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__NOTOC__
 
__NOTOC__
   
These are Haskell translations of [http://www.ic.unicamp.br/~meidanis/courses/mc336/2006s2/funcional/L-99_Ninety-Nine_Lisp_Problems.html Ninety Nine Lisp Problems].
+
This is part of [[H-99:_Ninety-Nine_Haskell_Problems|Ninety-Nine Haskell Problems]], based on [https://sites.google.com/site/prologsite/prolog-problems Ninety-Nine Prolog Problems] and [http://www.ic.unicamp.br/~meidanis/courses/mc336/2006s2/funcional/L-99_Ninety-Nine_Lisp_Problems.html Ninety-Nine Lisp Problems].
 
If you want to work on one of these, put your name in the block so we know someone's working on it. Then, change n in your block to the appropriate problem number, and fill in the <Problem description>,<example in lisp>,<example in Haskell>,<solution in haskell> and <description of implementation> fields.
 
   
 
== Problem 1 ==
 
== Problem 1 ==
   
(*) Find the last box of a list.
+
(*) Find the last element of a list.
   
Example:
+
(Note that the Lisp transcription of this problem is incorrect.)
 
<pre>
 
* (my-last '(a b c d))
 
(D)
 
</pre>
 
   
 
Example in Haskell:
 
Example in Haskell:
   
 
<haskell>
 
<haskell>
Prelude> last [1,2,3,4]
+
Prelude> myLast [1,2,3,4]
 
4
 
4
Prelude> last ['x','y','z']
+
Prelude> myLast ['x','y','z']
 
'z'
 
'z'
 
</haskell>
 
</haskell>
   
Solution:
+
[[99 questions/Solutions/1 | Solutions]]
   
<haskell>
 
last :: [a] -> a
 
last [x] = x
 
last (_:xs) = last xs
 
</haskell>
 
 
This function is defined in Prelude.
 
   
 
== Problem 2 ==
 
== Problem 2 ==
   
(*) Find the last but one box of a list.
+
(*) Find the last but one element of a list.
<pre>
 
Example:
 
* (my-but-last '(a b c d))
 
(C D)
 
</pre>
 
   
This can be done by dropping all but the last two elements of a list:
+
(Note that the Lisp transcription of this problem is incorrect.)
  +
  +
Example in Haskell:
   
 
<haskell>
 
<haskell>
myButLast :: [a] -> [a]
+
Prelude> myButLast [1,2,3,4]
myButLast list = drop ((length list) - 2) list
+
3
  +
Prelude> myButLast ['a'..'z']
  +
'y'
 
</haskell>
 
</haskell>
  +
  +
[[99 questions/Solutions/2 | Solutions]]
  +
   
 
== Problem 3 ==
 
== Problem 3 ==
   
(*) Find the K'th element of a list.
+
(*) Find the K'th element of a list. The first element in the list is number 1.
The first element in the list is number 1.
+
<pre>
 
 
Example:
 
Example:
  +
  +
<pre>
 
* (element-at '(a b c d e) 3)
 
* (element-at '(a b c d e) 3)
C
+
c
 
</pre>
 
</pre>
   
This is (almost) the infix operator !! in Prelude, which is defined as:
+
Example in Haskell:
   
 
<haskell>
 
<haskell>
(!!) :: [a] -> Int -> a
+
Prelude> elementAt [1,2,3] 2
(x:_) !! 0 = x
+
2
(_:xs) !! n = xs !! (n-1)
+
Prelude> elementAt "haskell" 5
  +
'e'
 
</haskell>
 
</haskell>
   
Except this doesn't quite work, because !! is zero-indexed, and element-at should be one-indexed. So:
+
[[99 questions/Solutions/3 | Solutions]]
   
<haskell>
 
elementAt :: [a] -> Int -> a
 
elementAt list i = list !! (i-1)
 
</haskell>
 
   
 
== Problem 4 ==
 
== Problem 4 ==
Line 67: Line 61:
 
(*) Find the number of elements of a list.
 
(*) Find the number of elements of a list.
   
