1. Binary Search and 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. Demo
binarySearch() on different types of lists
Ordered
Odd
Reverse

13. Demo binarySearch() on different types of lists
Ordered
Odd
Reverse
The reverse list doesn’t work because the list needs to be sorted in ascending order.
How do we sort?

14. Intro to Sorting Let’s watch a quick video
How can we know which sort is really faster?
Bubble Sort
Insertion Sort
Quick Sort
We need to use Big “O” analysis (next time…)