Implement Heap using a Binary Tree

Question

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Link to the previously asked question: Binary Heap Implemented via a Binary Tree Struct

Answer 1

HEAP IMPLEMENTATION USING TREE

I am answering my own question that takes O(log n), but the limitation is to keep a pointer to the parent. if we don't keep a pointer to the parent, we need approximately O(n). I posted this question to get a solution for O(log n)

Here are the steps to calculate next unoccupied leaf (we have a pointer to the parent node):

x = last inserted node. We save this after every insertion.
y = tmp node
z = next unoccupied node (next insertion)
   if x is left child
      z = x -> parent -> rightchild (problem solved.. that was easy)
   else if x is right child
      go to x's parent, until parent becomes left child. Let this node be y
      (subtree rooted at y's sibling will contain the next unoccupied node)
      z = y -> parent -> right -> go left until null

This is O(log n), but needs a pointer to the parent.

O(n) solution would be pretty easy, just level order the tree and we get the location of the next unoccupied node.

My question is: how to locate next unoccupied node in O(log n) without using a parent pointer.

Thanks.