Note that, for our current purposes, it is indifferent whether to use
Integer, so don't worry if you have used one and the solutions below the other.
takeInt :: Int -> [a] -> [a] takeInt 0 _ =  takeInt _  =  takeInt n (x:xs) = x : takeInt (n-1) xs
dropInt :: Int -> [a] -> [a] dropInt 0 list = list dropInt _  =  dropInt n (x:xs) = dropInt (n-1) xs
sumInt :: [Int] -> Int sumInt  = 0 sumInt (x:xs) = x + sumInt xs
-- "Direct" solution with pattern matching. scanSum :: [Int] -> [Int] scanSum  =  scanSum [x] = [x] scanSum (x:y:xs) = x : scanSum ((x + y) : xs) -- Alternatively, using a helper function with an accumulator argument: scanSum :: [Int] -> [Int] scanSum = scanSum' 0 where -- The following type signature is entirely optional. -- We have added it just for extra clarity. scanSum' :: Int -> [Int] -> [Int] scanSum' tot  =  scanSum' tot (x:xs) = tot' : scanSum' tot' xs where tot' = x + tot -- Alternatively, using takeInt, dropInt and sumInt: scanSum :: [Int] -> [Int] scanSum  =  scanSum [x] = [x] scanSum (x:xs) = x : scanSum ((x + sumInt (takeInt 1 xs)) : dropInt 1 xs)
diffs :: [Int] -> [Int] diffs  =  diffs (x:xs) = diffs' (x:xs) xs where diffs' :: [Int] -> [Int] -> [Int] diffs' _  =  diffs'  _ =  diffs' (x:xs) (y:ys) = (y-x) : diffs' xs ys -- Alternatively, without the auxiliary function: diffs :: [Int] -> [Int] diffs  =  diffs [x] =  diffs (x:y:xs) = (y-x) : diffs (y:xs)
1. A handful of variations for each function will be shown below, in a single block:
negateList, negateList2 :: [Int] -> [Int] negateList = map negate negateList2 xs = map negate xs divisorsList, divisorsList2 :: [Int] -> [[Int]] divisorsList = map divisors divisorsList2 xs = map divisors xs -- Note that there are even more possible ways of writing this one. -- Remember that the dot operator composes functions: (g . f) x = g (f x) negateDivisorsList, negateDivisorsList2, negateDivisorsList3, negateDivisorsList4 :: [Int] -> [[Int]] negateDivisorsList = map (negateList . divisors) negateDivisorsList2 = map negateList . divisorsList negateDivisorsList3 list = map (negateList . divisors) list negateDivisorsList4 list = map (map negate) (map divisors list)
2. One possible solution:
import Data.List myRLEencoder :: String -> [(Int, Char)] myRLEencoder s = map pairRLE (group s) where pairRLE xs = (length xs, head xs) myRLEdecoder :: [(Int, Char)] -> String myRLEdecoder l = concat (map expandRLE l) where expandRLE (n, x) = replicate n x
N.B.: the RLE example is inspired from a blog post by Don Stewart on the same subject. If you are curious, check Don's post for a neat solution which likely won't not be immediately understandable, as it uses some things we didn't see yet.
Tips and tricksEdit
scanSum (takeInt 10 [1..]) and
takeInt 10 (scanSum [1..]) have the same value. This is possible because Haskell is a lazy language, thus in both cases the result is only evaluated as needed.
-- This is just like the Prelude function last. lastOf :: [a] -> a lastOf  = error "Empty list" lastOf [x] = x lastOf (_:xs) = lastOf xs -- This is just like the Prelude init. dropLast :: [a] -> [a] dropLast  = error "Empty list" dropLast [x] =  dropLast (x:xs) = x : (dropLast xs)