99 questions/11 to 20
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m (Changed "... the i'th and and i'th ..." to "... the i'th and k'th ..." in problem 18) 
Lyklykkkkkkk (Talk  contribs) m (→Problem 20) 

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== Problem 11 == 
== Problem 11 == 

−  (*) Modified runlength encoding. 
+  (*) Modified runlength encoding. 
+  
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. 
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: 

<pre> 
<pre> 

−  Example: 

* (encodemodified '(a a a a b c c a a d e e e e)) 
* (encodemodified '(a a a a b c c a a d e e e e)) 

((4 A) B (2 C) (2 A) D (4 E)) 
((4 A) B (2 C) (2 A) D (4 E)) 

+  </pre> 

Example in Haskell: 
Example in Haskell: 

−  P11> encodeModified "aaaabccaadeeee" 

−  [Multiple 4 'a',Single 'b',Multiple 2 'c',Multiple 2 'a',Single 'd',Multiple 4 'e'] 

−  </pre> 

−  Solution: 

<haskell> 
<haskell> 

−  data ListItem a = Single a  Multiple Int a 
+  P11> encodeModified "aaaabccaadeeee" 
−  deriving (Show) 
+  [Multiple 4 'a',Single 'b',Multiple 2 'c', 
−  +  Multiple 2 'a',Single 'd',Multiple 4 'e'] 

−  encodeModified :: Eq a => [a] > [ListItem a] 

−  encodeModified = map encodeHelper . encode 

−  where 

−  encodeHelper (1,x) = Single x 

−  encodeHelper (n,x) = Multiple n x 

</haskell> 
</haskell> 

−  Again, like in problem 7, we need a utility type because lists in haskell are homogeneous. Afterwards we use the <hask>encode</hask> function from problem 10 and map single instances of a list item to <hask>Single</hask> and multiple ones to <hask>Multiple</hask>. 
+  [[99 questions/Solutions/11  Solutions]] 
−  The ListItem definition contains 'deriving (Show)' so that we can get interactive output. 

−  
== Problem 12 == 
== Problem 12 == 

−  (**) Decode a runlength encoded list. 
+  (**) Decode a runlength encoded list. 
+  
Given a runlength code list generated as specified in problem 11. Construct its uncompressed version. 
Given a runlength code list generated as specified in problem 11. Construct its uncompressed version. 

−  <pre> 

Example in Haskell: 
Example in Haskell: 

−  P12> decodeModified [Multiple 4 'a',Single 'b',Multiple 2 'c',Multiple 2 'a',Single 'd',Multiple 4 'e'] 

−  "aaaabccaadeeee" 

−  </pre> 

−  Solution: 

<haskell> 
<haskell> 

−  decodeModified :: [ListItem a] > [a] 
+  P12> decodeModified 
−  decodeModified = concatMap decodeHelper 
+  [Multiple 4 'a',Single 'b',Multiple 2 'c', 
−  where 
+  Multiple 2 'a',Single 'd',Multiple 4 'e'] 
−  decodeHelper (Single x) = [x] 
+  "aaaabccaadeeee" 
−  decodeHelper (Multiple n x) = replicate n x 

</haskell> 
</haskell> 

−  We only need to map single instances of an element to a list containing only one element and multiple ones to a list containing the specified number of elements and concatenate these lists. 
+  [[99 questions/Solutions/12  Solutions]] 
−  +  
== Problem 13 == 
== Problem 13 == 

(**) Runlength encoding of a list (direct solution). 
(**) Runlength encoding of a list (direct solution). 

+  
Implement the socalled runlength 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. 
Implement the socalled runlength 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. 

−  <pre> 

Example: 
Example: 

+  
+  <pre> 

* (encodedirect '(a a a a b c c a a d e e e e)) 
* (encodedirect '(a a a a b c c a a d e e e e)) 

((4 A) B (2 C) (2 A) D (4 E)) 
((4 A) B (2 C) (2 A) D (4 E)) 

+  </pre> 

Example in Haskell: 
Example in Haskell: 

−  P13> encodeDirect "aaaabccaadeeee" 

−  [Multiple 4 'a',Single 'b',Multiple 2 'c',Multiple 2 'a',Single 'd',Multiple 4 'e'] 

−  </pre> 

−  Solution: 

