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99 questions/1 to 10

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<pre>
<pre>
* (element-at '(a b c d e) 3)
* (element-at '(a b c d e) 3)
-
C
+
c
</pre>
</pre>
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</haskell>
</haskell>
-
Solution:
+
[[99 questions/Solutions/6 | Solutions]]
-
<haskell>
 
-
isPalindrome :: (Eq a) => [a] -> Bool
 
-
isPalindrome xs = xs == (reverse xs)
 
-
</haskell>
 
== Problem 7 ==
== Problem 7 ==
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</haskell>
</haskell>
-
Solution:
+
[[99 questions/Solutions/7 | Solutions]]
-
<haskell>
 
-
data NestedList a = Elem a | List [NestedList a]
 
-
 
-
flatten :: NestedList a -> [a]
 
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flatten (Elem x) = [x]
 
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flatten (List x) = concatMap flatten x
 
-
</haskell>
 
-
 
-
We have to define a new data type, because lists in Haskell are homogeneous.
 
-
[1, [2, [3, 4], 5]] is a type error. Therefore, we must have a way of
 
-
representing a list that may (or may not) be nested.
 
-
 
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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]).
 
== Problem 8 ==
== Problem 8 ==
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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:
 +
 +
<haskell>
*Main> compress ['a','a','a','a','b','c','c','a','a','d','e','e','e','e']
*Main> 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>
 
-
 
-
Solution:
 
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<haskell>
 
-
compress :: Eq a => [a] -> [a]
 
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compress = map head . group
 
</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:
 
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`Eq a'
 
-
arising from use of `group'
 
-
Possible cause: the monomorphism restriction applied to the following:
 
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compress :: [a] -> [a]
 
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Probable fix: give these definition(s) an explicit type signature
 
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or use -fno-monomorphism-restriction
 
-
</haskell>
 
-
 
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We can circumvent the monomorphism restriction by writing ''compress'' this way (See: section 4.5.4 of [http://haskell.org/onlinereport the report]):
 
-
 
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<haskell>compress xs = map head $ group xs</haskell>
 
-
 
-
An alternative solution is
 
-
 
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<haskell>
 
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compress [] = []
 
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compress [a] = [a]
 
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compress (x : y : xs) = (if x == y then [] else [x]) ++ compress (y : xs)
 
-
</haskell>
 
== Problem 9 ==
== Problem 9 ==
Line 210: Line 168:
(**) Pack consecutive duplicates of list elements into sublists.
(**) Pack consecutive duplicates of list elements into sublists.
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:
 +
 +
<haskell>
*Main> pack ['a', 'a', 'a', 'a', 'b', 'c', 'c', 'a', 'a', 'd', 'e', 'e', 'e', 'e']
*Main> pack ['a', 'a', 'a', 'a', 'b', 'c', 'c', 'a', 'a', 'd', 'e', 'e', 'e', 'e']
["aaaa","b","cc","aa","d","eeee"]
["aaaa","b","cc","aa","d","eeee"]
-
</pre>
 
-
 
-
Solution:
 
-
<haskell>
 
-
pack (x:xs) = let (first,rest) = span (==x) xs
 
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in (x:first) : pack rest
 
-
pack [] = []
 
</haskell>
</haskell>
-
A more verbose solution is
+
[[99 questions/Solutions/9 | Solutions]]
-
<haskell>
+
-
pack :: Eq a => [a] -> [[a]]
+
-
pack [] = []
+
-
pack (x:xs) = (x:first) : pack rest
+
-
where
+
-
getReps [] = ([], [])
+
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getReps (y:ys)
+
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| y == x = let (f,r) = getReps ys in (y:f, r)
+
-
| otherwise = ([], (y:ys))
+
-
(first,rest) = getReps xs
+
-
</haskell>
+
-
This is implemented as <hask>group</hask> in <hask>Data.List</hask>.
 
== Problem 10 ==
== Problem 10 ==
Line 251: Line 193:
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))
+
((4 A) (1 B) (2 C) (2 A) (1 D)(4 E))
</pre>
</pre>
Example in Haskell:
Example in Haskell:
-
<pre>
+
<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')]
-
</pre>
 
-
 
-
Solution:
 
-
<haskell>
 
-
encode xs = map (\x -> (length x,head x)) (group xs)
 
</haskell>
</haskell>
-
which can also be expressed as a list comprehension:
+
[[99 questions/Solutions/10 | Solutions]]
-
<haskell>
 
-
[(length x, head x) | x <- group xs]
 
-
</haskell>
 
-
Or writing it [[Pointfree]]:
 
-
 
-
<haskell>
 
-
encode :: Eq a => [a] -> [(Int, a)]
 
-
encode = map (\x -> (length x, head x)) . group
 
-
</haskell>
 
-
 
-
Or (ab)using the "&&&" arrow operator for tuples:
 
-
 
-
<haskell>
 
-
encode :: Eq a => [a] -> [(Int, a)]
 
-
encode xs = map (length &&& head) $ group xs
 
-
</haskell>
 
[[Category:Tutorials]]
[[Category:Tutorials]]

Revision as of 15:27, 13 July 2010


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

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: 

*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: 

*Main> 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

Retrieved from "http://www.haskell.org/haskellwiki/99_questions/1_to_10"

Category: Tutorials