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

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

3. Sorting Methods Bubble Sort Higher elements “bubble” to the end
Compare two elements
Move the lower element to the left
Look at the next element
Repeat
Higher elements “bubble” to the end
After each run, one more high element is in order
Lower elements slowly “bubble” to the bottom

4. Bubble Sort
See sortingAlgorithms.py

5. 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

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

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

8. Insertion Sort
See sortingAlgorithms.py

9. Quicksort
We won’t be looking at the code, because it needs something called recursion to run
We don’t have time to introduce this
Instead, let’s think generally about how it works

10. Quicksort Pick a middle element
Place all elements lower than the middle partition into one list
Place all elements higher than the partition into another list
Repeat with lists until lists are small
Sort small lists with bubble or insertion sort
Merge sorted lists back together

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