Verify Preorder Serialization of a Binary Tree

Verify Preorder Serialization of a Binary Tree

What is this problem about?

The "Verify Preorder Serialization of a Binary Tree" interview question asks you to determine if a given string, representing a comma-separated sequence of values and '#' (for null nodes), is a valid preorder traversal of a binary tree. Unlike other problems, you are not given the actual tree; you must validate the structure based solely on the serialized string.

Why is this asked in interviews?

Amazon and Google use the "Verify Preorder Serialization of a Binary Tree" coding problem to test a candidate's understanding of tree properties, specifically how many null pointers a valid tree should have. It challenges you to find an efficient way to validate a tree structure without using recursion or actually building the tree in memory.

Algorithmic pattern used

The most elegant algorithmic pattern for this problem is the "Slots/Degree Counting" approach. Every non-null node in a binary tree provides two "slots" for children and consumes one "slot" (itself). A null node ('#') consumes one slot but provides zero slots. You start with one initial slot (for the root) and iterate through the string, updating the slot count. If the slot count ever drops to zero before the end, or is not exactly zero at the very end, the serialization is invalid.

Example explanation

Serialization: "9,3,#,#,1,#,#"

1. Start with slots = 1.
2. Token "9": Consume 1, Add 2. slots = 1 - 1 + 2 = 2.
3. Token "3": Consume 1, Add 2. slots = 2 - 1 + 2 = 3.
4. Token "#": Consume 1, Add 0. slots = 3 - 1 = 2.
5. Token "#": Consume 1, Add 0. slots = 2 - 1 = 1.
6. Token "1": Consume 1, Add 2. slots = 1 - 1 + 2 = 2.
7. Token "#": Consume 1, Add 0. slots = 2 - 1 = 1.
8. Token "#": Consume 1, Add 0. slots = 1 - 1 = 0.
9. End of string. slots is 0. Result: Valid.

Common mistakes candidates make

A common mistake is trying to use a stack to simulate the tree construction, which is more complex and uses O(n) space. Another error is not checking if the slot count becomes zero during the process; for example, "#,9,3" is invalid because the first '#' consumes the only slot, leaving no room for the '9'. Candidates also often forget to handle the case where the string is just "#".

Interview preparation tip

For the "Verify Preorder Serialization of a Binary Tree" coding problem, focusing on the "Slots" approach allows you to solve the problem in O(n) time and O(1) space (excluding the string tokens). Mentioning this space optimization will highly impress your interviewer.