Elm binary tree exercises from http://elm-lang.org/examples/binary-tree

elm-binary-tree.elm

{- OVERVIEW ------------------------------------------------------

A "Tree" represents a binary tree. A "Node" in a binary tree
always has two children. A tree can also be "Empty". Below I have
defined "Tree" and a number of useful functions.

This example also includes some challenge problems!

-----------------------------------------------------------------}


import Html exposing (Html, div, text)
import Html.Attributes exposing (style)



-- TREES


type Tree a
    = Empty
    | Node a (Tree a) (Tree a)


empty : Tree a
empty =
    Empty


singleton : a -> Tree a
singleton v =
    Node v Empty Empty


insert : comparable -> Tree comparable -> Tree comparable
insert x tree =
    case tree of
      Empty ->
          singleton x

      Node y left right ->
          if x > y then
              Node y left (insert x right)

          else if x < y then
              Node y (insert x left) right

          else
              tree


fromList : List comparable -> Tree comparable
fromList xs =
    List.foldl insert empty xs


depth : Tree a -> Int
depth tree =
    case tree of
      Empty -> 0
      Node v left right ->
          1 + max (depth left) (depth right)


map : (a -> b) -> Tree a -> Tree b
map f tree =
    case tree of
      Empty -> Empty
      Node v left right ->
          Node (f v) (map f left) (map f right)

sum : Tree number -> number
sum tree =
  case tree of
    Empty -> 0
    Node v left right ->
      v + (sum left) + (sum right)

flatten : Tree a -> List a
flatten tree =
  case tree of
    Empty -> []
    Node v left right ->
      [v] ++ flatten left ++ flatten right
      
isElement : a -> Tree a -> Bool
isElement element tree =
  case tree of
    Empty -> False
    Node v left right ->
      if v == element then True
      else (isElement element left) || (isElement element right)

fold : (a -> b -> b) -> b -> Tree a -> b
fold f b tree =
  let
    asList = flatten tree
    fold' acc list =
      case List.head list of
        Just h -> fold' (f h acc) (List.drop 1 list)
        Nothing -> acc
  in
    fold' b asList
    
olSum : Tree number -> number
-- olSum tree = fold (\a -> (\b -> a+b)) 0 tree
olSum t = fold (+) 0 t

olFlatten : Tree a -> List a
olFlatten tree = fold (\a -> (\b -> b ++ [a])) [] tree
{-- this implementation will flatten bottom-up
olFlatten tree = fold (::) [] tree
--}

olIsElement : a -> Tree a -> Bool
olIsElement element tree = (fold (\a -> (\b -> if a == element then Just(True) else Nothing)) Nothing tree) /= Nothing

-- PLAYGROUND


deepTree =
  fromList [1,2,3,5,7,6]


niceTree =
  fromList [2,1,3]


main =
  div [ style [ ("font-family", "monospace") ] ]
    [ display "depth deepTree" (depth deepTree)
    , display "depth niceTree" (depth niceTree)
    , display "incremented" (map (\n -> n + 1) niceTree)
    , display "sum deepTree: " (sum deepTree)
    , display "flatten deepTree: " (flatten deepTree)
    , display "is 5 in deepTree? " (isElement 5 deepTree)
    , display "fold deepTree with sum = " (fold (\a -> (\b -> a + b)) 0 deepTree)
    , display "oneline-sum deepTree: " (olSum deepTree)
    , display "oneline-flatten deepTree: " (olFlatten deepTree)
    , display "oneline-is 5 in deepTree? " (isElement 5 deepTree)
    ]


display : String -> a -> Html msg
display name value =
  div [] [ text (name ++ " ==> " ++ toString value) ]



{-----------------------------------------------------------------

Exercises:

(1) Sum all of the elements of a tree.

       sum : Tree number -> number

(2) Flatten a tree into a list.

       flatten : Tree a -> List a

(3) Check to see if an element is in a given tree.

       isElement : a -> Tree a -> Bool

(4) Write a general fold function that acts on trees. The fold
    function does not need to guarantee a particular order of
    traversal.

       fold : (a -> b -> b) -> b -> Tree a -> b

(5) Use "fold" to do exercises 1-3 in one line each. The best
    readable versions I have come up have the following length
    in characters including spaces and function name:
      sum: 16
      flatten: 21
      isElement: 46
    See if you can match or beat me! Don't forget about currying
    and partial application!

(6) Can "fold" be used to implement "map" or "depth"?

(7) Try experimenting with different ways to traverse a
    tree: pre-order, in-order, post-order, depth-first, etc.
    More info at: http://en.wikipedia.org/wiki/Tree_traversal

-----------------------------------------------------------------}