Stackless pre-order traversal in a binary tree

Question

Is it possible to perform iterative *pre-order* traversal on a binary tree without using node-stacks or "visited" flags?

As far as I know, such approaches usually require the nodes in the tree to have pointers to their parents. Now, to be sure, I know how to perform pre-order traversal using parent-pointers and visited-flags thus eliminating any requirement of stacks of nodes for iterative traversal.

But, I was wondering if visited-flags are really necessary. They would occupy a lot of memory if the tree has a lot of nodes. Also, having them would not make much sense if many pre-order tree traversals of a binary-tree are going on simultaneously in parallel.

If it is possible to perform this, some pseudo-code or better a short C++ code sample would be really useful.

EDIT: I specifically do not want to use recursion for pre-order traversal. The context for my question is that I have an octree (which is like a binary tree) which I have constructed on the GPU. I want to launch many threads, each of which does a tree-traversal independently and in parallel.

Firstly, CUDA does not support recursion. Seoncdly, the concept of visited flags applies only for a single traversal. Since many traversals are going on simultaneously , having visited-flags field in the node data structure is of no use. They would make sense only on the CPU where all independent tree traversals are/can be serialised. To be more specific, after every tree-traversal we can set the visited-flags to false before performing another pre-order tree-traversal

Answer 1

You can use this algorithm, which only needs parent pointers and no additional storage:

For an inner node, the next node in a pre-order traversal is its leftmost child.

For a leaf node: Keep going upwards in the tree until you are coming from the left child of a node with two children. That node's right child will then be the next node to traverse.

function nextNode(node):
    # inner node: return leftmost child
    if node.left != null:
        return node.left
    if node.right != null:
        return node.right

    # leaf node
    while (node.parent != null)
        if node == node.parent.left and node.parent.right != null:
            return node.parent.right
        node = node.parent

    return null  #no more nodes