H-99: Ninety-Nine Haskell Problems

From HaskellWiki
Revision as of 05:54, 12 December 2006 by Jcreigh (talk | contribs) (formatting change)
Jump to navigation Jump to search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

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.