<haskell> 
<haskell> 

−  encode' :: Eq a => [a] > [(Int,a)] 
+  P13> encodeDirect "aaaabccaadeeee" 
−  encode' = foldr helper [] 
+  [Multiple 4 'a',Single 'b',Multiple 2 'c', 
−  where 
+  Multiple 2 'a',Single 'd',Multiple 4 'e'] 
−  helper x [] = [(1,x)] 

−  helper x (y:ys) 

−   x == snd y = (1+fst y,x):ys 

−   otherwise = (1,x):y:ys 

−  
−  encodeDirect :: Eq a => [a] > [ListItem a] 

−  encodeDirect = map encodeHelper . encode' 

−  where 

−  encodeHelper (1,x) = Single x 

−  encodeHelper (n,x) = Multiple n x 

</haskell> 
</haskell> 

−  First of all we could rewrite the function <hask>encode</hask> from problem 10 in a way that is does not create the sublists. Thus, I decided to traverse the original list from right to left (using <hask>foldr</hask>) and to prepend each element to the resulting list in the proper way. Thereafter we only need to modify the function <hask>encodeModified</hask> from problem 11 to use <hask>encode'</hask>. 
+  [[99 questions/Solutions/13  Solutions]] 
−  +  
== Problem 14 == 
== Problem 14 == 

(*) Duplicate the elements of a list. 
(*) Duplicate the elements of a list. 

−  <pre> 

Example: 
Example: 

+  
+  <pre> 

* (dupli '(a b c c d)) 
* (dupli '(a b c c d)) 

(A A B B C C C C D D) 
(A A B B C C C C D D) 

+  </pre> 

Example in Haskell: 
Example in Haskell: 

+  
+  <haskell> 

> dupli [1, 2, 3] 
> dupli [1, 2, 3] 

[1,1,2,2,3,3] 
[1,1,2,2,3,3] 

−  </pre> 

−  
−  Solution: 

−  <haskell> 

−  dupli [] = [] 

−  dupli (x:xs) = x:x:dupli xs 

</haskell> 
</haskell> 

−  or, using list comprehension syntax: 
+  [[99 questions/Solutions/14  Solutions]] 
−  <haskell> 

−  dupli list = concat [[x,x]  x < list] 

−  </haskell> 

−  or, using the list monad: 

−  <haskell> 

−  dupli xs = xs >>= (\x > [x,x]) 

−  </haskell> 

−  
== Problem 15 == 
== Problem 15 == 

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

+  
+  Example: 

<pre> 
<pre> 

−  Example: 

* (repli '(a b c) 3) 
* (repli '(a b c) 3) 

(A A A B B B C C C) 
(A A A B B B C C C) 

+  </pre> 

Example in Haskell: 
Example in Haskell: 

−  > repli "abc" 3 

−  "aaabbbccc" 

−  </pre> 

−  Solution: 

<haskell> 
<haskell> 

−  repli :: [a] > Int > [a] 
+  > repli "abc" 3 
−  repli xs n = concatMap (replicate n) xs 
+  "aaabbbccc" 
</haskell> 
</haskell> 

+  
+  [[99 questions/Solutions/15  Solutions]] 

+  
== Problem 16 == 
== Problem 16 == 

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

−  <pre> 

Example: 
Example: 

+  
+  <pre> 

* (drop '(a b c d e f g h i k) 3) 
* (drop '(a b c d e f g h i k) 3) 

(A B D E G H K) 
(A B D E G H K) 

+  </pre> 

Example in Haskell: 
Example in Haskell: 

+  
+  <haskell> 

*Main> dropEvery "abcdefghik" 3 
*Main> dropEvery "abcdefghik" 3 

"abdeghk" 
"abdeghk" 

−  </pre> 
+  </haskell> 
−  An iterative solution: 
+  [[99 questions/Solutions/16  Solutions]] 
−  <haskell> 

−  dropEvery :: [a] > Int > [a] 

−  dropEvery [] _ = [] 

−  dropEvery (x:xs) n = dropEvery' (x:xs) n 1 where 

−  dropEvery' (x:xs) n i = (if (n `divides` i) then 

−  [] else 

−  [x]) 

−  ++ (dropEvery' xs n (i+1)) 

−  dropEvery' [] _ _ = [] 

−  divides x y = y `mod` x == 0 

−  </haskell> 

−  or using zip: 

−  <haskell> 

−  dropEvery n = map snd . filter ((n/=) . fst) . zip (cycle [1..n]) 

−  </haskell> 

== Problem 17 == 
== Problem 17 == 

Line 150:  Line 132:  
Do not use any predefined predicates. 
Do not use any predefined predicates. 

