Intro to Sorting Intro to Computer Science CS

Intro to Sorting Intro to Computer Science CS 1510 Dr. Sarah Diesburg

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 2

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 3

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

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 5

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 6

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

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

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? 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 is about 20 guesses 2^10 = 1024 One million is 1000 squared, so twice as much 10

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

Demo binary. Search() on different types of lists Ordered Odd Reverse 12

Demo binary. Search() 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? 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 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 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 18

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. 19