# Difference between revisions of "99 questions/Solutions/7"

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< 99 questions | Solutions

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rec acc (Elem x) = x:acc |
rec acc (Elem x) = x:acc |
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rec acc (List (x:xs)) = rec (rec acc x) (List xs) |
rec acc (List (x:xs)) = rec (rec acc x) (List xs) |
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+ | </haskell> |
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+ | |||

+ | or making NestedList an instance of Fordable: |
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+ | <haskell> |
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+ | import qualified Data.Foldable as F |
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+ | instance F.Foldable NestedList where |
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+ | foldMap f (Elem x) = f x |
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+ | foldMap f (List []) = mempty |
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+ | foldMap f (List (x:xs)) = F.foldMap f x `mappend` F.foldMap f (List xs) |
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+ | |||

+ | flatten5 :: NestedList a -> [a] |
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+ | flatten5 = F.foldMap (\x -> [x]) |
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</haskell> |
</haskell> |
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## Revision as of 17:39, 23 March 2017

(**) Flatten a nested list structure.

```
data NestedList a = Elem a | List [NestedList a]
flatten :: NestedList a -> [a]
flatten (Elem x) = [x]
flatten (List x) = concatMap flatten x
```

or without concatMap

```
flatten :: NestedList a -> [a]
flatten (Elem a ) = [a]
flatten (List (x:xs)) = flatten x ++ flatten (List xs)
flatten (List []) = []
```

or using things that act just like `concatMap`

```
flatten (Elem x) = return x
flatten (List x) = flatten =<< x
flatten (Elem x) = [x]
flatten (List x) = foldMap flatten x
```

```
flatten2 :: NestedList a -> [a]
flatten2 a = flt' a []
where flt' (Elem x) xs = x:xs
flt' (List (x:ls)) xs = flt' x (flt' (List ls) xs)
flt' (List []) xs = xs
```

or with foldr

```
flatten3 :: NestedList a -> [a]
flatten3 (Elem x ) = [x]
flatten3 (List xs) = foldr (++) [] $ map flatten3 xs
```

or with an accumulator function:

```
flatten4 = reverse . rec []
where
rec acc (List []) = acc
rec acc (Elem x) = x:acc
rec acc (List (x:xs)) = rec (rec acc x) (List xs)
```

or making NestedList an instance of Fordable:

```
import qualified Data.Foldable as F
instance F.Foldable NestedList where
foldMap f (Elem x) = f x
foldMap f (List []) = mempty
foldMap f (List (x:xs)) = F.foldMap f x `mappend` F.foldMap f (List xs)
flatten5 :: NestedList a -> [a]
flatten5 = F.foldMap (\x -> [x])
```

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]).