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.


func preorder(t) {
    t ? [t[0], __FUNC__(t[1])..., __FUNC__(t[2])...] : [];
}
 
func inorder(t) {
    t ? [__FUNC__(t[1])..., t[0], __FUNC__(t[2])...] : [];
}
 
func postorder(t) {
    t ? [__FUNC__(t[1])..., __FUNC__(t[2])..., t[0]] : [];
}
 
func depth(t) {
    var a = [t];
    var ret = [];
    while (a.len > 0) {
        var v = (a.shift \\ next);
        ret « v[0];
        a += [v[1,2]];
    };
    return ret;
}
 
var x = [1,[2,[4,[7]],[5]],[3,[6,[8],[9]]]];
say "pre:   #{preorder(x)}";
say "in:    #{inorder(x)}";
say "post:  #{postorder(x)}";
say "depth: #{depth(x)}";