Beh01 at 13:23, 15 October 2024

2024-10-15T13:23:39Z

Beh01: Created page with " == Binary Trees == * Create a data type `Tree` that defines binary tree where values are stored in leaves and also in branches.

2022-09-30T09:42:31Z

Created page with " == Binary Trees == * Create a data type <code>Tree</code> that defines binary tree where values are stored in leaves and also in branches. <div class="mw-collapsible mw-coll..."

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== Binary Trees ==
* Create a data type <code>Tree</code> that defines binary tree where values are stored in leaves and also in branches.
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<syntaxhighlight lang="Haskell">
data Tree a = Leaf a
| Branch a (Tree a) (Tree a) deriving (Show)
</syntaxhighlight>
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* Prepare an example of a binary tree.
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<syntaxhighlight lang="Haskell">
testTree1 :: Tree Int
testTree1 = Branch 12 (Branch 23 (Leaf 34) (Leaf 45)) (Leaf 55)

testTree2 :: Tree Char
testTree2 = Branch 'a' (Branch 'b' (Leaf 'c') (Leaf 'd')) (Leaf 'e')
</syntaxhighlight>
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* Create a function that sums all values stored in the tree.
<syntaxhighlight lang="Haskell">
sum' :: Tree Int -> Int
</syntaxhighlight>

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<syntaxhighlight lang="Haskell">
sum' :: Tree Int -> Int
sum' (Leaf x) = x
sum' (Branch x l r) = sum' l + x + sum' r
</syntaxhighlight>
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* Create a function that extracts all values from the tree into an list.
<syntaxhighlight lang="Haskell">
toList :: Tree a -> [a]
</syntaxhighlight>

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<syntaxhighlight lang="Haskell">
toList :: Tree a -> [a]
toList (Leaf x) = [x]
toList (Branch x l r) = toList l ++ [x] ++ toList r
</syntaxhighlight>
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* One possibility how to represent a tree in a textual form is <code>a(b(d,e),c(e,f(g,h)))</code>. Create functions that are able to read and store a tree in such a notation.
<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/b0EF9WQw-uw]]</div>
<syntaxhighlight lang="Haskell">
toString :: Show a => Tree a -> String
fromString :: Read a => String -> Tree a
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
toString :: Show a => Tree a -> String
toString (Leaf x) = show x
toString (Branch x l r) = show x ++ "(" ++ (toString l) ++ "," ++ (toString r) ++ ")"

fromString :: Read a => String -> Tree a
fromString inp = fst (fromString' inp) where
fromString' :: Read a => String -> (Tree a,String)
fromString' inp =
let
before = takeWhile (\x -> x /='(' && x /=',' && x/=')') inp
after = dropWhile (\x -> x /='(' && x /=',' && x/=')') inp
value = read before
in if null after || head after /= '(' then (Leaf value, after) else
let
(l,after') = fromString' (tail after)
(r,after'') = fromString' (tail after')
in (Branch value l r, tail after'')
</syntaxhighlight>
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@@ Line 76: / Line 76: @@
            (r,after'') = fromString' (tail after')
          in (Branch value l r, tail after'')
 </syntaxhighlight>
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