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92 lines
2.3 KiB
Elm
92 lines
2.3 KiB
Elm
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{-----------------------------------------------------------------
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Overview: A "Tree" represents a binary tree. A "Node" in a binary
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tree always has two children. A tree can also be "Empty". Below
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I have defined "Tree" and a number of useful functions.
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This example also includes some challenge problems :)
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-----------------------------------------------------------------}
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data Tree a = Node a (Tree a) (Tree a) | Empty
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empty = Empty
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singleton v = Node v Empty Empty
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insert x tree =
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case tree of
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Empty -> singleton x
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Node y left right ->
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if x == y then tree else
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if x < y then Node y (insert x left) right
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else Node y left (insert x right)
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fromList xs = foldl insert empty xs
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depth tree =
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case tree of
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Node v left right -> 1 + max (depth left) (depth right)
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Empty -> 0
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map f tree =
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case tree of
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Node v left right -> Node (f v) (map f left) (map f right)
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Empty -> Empty
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t1 = fromList [1,2,3]
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t2 = fromList [2,1,3]
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main = flow down [ display "depth" depth t1
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, display "depth" depth t2
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, display "map ((+)1)" (map ((+)1)) t2
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]
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display name f v =
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text . monospace . toText $
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concat [ show (f v), " ⇐ ", name, " ", show v ]
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{-----------------------------------------------------------------
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Exercises:
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(1) Sum all of the elements of a tree.
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sum :: Tree Number -> Number
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(2) Flatten a tree into a list.
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flatten :: Tree a -> [a]
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(3) Check to see if an element is in a given tree.
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isElement :: a -> Tree a -> Bool
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(4) Write a general fold function that acts on trees. The fold
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function does not need to guarantee a particular order of
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traversal.
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fold :: (a -> b -> b) -> b -> Tree a -> b
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(5) Use "fold" to do exercises 1-3 in one line each. The best
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readable versions I have come up have the following length
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in characters including spaces and function name:
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sum: 16
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flatten: 21
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isElement: 46
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See if you can match or beat me! Don't forget about currying
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and partial application!
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(6) Can "fold" be used to implement "map" or "depth"?
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(7) Try experimenting with different ways to traverse a
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tree: pre-order, in-order, post-order, depth-first, etc.
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More info at: http://en.wikipedia.org/wiki/Tree_traversal
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-----------------------------------------------------------------}
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