H-99: Ninety-Nine Haskell Problems

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These are Haskell translations of Ninety Nine Lisp Problems.

Problem 1

(*) Find the last box of a list. 

Example:
* (my-last '(a b c d))
(D)

This is "last" in Prelude, which is defined as: 

last :: [a] -> a
last [x] = x
last (_:xs) = last xs

Problem 2

(*) Find the last but one box of a list. 

Example:
* (my-but-last '(a b c d))
(C D)

This can be done by dropping all but the last two elements of a list: 

myButLast :: [a] -> [a]
myButLast list = drop ((length list) - 2) list

Problem 3

(*) Find the K'th element of a list. The first element in the list is number 1. 

Example:
* (element-at '(a b c d e) 3)
C

This is (almost) the infix operator !! in Prelude, which is defined as: 

(!!)                :: [a] -> Int -> a
(x:_)  !! 0         =  x
(_:xs) !! n         =  xs !! (n-1)

Except this doesn't quite work, because !! is zero-indexed, and element-at should be one-indexed. So: 

elementAt :: [a] -> Int -> a
elementAt list i = list !! (i-1)

Problem 4

(*) Find the number of elements of a list.

This is "length" in Prelude, which is defined as: 

length           :: [a] -> Int
length []        =  0
length (_:l)     =  1 + length l

Problem 5

(*) Reverse a list.

This is "reverse" in Prelude, which is defined as: 

reverse          :: [a] -> [a]
reverse          =  foldl (flip (:)) []

The standard definition is concise, but not very readable. Another way to define reverse is: 

reverse :: [a] -> [a]
reverse [] = []
reverse (x:xs) = reverse xs ++ [x]

Problem 6

(*) Find out whether a list is a palindrome. A palindrome can be read forward or backward; e.g. (x a m a x).

This is trivial, because we can use reverse: 

isPalindrome :: (Eq a) => [a] -> Bool
isPalindrome xs = xs == (reverse xs)

Problem 7

(**) Flatten a nested list structure.

Transform a list, possibly holding lists as elements into a `flat' list by replacing each list with its elements (recursively). 

Example:
* (my-flatten '(a (b (c d) e)))
(A B C D E)

This is tricky, because lists in Haskell are homogeneous. [1, [2, [3, 4], 5]] is a type error. We have to devise some way of represent a list that may (or may not) be nested: 

data NestedList a = Elem a | List [NestedList a]

flatten :: NestedList a -> [a]
flatten (Elem x) = [x]
flatten (List []) = []
flatten (List (x:xs)) = flatten x ++ flatten (List xs)

Our NestedList datatype is either a single element of some type (Elem a), or a list of NestedLists of the same type. (List [NestedList a]). Let's try it out in ghci: 

*Main> flatten (Elem 5)
[5]
*Main> flatten (List [Elem 1, List [Elem 2, List [Elem 3, Elem 4], Elem 5]])
[1,2,3,4,5]
*Main> flatten (List [])
[]

Problem 8

(**) Eliminate consecutive duplicates of list elements.

If a list contains repeated elements they should be replaced with a single copy of the element. The order of the elements should not be changed. 

Example:
* (compress '(a a a a b c c a a d e e e e))
(A B C A D E)

Example in Haskell:
*Main> compress ['a','a','a','a','b','c','c','a','a','d','e','e','e','e']
['a','b','c','a','d','e']

Solution: 

compress = map head . group

We simply group equal values together (group), then take the head of each.

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