Problem 68c

Write a function to traverse a tree and return the values in a list in post-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))

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

Unit Test

import Html
import List

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


postorder : Tree a -> List a
postorder 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)
      [ postorder Empty == []
      , postorder tree67 == ['d', 'e', 'b', 'g', 'f', 'c', 'a'] 
      , postorder tree68 == [3, 4, 2, 9, 8, 7, 6, 5, 1] 
      , postorder tree == [1, 3, 5, 4, 2, 7, 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