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Microsoft·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Apr 2026

Summary

Microsoft coding screen, one question, pretty standard binary search territory. Nothing fancy about the setup but the constraint about not using built-in exponent functions is the kind of thing that trips you up if you just autopilot.

Questions Asked (1)

Q1

Given a non-negative integer x, implement a function that returns the integer square root of x rounded down, without using any built-in exponent functions or operators.

Algorithms & Data Structures
Author's notes

The no-exponent constraint is what makes this more than a throwaway warmup.

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AI HintsAI Generated

Suggested Approach

Clarify constraints and edge cases, then propose a binary search on the range [0, x] to find the largest integer whose square is ≤ x. Discuss time and space complexity, and optionally mention Newton's method as an alternative.

Pro tip: Mention that binary search avoids overflow by using mid <= x / mid instead of mid * mid, and note that for large x, Newton's method converges faster.

1. Clarify requirements and edge cases

Ask about input size, overflow concerns, and expected time complexity. Confirm that x is non-negative and that built-in exponent functions are prohibited.

2. Choose an algorithm

Propose binary search as a simple O(log x) solution. Alternatively, mention Newton's method for faster convergence.

3. Implement binary search

Set low=0, high=x. While low <= high, compute mid, and if mid <= x / mid, update result and low; else high = mid - 1. Return result.

4. Analyze complexity and test

State O(log x) time and O(1) space. Walk through edge cases like x=0, x=1, and perfect squares.

Key Points to Mention

  • Binary search on the answer space [0, x]
  • Avoiding overflow by using division instead of multiplication
  • Time complexity O(log x) and space complexity O(1)
  • Handling edge cases: x=0, x=1, and large x
  • Alternative approach: Newton's method for faster convergence
  • No built-in exponent functions or operators used

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