Iterating over a Binary Tree with O(1) Auxiliary Space

Question

Is it possible to iterate over a binary tree in O(1) auxiliary space (w/o using a stack, queue, etc.), or has this been proven impossible? If it is possible, how can it be

Answer 1

"Datastructures and their algorithms" by Harry Lewis and Larry Denenberg describe link inversion traversal for constant space traversal of a binary tree. For this you do not need parent pointer at each node. The traversal uses the existing pointers in the tree to store path for back tracking. 2-3 additional node references are needed. Plus a bit on each node to keep track of traversal direction (up or down) as we move down. In my implementation of this algorithms from the book, profiling shows that this traversal has far less memory / processor time. An implementation in java is here.