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Pinterest·Software Engineer·Onsite - System Design / Architecture·Senior

SeniorPrefer not to say
Apr 2026

Summary

Pinterest system design round focused on sparse matrix storage and operations. Pretty niche problem, not the usual distributed systems stuff I prepped for.

Questions Asked (1)

Q1

Design a data structure for storing a sparse matrix efficiently, and implement addition and multiplication operations on two such matrices without wasting computation on zero elements.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs
Author's notes

I went with a hash map keyed on (row, col) pairs storing only non-zero values, which felt reasonable.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the requirements and constraints (e.g., matrix dimensions, sparsity level, expected operations). Then propose a sparse representation such as CSR (Compressed Sparse Row) or a list of (row, col, value) tuples, and outline algorithms for addition and multiplication that skip zero elements. Finally, analyze time and space complexity and discuss trade-offs between different representations.

Pro tip: Mention that for multiplication, you can optimize by iterating only over non-zero elements and using a hash map for the result to avoid dense intermediate storage. Also, relate the choice of data structure to Pinterest's use cases, such as storing user-item interaction matrices or graph adjacency matrices.

1. Clarify Requirements and Constraints

Ask about matrix size, sparsity, expected operations, memory limits, and whether the matrices are static or dynamic. This shows you consider practical constraints before diving into design.

2. Choose a Sparse Representation

Propose a suitable format like CSR, CSC, or list of triples. Explain why it saves space and how it facilitates efficient iteration over non-zero elements.

3. Design Addition Algorithm

Outline an algorithm that merges non-zero elements from both matrices, summing values where indices match. Use two pointers if using sorted lists, or a hash map for unsorted.

4. Design Multiplication Algorithm

Describe an algorithm that iterates over non-zero elements of the first matrix and multiplies with corresponding non-zero elements of the second matrix. Use a hash map or sorted merge to accumulate results efficiently.

5. Analyze Complexity and Trade-offs

Discuss time and space complexity for each operation and compare with dense representations. Mention scenarios where one representation outperforms another.

Key Points to Mention

  • Compressed Sparse Row (CSR) and Compressed Sparse Column (CSC) formats, and their trade-offs.
  • Coordinate list (COO) or list of triples for simplicity and ease of construction.
  • Time complexity of addition: O(nnz(A) + nnz(B)) and multiplication: O(nnz(A) * nnz(B)) in worst case, but often much less.
  • Use of hash maps to accumulate results during multiplication, avoiding dense intermediate matrices.
  • Handling of duplicate indices and merging sorted lists for addition.
  • Space complexity: O(nnz) versus O(m*n) for dense, and the impact of sparsity level.

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