Right Threading a Binary Tree

Question

I'm having a hell of a time trying to figure this one out. Everywhere I look, I seem to be only running into explanations on how to actually traverse through the list non-recursively (the part I actually understand). Can anyone out there hammer in how exactly I can go through the list initially and find the actual predecessor/successor nodes so I can flag them in the node class? I need to be able to create a simple Binary Search Tree and go through the list and reroute the null links to the predecessor/successor. I've had some luck with a solution somewhat like the following:

thread(node n, node p) {
     if (n.left !=null)
        thread (n.left, n);
     if (n.right !=null) {
        thread (n.right, p);
     }
     n.right = p;
}

Answer 1

From your description, I'll assume you have a node with a structure looking something like:

Node {
  left
  right
}

... and that you have a binary tree of these set up using the left and right, and that you want to re-assign values to left and right such that it creates a doublely-linked-list from a depth first traversal of the tree.

The root (no pun intended) problem with what you've got so far is that the "node p" (short for previous?) that is passed during the traversal needs to be independent of where in the tree you currently are - it always needs to contain the previously visited node. To do that, each time thread is run it needs to reference the same "previous" variable. I've done some Python-ish pseudo code with one C-ism - if you're not familiar, '&' means "reference to" (or "ref" in C#), and '*' means "dereference and give me the object it is pointing to".

Node lastVisited
thread(root, &lastVisisted)

function thread(node, lastVisitedRef)
  if (node.left)
    thread(node.left, lastVisitedRef)
  if (node.right)
    thread(node.right, lastVisitedRef)

  // visit this node, reassigning left and right
  if (*lastVisitedRef)
    node.right = *lastVisitedRef
    (*lastVisitedRef).left = node
  // update reference lastVisited
  lastVisitedRef = &node

If you were going to implement this in C, you'd actually need a double pointer to hold the reference, but the idea is the same - you need to persist the location of the "last visited node" during the entire traversal.