# 99 questions/Solutions/3

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< 99 questions | Solutions(Difference between revisions)

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<haskell> |
<haskell> |
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elementAt :: [a] -> Int -> a |
elementAt :: [a] -> Int -> a |
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− | elementAt list i = list !! (i-1) |
+ | elementAt list i = list !! (i-1) |

</haskell> |
</haskell> |
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<haskell> |
<haskell> |
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elementAt' :: [a] -> Int -> a |
elementAt' :: [a] -> Int -> a |
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− | elementAt' (x:_) 1 = x |
+ | elementAt' (x:_) 1 = x |

− | elementAt' [] _ = error "Index out of bounds" |
+ | elementAt' [] _ = error "Index out of bounds" |

elementAt' (_:xs) k |
elementAt' (_:xs) k |
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− | | k < 1 = error "Index out of bounds" |
+ | | k < 1 = error "Index out of bounds" |

− | | otherwise = elementAt' xs (k - 1) |
+ | | otherwise = elementAt' xs (k - 1) |

</haskell> |
</haskell> |
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<haskell> |
<haskell> |
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elementAt'' :: [a] -> Int -> a |
elementAt'' :: [a] -> Int -> a |
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− | elementAt'' (x:_) 1 = x |
+ | elementAt'' (x:_) 1 = x |

− | elementAt'' (_:xs) i = elementAt xs (i - 1) |
+ | elementAt'' (_:xs) i = elementAt'' xs (i - 1) |

− | elementAt'' _ _ = error "Index out of bounds" |
+ | elementAt'' _ _ = error "Index out of bounds" |

</haskell> |
</haskell> |
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'''This does not work correctly on invalid indexes and infinite lists, e.g.:''' |
'''This does not work correctly on invalid indexes and infinite lists, e.g.:''' |
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A few more solutions using prelude functions: |
A few more solutions using prelude functions: |
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+ | |||

+ | <haskell> |
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+ | elementAt'' xs n | length xs < n = error "Index out of bounds" |
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+ | | otherwise = fst . last $ zip xs [1..n] |
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+ | </haskell> |
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+ | |||

+ | <haskell> |
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+ | elementAt''' xs n = head $ foldr ($) xs |
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+ | $ replicate (n - 1) tail |
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+ | </haskell> |
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<haskell> |
<haskell> |
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<haskell> |
<haskell> |
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− | elementAt''' xs n = head . drop (n - 1) $ xs |
+ | elementAt_w''' xs n = head . drop (n - 1) $ xs -- wrong |

+ | -- Main> map (elementAt_w''' [1..4]) [0..10] |
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+ | -- [1,1,2,3,4,*** Exception: Prelude.head: empty list |
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+ | </haskell> |
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+ | |||

+ | or <hask>elementAt_w'</hask> correctly in point-free style: |
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+ | <haskell> |
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+ | elementAt_w'pf = (last .) . take . (+ 1) |
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+ | </haskell> |
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+ | |||

+ | Pedantic note: the above definition of <hask>elementAt_w'pf</hask> does not conform to the order of arguments specified by the question, but the following does: |
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+ | <haskell> |
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+ | elementAt_w'pf' = flip $ (last .) . take . (+ 1) |
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</haskell> |
</haskell> |

## Revision as of 18:58, 30 November 2012

(*) Find the K'th element of a list. The first element in the list is number 1.

This is (almost) the infix operator !! in Prelude, which is defined as:

(!!) :: [a] -> Int -> a (x:_) !! 0 = x (_:xs) !! n = xs !! (n-1)

Except this doesn't quite work, because !! is zero-indexed, and element-at should be one-indexed. So:

elementAt :: [a] -> Int -> a elementAt list i = list !! (i-1)

Or without using the infix operator:

elementAt' :: [a] -> Int -> a elementAt' (x:_) 1 = x elementAt' [] _ = error "Index out of bounds" elementAt' (_:xs) k | k < 1 = error "Index out of bounds" | otherwise = elementAt' xs (k - 1)

Alternative version:

elementAt'' :: [a] -> Int -> a elementAt'' (x:_) 1 = x elementAt'' (_:xs) i = elementAt'' xs (i - 1) elementAt'' _ _ = error "Index out of bounds"

**This does not work correctly on invalid indexes and infinite lists, e.g.:**

elementAt'' [1..] 0

A few more solutions using prelude functions:

elementAt'' xs n | length xs < n = error "Index out of bounds" | otherwise = fst . last $ zip xs [1..n]

elementAt''' xs n = head $ foldr ($) xs $ replicate (n - 1) tail

elementAt_w' xs n = last . take n $ xs -- wrong -- Main> map (elementAt_w' [1..4]) [1..10] -- [1,2,3,4,4,4,4,4,4,4]

elementAt_w'' xs n = head . reverse . take n $ xs -- wrong -- Main> map (elementAt_w'' [1..4]) [1..10] -- [1,2,3,4,4,4,4,4,4,4]

elementAt_w''' xs n = head . drop (n - 1) $ xs -- wrong -- Main> map (elementAt_w''' [1..4]) [0..10] -- [1,1,2,3,4,*** Exception: Prelude.head: empty list

elementAt_w'

elementAt_w'pf = (last .) . take . (+ 1)

elementAt_w'pf

elementAt_w'pf' = flip $ (last .) . take . (+ 1)