data being merged.
When we mergesort 32 items:
Row 1 has 1 person who does 31 comparisons
Row 2 has 2 people who do 15 comparisons each
Row 3 has 4 people who do 7 comparisons each … 1

9. How many rows?
How many times can we half a number before we get to 1?
2 1 (once if we start at 2)
4 2 1 (twice if we start at 4)
(three times if we start at 8)
Mathematically the answer is the log2n
log2 is just a symbol meaning how many times you can half a number!
Each time we double the number it takes one more halving! 1

10. How much work?
So to mergesort 32 items we will go back 5 levels of recursive calls - 5 rows of people.
So if we go back 5 levels …
When we mergesort 32 items: TOTAL
Row 1: 1 person who does 31 comparisons
Row 2: 2 people who do 15 comparisons
Row 3: 4 people who do 7 comparisons
Row 3: 8 people who do 3 comparisons
Row 3: 16 people who do 1 comparison … 1

11. Compare this to bubble sort
When we bubble sort (efficiently) 32 items: TOTAL
Pass
Pass
Pass …
Pass
Now consider the comparison when sorting a million items.
NB log2 (1 million) = 20

12. 1 Quicksort To quicksort an array:
partition the array into two parts around a pivot
quicksort those smaller arrays
concatenate the two sorted arrays end to end
Note it does option 2
- split takes time but combining them at the end is easy 1

13. The Partition Algorithm
Partition is the key to this as it does all the work
To Partition two sorted arrays
Pick a pivot value
Repeat until all entries processed
Compare each value with the pivot
Put those smaller to the left
Put those larger to the right 1

14. Computational Thinking Lessons
Algorithmic thinking
Decomposition
Evaluation
Logical Thinking
Generalisation
Abstraction

15. Summary Focus on understanding algorithm first
Sort algorithms can be introduced unplugged in a constructivist way
Focus on understanding algorithm first
Important it is directly linked to code too
Also to do dry run exercises

16. Twitter: @TeachingLDNComp
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