Uber·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Apr 2026

Summary

Uber SWE interview with a tree construction problem that looks straightforward until you're actually in it. The recursive structure is clean in theory but I kept second-guessing my base cases.

Questions Asked (1)

Given an n x n binary matrix, build a Quad-Tree representation where each node stores whether it's a leaf and its value, recursively subdividing regions that aren't uniform.

Algorithms & Data Structures

Author's notes

I got the general idea pretty fast, uniform region becomes a leaf, otherwise split into four quadrants and recurse.

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AI HintsAI Generated

Suggested Approach

Use a recursive divide-and-conquer strategy: for each submatrix, check if all values are the same; if so, create a leaf node, otherwise create an internal node and recurse on the four quadrants. Optimize the uniformity check with prefix sums or early termination to avoid redundant scans.

Pro tip: Clarify the node definition upfront (e.g., leaf nodes store value, internal nodes store children) and discuss trade-offs between recursion depth and iterative approaches, especially for large n. Mention that the tree depth is O(log n) and total nodes O(n^2) in the worst case.

1. Define the Node Structure

Specify the fields: isLeaf (boolean), val (0 or 1 for leaves), and four children (topLeft, topRight, bottomLeft, bottomRight). For internal nodes, val can be arbitrary (e.g., True) and children are non-null.

2. Recursive Function Signature

Design a function that takes the matrix, current row and column offsets, and the size of the current submatrix. It returns the root node of the quad-tree for that region.

3. Check Uniformity

Efficiently determine if all cells in the current submatrix have the same value. Use a helper that scans the region, or precompute prefix sums for O(1) range sum queries to check if sum is 0 or area.

4. Base Case and Recursive Case

If uniform, return a leaf node with that value. Otherwise, split the region into four equal quadrants and recursively build child nodes, then return an internal node with those children.

5. Analyze Complexity and Edge Cases

Discuss time complexity: O(n^2) with prefix sums or O(n^2 log n) with naive scanning; space O(n^2) worst-case. Handle n=0 or n=1 as edge cases.

Key Points to Mention

Recursive divide-and-conquer approach with base case for uniform regions.
Node structure: isLeaf, val, and four children (topLeft, topRight, bottomLeft, bottomRight).
Optimization using prefix sums to check uniformity in O(1) time per submatrix.
Time complexity: O(n^2) with prefix sums, O(n^2 log n) with naive scanning; space O(n^2) worst-case.
Handling edge cases: n=0, n=1, and non-square matrices (though problem states n x n).
Potential follow-up: serialization/deserialization of the quad-tree or iterative construction.

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