Intro to Sorting

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

15. 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

16. Sorting Methods • Bubble Sort • 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

17. 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

18. 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 • Let’s start to think about how long each of these will take in the worst case

19. Big O (Worst Case) • Selection sort • First pass – compare 13 cards and set aside lowest • Second pass – compare 12 cards and set aside lowest • Etc…. • How many passes do I make? – 13 • N^2 = 169 but actually 91 • As you double your data, you quadruple your time.