NVIDIA·Software Engineer·Technical Phone Screen·Senior

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Jun 2026

Summary

NVIDIA software engineer interview with a low-level C coding question that went deeper than I expected. They weren't just asking you to write a loop, they wanted a full library-quality design discussion on top of the implementation.

Questions Asked (1)

Implement polynomial multiplication in C. Given two polynomials as coefficient arrays with their sizes, design a library-quality function: define your own API, handle memory ownership of the result buffer, account for edge cases like zero polynomials and leading zeros, and analyze the time complexity.

System DesignTechnical Trade-offsAlgorithms & Data Structures

Author's notes

I started coding the O(n*m) nested loop pretty fast and felt good about it.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the API design, including memory ownership and error handling, then walk through the algorithm and edge cases, and finally analyze time and space complexity. Emphasize modularity and robustness, as expected in a library-quality implementation.

Pro tip: Explicitly state that the caller owns the result buffer and must free it, and consider providing a function to free the polynomial to avoid mismatched allocators. Also, mention that you would validate inputs (e.g., NULL pointers, negative sizes) to prevent undefined behavior.

1. Define the API and Memory Ownership

Specify the function signature, return type, and who is responsible for allocating and freeing the result. Decide whether to return a dynamically allocated array or require the caller to provide a buffer.

2. Handle Edge Cases and Input Validation

Check for NULL pointers, zero sizes, and zero polynomials. Decide how to represent zero polynomials (e.g., size 0 or array with all zeros) and how to handle leading zeros in inputs.

3. Implement the Multiplication Algorithm

Use nested loops to multiply each term and accumulate results into the correct degree. Allocate the result array of size (size1 + size2 - 1) and initialize to zero.

4. Normalize the Result and Manage Memory

After multiplication, trim leading zeros to get the actual degree, and reallocate if necessary to save memory. Ensure the returned polynomial is in a consistent format.

5. Analyze Complexity and Discuss Trade-offs

State that the time complexity is O(n*m) and space complexity is O(n+m). Mention potential optimizations like using FFT for large polynomials, but note the added complexity.

Key Points to Mention

API design: function signature, return type, and error handling (e.g., return NULL on failure).
Memory ownership: caller frees the result, and provide a dedicated free function to avoid allocator mismatch.
Edge cases: zero polynomials, leading zeros, NULL inputs, and negative sizes.
Algorithm: nested loops, result array size (n+m-1), and accumulation.
Normalization: trimming leading zeros and reallocating to exact size.
Complexity: O(n*m) time, O(n+m) space, and mention of FFT for large inputs.

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