Traverse binary tree - no recursion, no stack, no tree modification - data-structures

Question

So for an application I am building I need to be able to traverse a binary tree without using recursion, stack or modifying the tree in any way after it's been created. My node struct is as follows:
typedef struct
{
ValueType value; //Data stored in node
int left_index; //Left child
int right_index; //Right child
int parent_index; //Parent node
}
I am storing my tree as a 1D array where the left child of each node is at index 2*i + 1, the right child is at 2*i + 2 and the parent is at [i-1]/2. If a node doesn't have a parent or child, it's associated index is -1.
The only iterative non-stack based algorithm I found was something called "Morris Traversal" as seen here: http://www.geeksforgeeks.org/inorder-tree-traversal-without-recursion-and-without-stack/
However Morris Traversal modifies the tree during the traversal which I cannot do.
I am willing to add whatever information is needed to each node just as long as I can write the algorithm given the above constraints.
Is what I'm asking for even possible? And if so, how would I go about doing it? Not really sure how to even begin.

Answer 1

Wouldn't a "while(!done)" loop be suffcient?

Answer 2

What you want is a threaded binary tree. The right pointer of all leaf nodes points to the node's in-order successor.
It's easy to create such a thing, and not difficult at all to update it when you insert or delete a node. If you have control of the node structure, then this is almost certainly what you want.

Answer 3

public class TreeNode {
int val;
TreeNode left;
TreeNode right;
TreeNode parent;
public void traverse() {
TreeNode current = this.leftMost();
while (current != null) {
System.out.println("Current at " + current.val);
current = current.inOrderNext();
}
}
public TreeNode inOrderNext() {
if (right != null) {
return right.leftMost();
} else {
TreeNode current = this;
TreeNode above = this.parent;
while (true) {
if (above == null) {
return null;
} else {
if (above.left == current) {
return above;
} else {
current = above;
above = above.parent;
}
}
}
}
}
public TreeNode leftMost() {
TreeNode result = this;
while (result.left != null) {
result = result.left;
}
return result;
}
public static void main(String args[]) {
TreeNode first = new TreeNode();
first.val = 4;
TreeNode second = new TreeNode();
second.val = 2;
second.parent = first;
first.left = second;
TreeNode third = new TreeNode();
third.val = 1;
third.parent = second;
second.left = third;
third = new TreeNode();
third.val = 3;
third.parent = second;
second.right = third;
second = new TreeNode();
second.val = 6;
second.parent = first;
first.right = second;
third = new TreeNode();
third.val = 5;
third.parent = second;
second.left = third;
third = new TreeNode();
third.val = 7;
third.parent = second;
second.right = third;
first.traverse();
}
}