How to determine whether a binary tree is complete?

Question

A complete binary tree is defined as a binary tree in which every level, except possibly the deepest, is completely filled. At deepest level, all nodes must be as far left a

Answer 1

There may be one possible algorithm which I feel would solve this problem. Consider the tree:

Level 0:    a  
Level 1:  b   c  
Level 2: d e f g  

• We employ breadth first traversal.

• For each enqueued element in the queue we have to make three checks in order:

  1. If there is a single child or no child terminate; else, check 2.
  2. If there exist both children set a global flag = true.
     1. Set flags for each node in the queue as true: flag[b] = flag[c] = true.
     2. Check for each entry if they have left n right child n then set the flags or reset them to false.
     3. (Dequeue) if(queue_empty())
        compare all node flags[]... if all true global_flag = true else global_flag = false.
     4. If global_flag = true go for proceed with next level in breadth first traversal else terminate

Advantage: entire tree may not be traversed
Overhead: maintaining flag entries