Uber·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Apr 2026

Summary

Uber SWE interview that came down to a single coding problem on quad trees. Not a topic I'd touched in a while so the first few minutes were a bit rough getting my bearings, but the structure of the problem was clean once I slowed down.

Questions Asked (1)

Implement a compressed QuadTree for an n x n grid where n is a power of two. Each region should be represented as a leaf node if all cells share the same value, otherwise split into four quadrants recursively. Build and return the root node.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I fumbled the first few minutes because I kept second-guessing whether to check uniformity before or after recursing.

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AI HintsAI Generated

Suggested Approach

Use a recursive divide-and-conquer strategy: for a given region, check if all cells have the same value; if so, return a leaf node with that value, otherwise split into four quadrants and recurse. Base case is a 1x1 region. Return the root node of the resulting tree.

Pro tip: Mention that early termination when a region is uniform avoids unnecessary recursion, and that the tree depth is O(log n) which is efficient. Also, discuss how this compression reduces space for sparse or uniform grids.

1. Define the Node Structure

Create a class or struct for the QuadTree node that can represent either a leaf (with a value) or an internal node (with four children). Include a boolean flag to distinguish between them.

2. Implement the Recursive Build Function

Write a function that takes the grid, current row, current column, and size of the region. Check if all cells in the region are the same; if so, return a leaf node. Otherwise, split into four quadrants of size n/2 and recursively build each child.

3. Handle Base Case and Uniformity Check

For a 1x1 region, return a leaf node with the cell's value. For larger regions, efficiently check uniformity by comparing each cell to the first cell in the region, stopping early if a mismatch is found.

4. Assemble and Return the Root

After recursively building the four children, create an internal node with those children and return it. The initial call to the build function with the full grid returns the root of the QuadTree.

5. Analyze Complexity and Optimizations

Discuss time complexity: O(n^2) in the worst case (all cells different) and O(1) if the entire grid is uniform. Space complexity is O(number of nodes). Mention potential optimizations like using a prefix sum to check uniformity in O(1) per region, but note the trade-off of extra space.

Key Points to Mention

Recursive divide-and-conquer approach with base case of 1x1 region.
Uniformity check: compare all cells in the region to the first cell, early exit on mismatch.
Node representation: leaf nodes store a value, internal nodes store four children.
Time complexity: O(n^2) worst-case, O(1) best-case for uniform grid; space complexity proportional to number of nodes.
Compression benefit: reduces space for grids with large uniform regions.
Potential optimization: use prefix sums to check uniformity in O(1) per region, but increases space complexity.

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