1. Intro to Computer Science CS1510 Dr. Sarah Diesburg
More Sorting
Intro to Computer Science
CS1510
Dr. Sarah Diesburg

2. Any Questions
Lab?
Programming assignment?

3. Summary What have we done so far?
Refreshed ourselves on definition of algorithm
Searches
Linear and binary
Big O notation
Sorts

4. Sorting Methods Bubble Sort Higher cards “bubble” to the top
Compare two cards
Move the higher card to the top
Pick out another card
Repeat
Higher cards “bubble” to the top
After each run, one more high card is in order
Lower cards slowly “bubble” to the bottom

5. Bubble Sort
See sortingAlgorithms.py

6. Big O of the Bubble Sort
Roughly how many comparisons do we make with the bubble sort in the worst case
Roughly n comparisons over n times = n2
What is this saying?
As n grows, the time the algorithm takes grows by roughly a square
Example: As you double your data, you quadruple your time

7. Big O
In fact, the big O of the other sorts we will talk about today is also n2!

8. Sorting Methods Insertion Sort
Two chunks of data (sorted and unsorted)
Go through unsorted data and insert it in order into sorted pile
As humans, if we could look at all cards at once, we would probably perform an insertion sort

9. Insertion Sort
See sortingAlgorithms.py

10. Sorting Methods Selection Sort Find smallest card by
Comparing two cards at a time
Saving out the current smallest card
Repeat until reach end of pile
Put smallest card in sorted pile
Repeat

11. Selection Sort
See sortingAlgorithms.py

12. Sorting
Humans will tend to want to fan out all the cards and scan them
With 13 cards, this works
But what if I gave you 10,000 student ID cards?
Computers can only compare a finite number of cards together at a time

13. Sorting Complexity All these algorithms are approximately n2
Can we do better?