This is "length" in Prelude, which is defined as:
+
Example in Haskell:
   
 
<haskell>
 
<haskell>
length :: [a] -> Int
+
Prelude> myLength [123, 456, 789]
length [] = 0
+
3
length (_:l) = 1 + length l
+
Prelude> myLength "Hello, world!"
  +
13
 
</haskell>
 
</haskell>
  +
  +
[[99 questions/Solutions/4 | Solutions]]
  +
   
 
== Problem 5 ==
 
== Problem 5 ==
Line 79: Line 76:
 
(*) Reverse a list.
 
(*) Reverse a list.
   
This is "reverse" in Prelude, which is defined as:
+
Example in Haskell:
   
 
<haskell>
 
<haskell>
reverse :: [a] -> [a]
+
Prelude> reverse "A man, a plan, a canal, panama!"
reverse = foldl (flip (:)) []
+
"!amanap ,lanac a ,nalp a ,nam A"
  +
Prelude> reverse [1,2,3,4]
  +
[4,3,2,1]
 
</haskell>
 
</haskell>
   
The standard definition is concise, but not very readable. Another way to define reverse is:
+
[[99 questions/Solutions/5 | Solutions]]
   
<haskell>
 
reverse :: [a] -> [a]
 
reverse [] = []
 
reverse (x:xs) = reverse xs ++ [x]
 
</haskell>
 
   
 
== Problem 6 ==
 
== Problem 6 ==
Line 98: Line 90:
 
(*) Find out whether a list is a palindrome. A palindrome can be read forward or backward; e.g. (x a m a x).
 
(*) 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:
+
Example in Haskell:
   
 
<haskell>
 
<haskell>
isPalindrome :: (Eq a) => [a] -> Bool
+
*Main> isPalindrome [1,2,3]
isPalindrome xs = xs == (reverse xs)
+
False
  +
*Main> isPalindrome "madamimadam"
  +
True
  +
*Main> isPalindrome [1,2,4,8,16,8,4,2,1]
  +
True
 
</haskell>
 
</haskell>
  +
  +
[[99 questions/Solutions/6 | Solutions]]
  +
   
 
== Problem 7 ==
 
== Problem 7 ==
Line 111: Line 106:
 
Transform a list, possibly holding lists as elements into a `flat' list by replacing each list with its elements (recursively).
 
Transform a list, possibly holding lists as elements into a `flat' list by replacing each list with its elements (recursively).
   
<pre>
 
 
Example:
 
Example:
  +
  +
<pre>
 
* (my-flatten '(a (b (c d) e)))
 
* (my-flatten '(a (b (c d) e)))
 
(A B C D E)
 
(A B C D E)
 
</pre>
 
</pre>
   
This is tricky, because lists in Haskell are homogeneous. [1, [2, [3, 4], 5]]
+
Example in Haskell:
is a type error. We have to devise some way of represent a list that may (or
 
may not) be nested:
 
   
  +
We have to define a new data type, because lists in Haskell are homogeneous.
 
<haskell>
 
<haskell>
data NestedList a = Elem a | List [NestedList a]
+
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)
 
 
</haskell>
 
</haskell>
   
Our NestedList datatype is either a single element of some type (Elem a), or a
+
<haskell>
list of NestedLists of the same type. (List [NestedList a]). Let's try it out in ghci:
 
 
<pre>
 
 
*Main> flatten (Elem 5)
 
*Main> flatten (Elem 5)
 
[5]
 
[5]
Line 130: Line 127:
 
*Main> flatten (List [])
 
*Main> flatten (List [])
 
[]
 
[]
</pre>
+
</haskell>
  +
  +
  +
  +
[[99 questions/Solutions/7 | Solutions]]
   
 
== Problem 8 ==
 
== Problem 8 ==
Line 138: Line 135:
 
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.
 
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.
   
