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

2. Last Time We looked at two basic algorithms for searching
Linear search
Binary search
Linear search was the easiest to write
But perhaps not the best from a complexity standpoint

3. Last Time
Big “O” measures how badly the problem grows as the data set grows
Study of complexity of algorithms
Worst case of linear search was N, where N is the number of comparisons that we need to perform
Double the number of items in list, double the amount of time needed to complete the search in the worst case

4. Last Time
The binary search was another solution that incurred less comparisons in the worst case
Only works on sorted list

5. Binary Search Binary search algorithm
Try the guess at middle index of the range
If the value we are searching for is higher than number at the index, then adjust your low range bound to be your guess+1
If the value we are searching for is lower than number at the index, then adjust your high range bound to be your guess-1
Repeat

6. Binary Search What is the worst-case scenario of the binary search?
Thinking of a number between 1 and 100
7 guesses in total – why?
1 guesses – cut down to 50 possibilities
2 guesses – cut down to 25
3 guesses – cut down to 12
4 guesses – cut down to 6
5 guesses – cut down to 3
6 guesses – cut down to 1
7 guesses – to figure out if last guess is right

7. Binary Search What is the complexity of a binary search? log2(100) = x
Big O value of log2 N
This is “log base 2”
log2(100) = x
What is this saying?

8. Binary Search What is the complexity of a binary search? log2(100) = x
Big O value of log2 N
This is “log base 2”
log2(100) = x
What is this saying?
2x = 100
Go “to the next power” when not exact

9. Binary Search How does that relate to our binary search?
Let’s say there are 16 items in our list. What is the worst case number of guesses? 32? 34? 64? One million?

10. Binary Search How does that relate to our binary search?
Let’s say there are 16 items in our list. What is the worst case number of guesses? 32? 34? 64? One million?
One million is about 20 guesses
2^10 = 1024
One million is 1000 squared, so twice as much

11. Searching
So which kind of search would amazon.com use to search their databases?

12. Searching
So which kind of search would amazon.com use to search their databases?
Binary search!!!
The downside is that the list needs to be sorted first…

13. Group Time! Let’s get into 4 big groups Put the cards in order
You can only look at two cards at a time

14. 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

15. 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

16. 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

17. Sorting Methods Quicksort
Choose a random card (called the “partition”)
Compare every card against the partition
Moving cards < partition to one side and cards > partition to the other
Now, within each partition….over and over again…
Compare every card against the partition, moving the cards on either side based on them being bigger or smaller
Sort the small amount of cards within each partition using a simple sort method, like insertion or selection sort