Binary Tree Postorder Traversal

Binary Tree Postorder Traversal

What is this problem about?

Binary Tree Postorder Traversal is one of the three fundamental ways to visit nodes in a tree. In this specific order, you visit the entire Left subtree first, then the entire Right subtree, and finally the Root node itself. This "bottom-up" approach is crucial for problems where you need to process children before their parents, such as deleting a tree or calculating the size of subtrees.

Why is this asked in interviews?

This is a core computer science topic frequently appearing in interviews at Google, Meta, and Bloomberg. While the recursive solution is trivial, the iterative solution is notoriously tricky and is often used to differentiate between junior and senior candidates. It tests your ability to manipulate stacks and your understanding of how to manage complex traversal states without the convenience of the recursion's hidden call stack.

Algorithmic pattern used

The recursive approach uses the Depth-First Search (DFS) pattern. The iterative approach uses the Stack interview pattern. A common trick for iterative postorder is to perform a modified preorder traversal (Root -> Right -> Left) and then reverse the entire result list to get (Left -> Right -> Root). Alternatively, one can use a single stack and a "last visited" pointer to track progress.

Example explanation

Consider this tree: 1

  2
 /
3

Postorder: Left -> Right -> Root

1. Start at 1. Left is empty.
2. Go to right child 2.
3. Before processing 2, go to its left child 3.
4. 3 has no children. Record [3].
5. Back to 2. It has no right child. Record [3, 2].
6. Back to root 1. Record [3, 2, 1]. Final result: [3, 2, 1].

Common mistakes candidates make

In the recursive version, the most common error is getting the order wrong (e.g., doing Root-Left-Right instead). In the iterative version, managing the stack is the biggest hurdle. Candidates often struggle with knowing when a node is being visited for the first time (to explore children) versus the second time (to finally record its value).

Interview preparation tip

Master the "reverse preorder" trick for iterative postorder traversal—it’s much easier to implement and less error-prone during a high-pressure interview. However, be prepared to explain the "real" iterative way (using a single stack) if the interviewer asks for an in-place approach.