<pre>
 
 
Example:
 
Example:
  +
  +
<pre>
 
* (compress '(a a a a b c c a a d e e e e))
 
* (compress '(a a a a b c c a a d e e e e))
 
(A B C A D E)
 
(A B C A D E)
  +
</pre>
   
 
Example in Haskell:
 
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']
 
</pre>
 
   
Solution:
 
 
<haskell>
 
<haskell>
compress :: Eq a => [a] -> [a]
+
> compress ["a","a","a","a","b","c","c","a","a","d","e","e","e","e"]
compress = map head . group
+
["a","b","c","a","d","e"]
 
</haskell>
 
</haskell>
   
We simply group equal values together (group), then take the head of each.
+
[[99 questions/Solutions/8 | Solutions]]
Note that (with GHC) we must give an explicit type to ''compress'' otherwise we get:
 
 
<haskell>
 
Ambiguous type variable `a' in the constraint:
 
`Eq a'
 
arising from use of `group'
 
Possible cause: the monomorphism restriction applied to the following:
 
compress :: [a] -> [a]
 
Probable fix: give these definition(s) an explicit type signature
 
or use -fno-monomorphism-restriction
 
</haskell>
 
 
We can circumvent the monomorphism restriction by writing ''compress'' this way (See: section 4.5.4 of [http://haskell.org/onlinereport the report]):
 
 
<haskell>compress xs = map head $ group xs</haskell>
 
   
 
== Problem 9 ==
 
== Problem 9 ==
Line 161: Line 156:
 
If a list contains repeated elements they should be placed in separate sublists.
 
If a list contains repeated elements they should be placed in separate sublists.
   
+
Example:
   
 
<pre>
 
<pre>
Example:
 
 
* (pack '(a a a a b c c a a d e e e e))
 
* (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))
 
((A A A A) (B) (C C) (A A) (D) (E E E E))
<example in lisp>
+
</pre>
   
 
Example in Haskell:
 
Example in Haskell:
</pre>
 
   
Solution:
 
 
<haskell>
 
<haskell>
group (x:xs) = let (first,rest) = span (==x) xs
+
*Main> pack ['a', 'a', 'a', 'a', 'b', 'c', 'c', 'a',
in (x:first) : group rest
+
'a', 'd', 'e', 'e', 'e', 'e']
group [] = []
+
["aaaa","b","cc","aa","d","eeee"]
 
</haskell>
 
</haskell>
   
'group' is also in the Prelude, here's an implementation using 'span'.
+
[[99 questions/Solutions/9 | Solutions]]
+
 
== Problem 10 ==
 
== Problem 10 ==
   
Line 188: Line 180:
 
Example:
 
Example:
 
<pre>
 
<pre>
* (encode '(a a a a b c c a a d e e e e))
+
* (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))<Problem description>
+
((4 A) (1 B) (2 C) (2 A) (1 D)(4 E))
+
</pre>
Example:
 
<example in lisp>
 
   
 
Example in Haskell:
 
Example in Haskell:
+
<haskell>
 
encode "aaaabccaadeeee"
 
encode "aaaabccaadeeee"
 
[(4,'a'),(1,'b'),(2,'c'),(2,'a'),(1,'d'),(4,'e')]
 
[(4,'a'),(1,'b'),(2,'c'),(2,'a'),(1,'d'),(4,'e')]
  +
</haskell>
  +
  +
[[99 questions/Solutions/10 | Solutions]]
   
</pre>
 
   
Solution:
 
<haskell>
 
encode xs = map (\x -> (length x,head x)) (group xs)
 
</haskell>
 
 
 
[[Category:Tutorials]]
 
[[Category:Tutorials]]

Revision as of 16:10, 5 October 2012


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

1 Problem 1

(*) Find the last element of a list.

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

Example in Haskell:

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

Solutions


2 Problem 2

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

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

Example in Haskell:

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

Solutions


3 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

Example in Haskell:

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

Solutions


4 Problem 4

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

Example in Haskell:

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

Solutions


5 Problem 5

(*) Reverse a list.

Example in Haskell:

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

Solutions


6 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).

Example in Haskell:

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

Solutions


7 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)

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]
*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 [])
[]


Solutions

8 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:

> compress ["a","a","a","a","b","c","c","a","a","d","e","e","e","e"]
["a","b","c","a","d","e"]

Solutions

9 Problem 9

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

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

Solutions

10 Problem 10

(*) Run-length encoding of a list. Use the result of problem P09 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:

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

Solutions