title: Uniqueness of Inorder, Preorder, and Postorder traversal with null elements
body: <p>We all know that different binary trees can have the same <em>inorder</em>, <em>preorder</em>, or <em>postorder</em> traversal. But if we were to include <code>null</code> elements into a <em>preorder</em> traversal, then result of the traversal would be unique as long as the trees are unique. Consider these two trees:</p>
  
  <pre><code>  3                      3
   /                        \
  4            vs.           4
  </code></pre>
  
  <p>Their normal <em>preorder</em> traversal would be <code>{3,4}</code> for both, but if we were to include <code>null</code> elements, then their traversal would be <code>{3,4,null,null,null}</code> and <code>{3,null,4,null,null}</code> respectfully, making the traversal unique.</p>
  
  <p><strong>My question is, would this be true for inorder and postorder traversals as well? And how can we prove it?</strong></p>