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Microsoft·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Apr 2026

Summary

Microsoft SWE interview with a clean algorithmic problem. Nothing too wild, but the binary search piece required you to actually think through the setup rather than just pattern-match.

Questions Asked (1)

Q1

You're given a sorted (non-decreasing) array of item prices and a list of queries. Each query gives you a starting index and a budget. For each query, return the maximum number of items you can purchase starting from that index without going over budget.

Algorithms & Data Structures
Author's notes

Prefix sums clicked pretty fast for me, but I fumbled the binary search part initially.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints and edge cases, then propose an efficient solution using prefix sums and binary search. Explain that for each query, you compute the remaining budget from the starting index and binary search for the farthest index where the cumulative sum fits within the budget.

Pro tip: Mention that you would precompute prefix sums to answer each query in O(log n) time, and discuss how to handle large inputs or multiple queries efficiently. Also, proactively address edge cases like empty array or budget insufficient for even one item.

1. Understand the problem

Restate the problem in your own words and ask clarifying questions about constraints, input sizes, and expected output format.

2. Identify the optimal approach

Recognize that since the array is sorted, prefix sums combined with binary search allow efficient query processing.

3. Design the algorithm

Precompute prefix sums. For each query, compute the target sum = prefix[start] + budget, then binary search for the largest index where prefix[index] <= target.

4. Analyze complexity

State that preprocessing takes O(n) time and each query takes O(log n) time, with O(n) space for prefix sums.

5. Handle edge cases

Discuss cases where start is out of bounds, budget is less than the first item, or the array is empty, and explain how to handle them.

Key Points to Mention

  • Prefix sums for cumulative sums
  • Binary search for efficient querying
  • Time complexity: O(n) preprocessing, O(log n) per query
  • Space complexity: O(n) for prefix sums
  • Edge cases: empty array, start index out of bounds, budget insufficient
  • Handling multiple queries efficiently

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