Efficient Array Storage for Binary Tree

Question

We have to write the nodes of a binary tree to a file. What is the most space efficient way of writing a binary tree . We can store it in array format with parent in positi

Answer 1

Think about XML. It's a kind of tree serialization. For example:

                                       1
                                           /   \
                                    2     3
                                         / \
                                              4   5
        
        
    

Then, why the spaces and tags ? We can omit them, step by step:

<1>
   <2>
   <3>
     <4>
     <5>
   

Remove the spaces: <1><2><3><4><5>.

Remove the angle brackets: 12/34/5///

Now the problem is: what if a node has a empty left subtree and non-empty right subtree? Then we can use another special charactor, '#' to represent an empty left sub-tree.

For example:

    1
  /   \
      2
     /  \
    3

This tree can be serialized as: 1#23///.