← Google Interview Insights

Google·Software Engineer·Onsite - Coding / Algorithms·Intermediate

IntermediatePrefer not to say
Jul 2026

Summary

Google SWE coding round with a tree problem that looked manageable until the follow-up optimization came up. The core idea is straightforward but the efficient version requires some thought about caching and path recomputation.

Questions Asked (1)

Q1

Given a valid boolean expression tree with AND, OR, and XOR internal nodes and boolean leaves, flip each leaf one at a time from left to right and return the root's evaluated value after each temporary flip.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

Brute force came to me pretty fast: inorder traversal to collect leaves, flip one, re-evaluate the whole tree, restore it, repeat.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

First, clarify the problem: we need to flip each leaf one at a time from left to right, evaluate the tree after each flip, and return the root value after each temporary flip. Then, propose an efficient solution that avoids re-evaluating the entire tree for each flip, such as precomputing subtree values and using a recursive traversal to update the root value in O(1) per flip after O(n) preprocessing.

Pro tip: Mention that the tree is static and flips are temporary, so we can precompute the contribution of each leaf to the root and update the root value in O(1) per flip by propagating the change up the tree. This demonstrates strong algorithmic maturity and awareness of trade-offs.

1. Clarify the problem and constraints

Confirm that the tree is valid, leaves are boolean, internal nodes are AND/OR/XOR, and flips are temporary and sequential from left to right. Ask about tree size and whether we can modify the tree.

2. Design an efficient algorithm

Propose a two-pass approach: first, compute the initial value of each subtree via post-order traversal. Then, for each leaf in left-to-right order, temporarily flip it, update the values along the path to the root, record the root value, and revert the flip.

3. Optimize with precomputation

To achieve O(1) per flip, precompute for each node the effect of flipping each child on the node's value. Alternatively, note that flipping a leaf only affects its ancestors, so we can update the root in O(depth) per flip, which is efficient for balanced trees.

4. Analyze time and space complexity

State that the initial evaluation takes O(n) time and O(n) space for storing subtree values. Each flip then takes O(depth) time, leading to O(n * depth) total time, which is O(n log n) for balanced trees. If O(1) per flip is required, discuss trade-offs.

5. Handle edge cases and test

Consider edge cases: single leaf, all leaves same value, deep tree, and ensure the temporary flip is reverted correctly. Walk through a small example to verify the approach.

Key Points to Mention

  • Post-order traversal to compute initial subtree values
  • Propagation of changes up the tree to update the root value efficiently
  • Time complexity: O(n) preprocessing and O(depth) per flip, or O(1) per flip with additional precomputation
  • Space complexity: O(n) for storing subtree values or auxiliary data
  • Temporary flip: ensure the leaf is reverted after evaluating the root
  • Trade-offs between simplicity (re-evaluate entire tree per flip) and efficiency (incremental updates)

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.