Flip Equivalent Binary Trees

Flip Equivalent Binary Trees

1. What is this problem about?

The Flip Equivalent Binary Trees interview question asks you to determine if two binary trees are equivalent under "flips." A flip operation consists of choosing any node and swapping its left and right subtrees. Two trees are flip equivalent if one can be transformed into the other using any number of flip operations.

2. Why is this asked in interviews?

Companies like Google and Amazon ask the Flip Equivalent coding problem to evaluate your understanding of Tree Recursion. It tests if you can handle multiple recursive cases: when subtrees match exactly and when they match after a swap. It’s a core Tree interview pattern for structural comparison.

3. Algorithmic pattern used

This problem follows the Recursive Tree Comparison pattern.

1. Base Cases:
   • If both nodes are null, return true.
   • If one is null or values don't match, return false.
2. Recursive Check: For nodes node1 and node2 to be equivalent, their children must satisfy one of two conditions:
   • No Flip: node1.left matches node2.left AND node1.right matches node2.right.
   • Flip: node1.left matches node2.right AND node1.right matches node2.left.
3. Combine: Return (No Flip) OR (Flip).

4. Example explanation

Tree 1: Root 1, Left 2, Right 3. Tree 2: Root 1, Left 3, Right 2.

1. Roots match (1 == 1).
2. Check children:
   • left1 (2) vs left2 (3): Fail.
   • Try flip: left1 (2) vs right2 (2): Match! AND right1 (3) vs left2 (3): Match!
3. Both conditions satisfied via flip. Result: True.

5. Common mistakes candidates make

• Ignoring Childless Nodes: Failing to handle cases where one child is null and the other is not.
• Incomplete Recursive Calls: Only checking for the "Flip" case and forgetting the "No Flip" case (or vice-versa).
• Value vs Reference: Only checking if the structure matches without verifying if the node values are equal.

6. Interview preparation tip

For any "Tree Equivalence" problem, start by identifying the Base Cases (nulls and value mismatches). The recursive logic then becomes much easier to visualize. This is a fundamental Tree interview pattern skill.