Task

Implement a binary tree where each node carries an integer,   and implement:

   pre-order,
   in-order, 
   post-order,     and 
   level-order   traversal. 


Use those traversals to output the following tree:

         1
        / \
       /   \
      /     \
     2       3
    / \     /
   4   5   6
  /       / \
 7       8   9

The correct output should look like this:

preorder:    1 2 4 7 5 3 6 8 9
inorder:     7 4 2 5 1 8 6 9 3
postorder:   7 4 5 2 8 9 6 3 1
level-order: 1 2 3 4 5 6 7 8 9



See also

   Wikipedia article:   Tree traversal.


procedure main()
    bTree := [1, [2, [4, [7]], [5]], [3, [6, [8], [9]]]]
    showTree(bTree, preorder|inorder|postorder|levelorder)
end
 
procedure showTree(tree, f)
    writes(image(f),":\t")
    every writes(" ",f(tree)[1])
    write()
end
 
procedure preorder(L)
    if \L then suspend L | preorder(L[2|3])
end
 
procedure inorder(L)
    if \L then suspend inorder(L[2]) | L | inorder(L[3])
end
 
procedure postorder(L)
    if \L then suspend postorder(L[2|3]) | L
end
 
procedure levelorder(L)
    if \L then {
        queue := [L]
        while nextnode := get(queue) do {
            every put(queue, \nextnode[2|3])
            suspend nextnode
            }
        }
end