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

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

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

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

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

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?

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

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?

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

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

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…

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

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

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

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

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