1. List Operations CSCE 314 Spring 2016

2. CSCE 314 – Programming Studio Tuple and List Patterns Pattern matching with wildcards for tuples fst (a, _) = a scd (_, b) = b Pattern matching with wildcards for lists pullsecond [_, a, _] = a This implies a list of 3 elements The _ indicates a single element of the list, when it is in the list. The _ can also indicate an entire list [ [a, b, c], _, _, [2, 4] ]

3. Spring 2016 CSCE 314 – Programming Studio Building a list: the cons operator ‘:’ : cons adds one element to the front of a list > 1 : [2, 3, 4] [1, 2, 3, 4] cons associates to the right: [1, 2, 3] = 1 : (2 : (3 : [])) = 1: 2: 3: [] Generally, should use parentheses to be clear! cons makes it easier to match list patterns (x:xs) – x is the first element in the list, xs is the remainder of the list

4. Spring 2016 CSCE 314 – Programming Studio Examples Patterns can be arbitrarily deep/complex. What are these patterns: f (a:b:c:d:e:fs) = a:b:c:d:e:[] list of at least 5 elements forms list of those first 5 g (_: (_, x): _) = x list of tuples, each with two elements takes second element of the second tuple h [[_]] = True singleton list, each element is a singleton list Identifies valid such lists, e.g. [[True]], or [[‘a’]], or [[1]]

5. Spring 2016 CSCE 314 – Programming Studio List Comprehensions (list generators) Can generate lists from other lists [x+x | x <-[1..10] ] [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] Can use multiple generators Applied left to right (like nested loops) [(x,y) | x <- [1..3], y <- [11..13]] [(1,11),(1,12),(1,13),(2,11),(2,12),(2,13),(3,11),(3,12), (3,13)] Notice that all the (1,_) elements come before the (2,_) ones Generators can use earlier generators (dependent generators) [(x,y) | x<-[1..3], y<-[x..3]] [(1,1),(1,2),(1,3),(2,2),(2,3),(3,3)]

6. Spring 2016 CSCE 314 – Programming Studio Dependent generator example What does this function do? somefunc xss = [x | xs <- xss, x <- xs] First, the type: somefunc :: [[a]] -> [a] Notice, we form xs from the elements of xss Then, we form x from the elements of xs And those x’s form the final list These are the elements of the elements of the list Basically, we concatenate the list somefunc [[1,2,3],[4],[5,6]] [1,2,3,4,5,6]

7. Spring 2016 CSCE 314 – Programming Studio Guards When using generators, we can apply guards, similar to the guards seen before Given as expressions, separated by commas Guards limit which combinations of generators are used (only the ones that give true guards [x | x <- [1..10], x<5] [1,2,3,4] [x | x <- [1..10], even x] [2,4,6,8,10]

8. Spring 2016 CSCE 314 – Programming Studio List Comprehension example Say we want a function that will list all primes up to n: primes :: Int -> [Int] First, we will create a function to compute all factors of a number: A number x is a factor of a number y if y mod x == 0 factors :: Int -> [Int] factors n = [x | x <- [1..n], n `mod` x == 0] Test: > factors 24 [1,2,3,4,6,8,12,24]

9. Spring 2016 CSCE 314 – Programming Studio List comprehension example (continued) Given factors, we want a function isprime A number x is prime if its only factors are 1 and x isprime :: Int -> Bool isprime n = factors n == [1,n] Test: > isprime 24 False > isprime 7 True

10. Spring 2016 CSCE 314 – Programming Studio List comprehension example (continued Given isprime, we can now write the primes function: primes :: Int -> [Int] primes n = [x | x <- [2..n], isprime x] Test > primes 20 [2,3,5,7,11,13,17,19]

11. Spring 2016 CSCE 314 – Programming Studio The zip function A useful list operation. Often as a tool in parts of bigger computation – to pair up items Take two lists and form a list of tuples Tuple is a pair, with one element from first list and corresponding from second Length of list is the length of the shortest input list > zip [1,2,3,4,5,6,7],[“red”,”green”,”blue”,”cyan”,”magenta”,”yellow”] [(1,”red”),(2,”green”),(3,”blue”),(4,”cyan”),(5,”magenta”),(6,”yellow”)]

12. Spring 2016 CSCE 314 – Programming Studio A zip example: testing for a sorted list Want a check to see if a list is sorted sorted :: Ord a => [a] -> Bool We first form pairs of adjacent elements in the list: pairs :: [a] -> [(a,a)] pairs xs = zip xs (tail xs) Test: > pairs [1, 5, 8, 9] [(1,5),(5,8),(8,9)]

13. Spring 2016 CSCE 314 – Programming Studio A zip example: testing for a sorted list (cont.) Given pairs, the list is sorted only if all pairs are in order Note: the and command, applied to a list, gives the “and” of all elements sorted :: Ord a => [a] -> Bool sorted xs = and [x<=y | (x,y) <- pairs xs] Test > sorted [1,5,8,9] True > sorted [1,8,5,9] False

14. Spring 2016 CSCE 314 – Programming Studio Recursion on lists Recursion works just like it did with integers Base case: typically the empty list [] Use the cons operator (:) to break/construct lists e.g. length [] = 0 length (_:xs) = 1 + length xs

15. Spring 2016 CSCE 314 – Programming Studio Example: quicksort Quicksort takes first element from a list, divides the remainder of the list into stuff before and stuff after, and then recursively sorts those. First, create a list of elements greater than a given value biggerlist :: Ord a => a -> [a] -> [a] biggerlist n xs = [x | x n] Likewise, create a list of elements less than or equal to a given value smallerlist :: Ord a => a -> [a] -> [a] smallerlist n xs = [x | x <- xs, x <= n]

16. Spring 2016 CSCE 314 – Programming Studio Example: quicksort (continued) Now, quicksort is straightforward: quicksort :: [a] -> [a] quicksort[] = [] quicksort (x:xs) = quicksort (smallerlist x xs) ++ [x] ++ quicksort (biggerlist x xs)

17. Spring 2016 CSCE 314 – Programming Studio Example: insert into ordered list insert :: Ord a => a -> [a] -> [a] insert x [] = [x] insert x (y:ys) | x <= y = x:y:ys | otherwise = y:insert x ys

18. Spring 2016 CSCE 314 – Programming Studio Example: Insertion sort Given the insert command, write insertion sort insort :: Ord a => [a] -> [a] insort [] = [] insort (x:xs) = insert x (insort xs)

19. Spring 2016 CSCE 314 – Programming Studio Additional notes Strings are just lists of characters So, all the list commands can be applied to strings Section 5.5 has an extended example of how to create, use, and crack the Caesar cipher You should read this section, try it yourself, and make sure you understand how it works! Ask questions if you have them, next class We will next be looking more closely at recursion next time