+  
+  Example: 

<pre> 
<pre> 

−  Example: 

* (split '(a b c d e f g h i k) 3) 
* (split '(a b c d e f g h i k) 3) 

( (A B C) (D E F G H I K)) 
( (A B C) (D E F G H I K)) 

+  </pre> 

Example in Haskell: 
Example in Haskell: 

+  
+  <haskell> 

*Main> split "abcdefghik" 3 
*Main> split "abcdefghik" 3 

("abc", "defghik") 
("abc", "defghik") 

−  </pre> 

−  
−  Solution using take and drop: 

−  <haskell> 

−  split xs n = (take n xs, drop n xs) 

</haskell> 
</haskell> 

−  Alternatively, we have the following recursive solution: 
+  [[99 questions/Solutions/17  Solutions]] 
−  <haskell> 

−  split :: [a] > Int > ([a], [a]) 

−  split [] _ = ([], []) 

−  split l@(x : xs) n  n > 0 = (x : fst splitSub, snd splitSub) 

−   otherwise = ([], l) 

−  where splitSub = split xs (n  1) 

−  </haskell> 

−  Note that this function, with the parameters in the other order, exists as <hask>splitAt</hask>. 

−  
== Problem 18 == 
== Problem 18 == 

Line 177:  Line 156:  
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. 
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. 

−  <pre> 

Example: 
Example: 

+  
+  <pre> 

* (slice '(a b c d e f g h i k) 3 7) 
* (slice '(a b c d e f g h i k) 3 7) 

(C D E F G) 
(C D E F G) 

+  </pre> 

Example in Haskell: 
Example in Haskell: 

−  *Main> slice ['a','b','c','d','e','f','g','h','i','k'] 3 7 

−  "cdefg" 

−  </pre> 

−  Solution: 

<haskell> 
<haskell> 

−  slice xs (i+1) k = take (ki) $ drop i xs 
+  *Main> slice ['a','b','c','d','e','f','g','h','i','k'] 3 7 
+  "cdefg" 

</haskell> 
</haskell> 

+  
+  [[99 questions/Solutions/18  Solutions]] 

+  
== Problem 19 == 
== Problem 19 == 

Line 197:  Line 177:  
Hint: Use the predefined functions length and (++). 
Hint: Use the predefined functions length and (++). 

+  
+  Examples: 

<pre> 
<pre> 

−  Examples: 

* (rotate '(a b c d e f g h) 3) 
* (rotate '(a b c d e f g h) 3) 

(D E F G H A B C) 
(D E F G H A B C) 

Line 205:  Line 186:  
* (rotate '(a b c d e f g h) 2) 
* (rotate '(a b c d e f g h) 2) 

(G H A B C D E F) 
(G H A B C D E F) 

+  </pre> 

Examples in Haskell: 
Examples in Haskell: 

+  
+  <haskell> 

*Main> rotate ['a','b','c','d','e','f','g','h'] 3 
*Main> rotate ['a','b','c','d','e','f','g','h'] 3 

"defghabc" 
"defghabc" 

Line 212:  Line 196:  
*Main> rotate ['a','b','c','d','e','f','g','h'] (2) 
*Main> rotate ['a','b','c','d','e','f','g','h'] (2) 

"ghabcdef" 
"ghabcdef" 

−  </pre> 

−  
−  Solution: 

−  <haskell> 

−  rotate [] _ = [] 

−  rotate l 0 = l 

−  rotate (x:xs) (n+1) = rotate (xs ++ [x]) n 

−  rotate l n = rotate l (length l + n) 

</haskell> 
</haskell> 

−  There are two separate cases: 
+  [[99 questions/Solutions/19  Solutions]] 
−  * If n > 0, move the first element to the end of the list n times. 

−  * If n < 0, convert the problem to the equivalent problem for n > 0 by adding the list's length to n. 

