99 questions/1 to 10

This is part of Ninety-Nine Haskell Problems, based on Ninety-Nine Prolog Problems and Ninety-Nine Lisp Problems.

Problem 1

(*) Find the last element of a list. Solutions

 

(Note that the Lisp transcription of this problem is incorrect.)

Example in Haskell:

λ> myLast [1,2,3,4]
4
λ> myLast ['x','y','z']
'z'

Problem 2

(*) Find the last-but-one (or second-last) element of a list. Solutions

 

(Note that the Lisp transcription of this problem is incorrect.)

Example in Haskell:

λ> myButLast [1,2,3,4]
3
λ> myButLast ['a'..'z']
'y'

Problem 3

(*) Find the K'th element of a list. Solutions

 

The first element in the list is number 1. Example:

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

Example in Haskell:

λ> elementAt [1,2,3] 2
2
λ> elementAt "haskell" 5
'e'

Problem 4

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

 

Example in Haskell:

λ> myLength [123, 456, 789]
3
λ> myLength "Hello, world!"
13

Problem 5

(*) Reverse a list. Solutions

 

Example in Haskell:

λ> myReverse "A man, a plan, a canal, panama!"
"!amanap ,lanac a ,nalp a ,nam A"
λ> myReverse [1,2,3,4]
[4,3,2,1]

Problem 6

(*) Find out whether a list is a palindrome. Solutions

 

Hint: A palindrome can be read forward or backward; e.g. (x a m a x).

Example in Haskell:

λ> isPalindrome [1,2,3]
False
λ> isPalindrome "madamimadam"
True
λ> isPalindrome [1,2,4,8,16,8,4,2,1]
True

Problem 7

(**) Flatten a nested list structure. Solutions

 

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)

Example in Haskell:

We have to define a new data type, because lists in Haskell are homogeneous.

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

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

Problem 8

(**) Eliminate consecutive duplicates of list elements. Solutions

 

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:

λ> compress "aaaabccaadeeee"
"abcade"

Problem 9

(**) Pack consecutive duplicates of list elements into sublists. Solutions

 

If a list contains repeated elements they should be placed in separate sublists.

Example:

* (pack '(a a a a b c c a a d e e e e))
((A A A A) (B) (C C) (A A) (D) (E E E E))

Example in Haskell:

λ> pack ['a', 'a', 'a', 'a', 'b', 'c', 'c', 'a', 
             'a', 'd', 'e', 'e', 'e', 'e']
["aaaa","b","cc","aa","d","eeee"]

Problem 10

(*) Run-length encoding of a list. Solutions

 

Use the result of Problem 9 to implement the so-called run-length encoding data compression method. Consecutive duplicates of elements are encoded as lists (N E) where N is the number of duplicates of the element E.

Example:

* (encode '(a a a a b c c a a d e e e e))
((4 A) (1 B) (2 C) (2 A) (1 D)(4 E))

Example in Haskell:

λ> encode "aaaabccaadeeee"
[(4,'a'),(1,'b'),(2,'c'),(2,'a'),(1,'d'),(4,'e')]