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Salesforce·Software Engineer·Technical Phone Screen·Senior

Senior
May 2026

Summary

Salesforce SWE interview that went deep into number theory territory pretty fast. The whole session was basically one extended problem about modular arithmetic with big numbers, and they wanted working code plus complexity analysis.

Questions Asked (1)

Q1

Implement a function to compute (a^b) mod m where a, b, and m can be up to 2^61 minus 1, using only 64-bit operations and without any intermediate overflow. Include both a fast modular multiplication helper and the exponentiation itself, plus tests and complexity analysis.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

This one genuinely stressed me out.

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AI HintsAI Generated

Suggested Approach

Start by explaining the need for a safe modular multiplication to avoid overflow when multiplying two numbers up to 2^61-1. Then present binary exponentiation (exponentiation by squaring) that uses this helper. Finally, discuss tests and complexity.

Pro tip: Mention that using unsigned 64-bit integers and the Russian peasant multiplication (double-and-add) with conditional subtraction ensures no overflow, and highlight that this approach is constant-time with respect to the exponent, which is important for cryptographic applications.

1. Clarify constraints and overflow risk

Restate that a, b, m can be up to 2^61-1, so direct multiplication overflows 64-bit. Emphasize the need for a safe modular multiplication helper.

2. Design modular multiplication

Implement a function that computes (a * b) % m without overflow using either Russian peasant multiplication (double-and-add) or splitting into high/low 32-bit parts. Ensure it handles m=1 and negative inputs if applicable.

3. Implement modular exponentiation

Use binary exponentiation (exponentiation by squaring) with the safe multiplication helper. Handle edge cases: b=0 (result 1 % m), m=1 (result 0), and a >= m (reduce a modulo m first).

4. Write tests

Include tests for small values (compare with naive), edge cases (b=0, m=1, a=0), and large values near 2^61-1 to verify no overflow and correctness.

5. Analyze complexity

State that modular multiplication is O(log b) and exponentiation is O(log b) multiplications, so overall O(log b) time and O(1) space.

Key Points to Mention

  • Overflow avoidance: use unsigned 64-bit and ensure intermediate results stay below 2^64.
  • Russian peasant multiplication (double-and-add) for modular multiplication.
  • Binary exponentiation (exponentiation by squaring) for O(log b) time.
  • Edge cases: b=0, m=1, a=0, a >= m.
  • Complexity: O(log b) time, O(1) space.
  • Testing strategy: compare with naive for small inputs, test large values near 2^61-1.

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