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Voleon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Apr 2026

Summary

Interviewed at Voleon for a software engineer role and got a sparse matrix problem that looked straightforward but had a few sharp edges around dimension validation and keeping things actually sparse. No fluff, just code.

Questions Asked (1)

Q1

Implement addition and multiplication for sparse matrices, with explicit error handling for incompatible dimensions. Dimensions can be up to 10^9, so dense storage is off the table.

Algorithms & Data StructuresTechnical Trade-offsSystem Design
Author's notes

I went with a dict keyed by (row, col) for non-zero values which felt natural.

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AI HintsAI Generated

Suggested Approach

Clarify the sparse matrix representation (e.g., coordinate list or hash map) and the operations' semantics, then design algorithms that iterate over non-zero elements, using hash maps for efficient lookup and merging. Explicitly handle dimension mismatches by checking compatibility before computation and raising appropriate errors. Analyze time and space complexity in terms of number of non-zero elements, and discuss trade-offs between different representations.

Pro tip: Mention that for multiplication, you can optimize by iterating over the smaller matrix's non-zero elements and using a hash map for the other matrix to avoid unnecessary lookups, and always validate dimensions upfront to fail fast.

1. Clarify requirements and constraints

Ask about the expected operations, error handling behavior, and any constraints on the number of non-zero elements. Confirm that dimensions can be up to 10^9, so dense storage is infeasible.

2. Choose a sparse representation

Select a data structure such as a hash map of (row, col) to value, or a list of (row, col, value) tuples. Discuss trade-offs: hash map offers O(1) access but higher memory overhead; list is compact but slower for lookups.

3. Design addition algorithm

Check if dimensions match; if not, raise an error. Iterate over non-zero elements of both matrices, combining values for matching coordinates and storing the result. Use a hash map to accumulate sums efficiently.

4. Design multiplication algorithm

Check if the number of columns of the first matrix equals the number of rows of the second; if not, raise an error. For each non-zero element (i, k, v) in the first matrix, iterate over non-zero elements (k, j, w) in the second matrix (e.g., using a hash map keyed by row), and accumulate v*w into the result at (i, j).

5. Analyze complexity and edge cases

Discuss time complexity: addition O(nnz1 + nnz2), multiplication O(nnz1 * avg_nnz_per_row2) or O(nnz1 * nnz2) worst-case. Mention space complexity O(nnz_result). Cover edge cases: empty matrices, zero result, and dimension mismatches.

Key Points to Mention

  • Sparse matrix representation: coordinate list (COO) or hash map (LIL) with trade-offs
  • Dimension compatibility checks: addition requires same dimensions; multiplication requires cols(A) == rows(B)
  • Error handling: raise ValueError with clear message for incompatible dimensions
  • Efficient iteration: only over non-zero elements, using hash maps for fast lookup during multiplication
  • Time and space complexity analysis in terms of number of non-zero elements (nnz)
  • Handling of duplicate coordinates and zero results (e.g., omit zeros to maintain sparsity)

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