Problem 68b

Write a function to traverse a tree and return the values in a list in in-order.

Example

tree67 = 
    Node 'a'
        (Node 'b'
            (Node 'd' Empty Empty)
            (Node 'e' Empty Empty))
        (Node 'c' 
            Empty 
            (Node 'f' 
                (Node 'g' Empty Empty) 
                Empty))

inorder tree67 == ['d', 'b', 'e', 'a', 'c', 'g', 'f']

Unit Test

import Html
import List

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


inorder : Tree a -> List a
inorder tree =
    -- your implementation goes here
    []


main =
    Html.text
        (if (test) then
            "Your implementation passed all tests."
         else
            "Your implementation failed at least one test."
        )


test : Bool
test =
    List.all ((==) True)
      [ inorder Empty == []
      , inorder tree == (List.range 1 7)
      , inorder tree67 == ['d', 'b', 'e', 'a', 'c', 'g', 'f'] 
      , inorder tree68 == [3, 2, 4, 1, 5, 7, 9, 8, 6] 
      ]


tree67 = 
    Node 'a'
        (Node 'b'
            (Node 'd' Empty Empty)
            (Node 'e' Empty Empty))
        (Node 'c' 
            Empty 
            (Node 'f' 
                (Node 'g' Empty Empty) 
                Empty))


tree68 = 
    Node 1
        (Node 2
            (Node 3 Empty Empty)
            (Node 4 Empty Empty))
        (Node 5 
            Empty 
            (Node 6 
                (Node 7 
                    Empty 
                    (Node 8 
                        (Node 9 Empty Empty) 
                        Empty))
                Empty))


tree = 
    Node 6
        (Node 2
            (Node 1 Empty Empty)
            (Node 4 
                (Node 3 Empty Empty) 
                (Node 5 Empty Empty)))
        (Node 7 Empty Empty)

Solution