−  or using cycle: 

−  <haskell> 

−  rotate xs n = take len . drop (n `mod` len) . cycle $ xs 

−  where len = length xs 

−  </haskell> 

−  
−  or 

−  
−  <haskell> 

−  rotate xs n = if n >= 0 then 

−  drop n xs ++ take n xs 

−  else let l = ((length xs) + n) in 

−  drop l xs ++ take l xs 

−  </haskell> 

−  
−  or 

−  
−  <haskell> 

−  rotate xs n = drop nn xs ++ take nn xs 

−  where 

−  nn = n `mod` length xs 

−  </haskell> 

== Problem 20 == 
== Problem 20 == 

Line 252:  Line 206:  
Example in Prolog: 
Example in Prolog: 

+  
<pre> 
<pre> 

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

Line 259:  Line 214:  
Example in Lisp: 
Example in Lisp: 

+  
<pre> 
<pre> 

* (removeat '(a b c d) 2) 
* (removeat '(a b c d) 2) 

(A C D) 
(A C D) 

</pre> 
</pre> 

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

Example in Haskell: 
Example in Haskell: 

−  <pre> 

−  *Main> removeAt 1 "abcd" 

−  ('b',"acd") 

−  </pre> 

−  Solution: 

<haskell> 
<haskell> 

−  removeAt :: Int > [a] > (a, [a]) 
+  *Main> removeAt 2 "abcd" 
−  removeAt k xs = case back of 
+  ('b',"acd") 
−  [] > error "removeAt: index too large" 

−  x:rest > (x, front ++ rest) 

−  where (front, back) = splitAt k xs 

</haskell> 
</haskell> 

−  Simply use the <hask>splitAt</hask> to split after k elements. 
+  [[99 questions/Solutions/20  Solutions]] 
−  If the original list has fewer than k+1 elements, the second list will be empty, and there will be no element to extract. 

−  Note that the Prolog and Lisp versions treat 1 as the first element in the list, and the Lisp version appends NIL elements to the end of the list if k is greater than the list length. 

−  or 

−  
−  <haskell> 

−  removeAt n xs = (xs!!n,take n xs ++ drop (n+1) xs) 

−  </haskell> 

[[Category:Tutorials]] 
[[Category:Tutorials]] 
Latest revision as of 08:05, 26 May 2012
This is part of NinetyNine Haskell Problems, based on NinetyNine Prolog Problems and NinetyNine Lisp Problems.
[edit] 1 Problem 11
(*) Modified runlength encoding.
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:
* (encodemodified '(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:
P11> encodeModified "aaaabccaadeeee" [Multiple 4 'a',Single 'b',Multiple 2 'c', Multiple 2 'a',Single 'd',Multiple 4 'e']
[edit] 2 Problem 12
(**) Decode a runlength encoded list.
Given a runlength code list generated as specified in problem 11. Construct its uncompressed version.
Example in Haskell:
P12> decodeModified [Multiple 4 'a',Single 'b',Multiple 2 'c', Multiple 2 'a',Single 'd',Multiple 4 'e'] "aaaabccaadeeee"
[edit] 3 Problem 13
(**) Runlength encoding of a list (direct solution).
Implement the socalled runlength 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:
* (encodedirect '(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:
P13> encodeDirect "aaaabccaadeeee" [Multiple 4 'a',Single 'b',Multiple 2 'c', Multiple 2 'a',Single 'd',Multiple 4 'e']
[edit] 4 Problem 14
(*) Duplicate the elements of a list.
Example:
* (dupli '(a b c c d)) (A A B B C C C C D D)
Example in Haskell:
> dupli [1, 2, 3] [1,1,2,2,3,3]
[edit] 5 Problem 15
(**) Replicate the elements of a list a given number of times.
Example:
* (repli '(a b c) 3) (A A A B B B C C C)
Example in Haskell:
> repli "abc" 3 "aaabbbccc"
[edit] 6 Problem 16
(**) Drop every N'th element from a list.
Example:
* (drop '(a b c d e f g h i k) 3) (A B D E G H K)
Example in Haskell:
*Main> dropEvery "abcdefghik" 3 "abdeghk"
[edit] 7 Problem 17
(*) Split a list into two parts; the length of the first part is given.
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:
*Main> split "abcdefghik" 3 ("abc", "defghik")
[edit] 8 Problem 18
(**) Extract a slice from a list.
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:
*Main> slice ['a','b','c','d','e','f','g','h','i','k'] 3 7 "cdefg"
[edit] 9 Problem 19
(**) Rotate a list N places to the left.
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:
*Main> rotate ['a','b','c','d','e','f','g','h'] 3 "defghabc" *Main> rotate ['a','b','c','d','e','f','g','h'] (2) "ghabcdef"
[edit] 10 Problem 20
(*) Remove the K'th element from a list.
Example in Prolog:
? remove_at(X,[a,b,c,d],2,R). X = b R = [a,c,d]
Example in Lisp:
* (removeat '(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:
*Main> removeAt 2 "abcd" ('b',"acd")