Difference between revisions of "99 questions/1 to 10"
(fixed broken links to solutions) 
(moved solutions 610 to new subpages of 99 questions/Solutions, and cleaned up formatting) 

Line 49:  Line 49:  
<pre> 
<pre> 

* (elementat '(a b c d e) 3) 
* (elementat '(a b c d e) 3) 

−  C 

+  c 

</pre> 
</pre> 

Line 111:  Line 111:  
</haskell> 
</haskell> 

−  Solution: 

+  [[99 questions/Solutions/6  Solutions]] 

−  <haskell> 

−  isPalindrome :: (Eq a) => [a] > Bool 

−  isPalindrome xs = xs == (reverse xs) 

−  </haskell> 

== Problem 7 == 
== Problem 7 == 

Line 142:  Line 138:  
</haskell> 
</haskell> 

−  Solution: 

+  [[99 questions/Solutions/7  Solutions]] 

−  <haskell> 

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

−  
−  flatten :: NestedList a > [a] 

−  flatten (Elem x) = [x] 

−  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. 

−  
−  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 == 

Line 165:  Line 147:  
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: 

−  <haskell> 

−  compress :: Eq a => [a] > [a] 

−  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: 

−  `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 fnomonomorphismrestriction 

−  </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> 

−  
−  An alternative solution is 

−  
−  <haskell> 

−  compress [] = [] 

−  compress [a] = [a] 

−  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 

−  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 [] = ([], []) 

−  getReps (y:ys) 

−   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)) 

−  +  ((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 NinetyNine Haskell Problems, based on NinetyNine Prolog Problems and NinetyNine 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
(*) 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'
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'
Problem 3
(*) Find the K'th element of a list. The first element in the list is number 1.
Example:
* (elementat '(a b c d e) 3) c
Example in Haskell:
Prelude> elementAt [1,2,3] 2
2
Prelude> elementAt "haskell" 5
'e'
Problem 4
(*) Find the number of elements of a list.
Example in Haskell:
Prelude> myLength [123, 456, 789]
3
Prelude> myLength "Hello, world!"
13
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]
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
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:
* (myflatten '(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 [])
[]
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']
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"]
Problem 10
(*) Runlength encoding of a list. Use the result of problem P09 to implement the socalled runlength 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')]