99 questions/11 to 20

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

Problem 11

(*) Modified run-length encoding. Solutions

 

Modify the result of problem 10 in such a way that if an element has no duplicates it is simply copied into the result list. Only elements with duplicates are transferred as (N E) lists.

Example:

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

Example in Haskell:

λ> encodeModified "aaaabccaadeeee"
[Multiple 4 'a',Single 'b',Multiple 2 'c',
 Multiple 2 'a',Single 'd',Multiple 4 'e']

Problem 12

(**) Decode a run-length encoded list. Solutions

 

Given a run-length code list generated as specified in problem 11. Construct its uncompressed version.

Example in Haskell:

λ> decodeModified 
       [Multiple 4 'a',Single 'b',Multiple 2 'c',
        Multiple 2 'a',Single 'd',Multiple 4 'e']
"aaaabccaadeeee"

Problem 13

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

 

Implement the so-called run-length encoding data compression method directly. I.e. don't explicitly create the sublists containing the duplicates, as in problem 9, but only count them. As in problem P11, simplify the result list by replacing the singleton lists (1 X) by X.

Example:

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

Example in Haskell:

λ> encodeDirect "aaaabccaadeeee"
[Multiple 4 'a',Single 'b',Multiple 2 'c',
 Multiple 2 'a',Single 'd',Multiple 4 'e']

Problem 14

(*) Duplicate the elements of a list. Solutions

 

Example:

* (dupli '(a b c c d))
(A A B B C C C C D D)

Example in Haskell:

λ> dupli [1, 2, 3]
[1,1,2,2,3,3]

Problem 15

(**) Replicate the elements of a list a given number of times. Solutions

Example:

* (repli '(a b c) 3)
(A A A B B B C C C)

Example in Haskell:

λ> repli "abc" 3
"aaabbbccc"

Problem 16

(**) Drop every N'th element from a list. Solutions

 

Example:

* (drop '(a b c d e f g h i k) 3)
(A B D E G H K)

Example in Haskell:

λ> dropEvery "abcdefghik" 3
"abdeghk"

Problem 17

(*) Split a list into two parts; the length of the first part is given. Solutions

 

Do not use any predefined predicates.

Example:

* (split '(a b c d e f g h i k) 3)
( (A B C) (D E F G H I K))

Example in Haskell:

λ> split "abcdefghik" 3
("abc", "defghik")

Problem 18

(**) Extract a slice from a list. Solutions

 

Given two indices, i and k, the slice is the list containing the elements between the i'th and k'th element of the original list (both limits included). Start counting the elements with 1.

Example:

* (slice '(a b c d e f g h i k) 3 7)
(C D E F G)

Example in Haskell:

λ> slice ['a','b','c','d','e','f','g','h','i','k'] 3 7
"cdefg"

Problem 19

(**) Rotate a list N places to the left. Solutions

 

Hint: Use the predefined functions length and (++).

Examples:

* (rotate '(a b c d e f g h) 3)
(D E F G H A B C)

* (rotate '(a b c d e f g h) -2)
(G H A B C D E F)

Examples in Haskell:

λ> rotate ['a','b','c','d','e','f','g','h'] 3
"defghabc"

λ> rotate ['a','b','c','d','e','f','g','h'] (-2)
"ghabcdef"

Problem 20

(*) Remove the K'th element from a list. Solutions

 

Example in Prolog:

?- remove_at(X,[a,b,c,d],2,R).
X = b
R = [a,c,d]

Example in Lisp:

* (remove-at '(a b c d) 2)
(A C D)

(Note that this only returns the residue list, while the Prolog version also returns the deleted element.)

Example in Haskell:

λ> removeAt 2 "abcd"
('b',"acd")