Meta·Backend Engineer·Technical Phone Screen·Senior

Senior

May 2026

Summary

Meta backend interview with a binary search problem that looks straightforward on paper but has a few gotchas if you haven't seen it before. Nothing too wild, just needed to get the feasibility check right.

Questions Asked (1)

Given an array of log lengths and an integer k, find the maximum cut length L such that you can produce at least k pieces total, where each log yields floor(log_i / L) pieces. Return 0 if no valid positive L exists.

Algorithms & Data Structures

Author's notes

Classic binary search on the answer.

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AI HintsAI Generated

Suggested Approach

Recognize that the number of pieces is monotonically non-increasing as L increases, so binary search on L in the range [1, max(logs)]. For each candidate L, compute the total pieces by summing floor(log_i / L) and check if it is at least k.

Pro tip: Clarify edge cases upfront: if k is 0 or the array is empty, return 0; also handle large sums with 64-bit integers to avoid overflow. Mention that binary search reduces time to O(n log(max_log)), which is optimal for this problem.

1. Understand the problem and constraints

Restate the problem: find the largest L such that sum(floor(log_i / L)) >= k. Note that L must be a positive integer, and if no such L exists, return 0.

2. Identify monotonicity and choose binary search

Observe that as L increases, the number of pieces decreases. This monotonic property allows binary search on L between 1 and max(logs).

3. Implement the feasibility check

For a given L, iterate through the logs and sum floor(log_i / L). Use 64-bit integers to prevent overflow. Return true if the sum >= k.

4. Binary search for the maximum L

Perform binary search: if feasible(mid) is true, record mid as a candidate and search higher; otherwise search lower. After the loop, return the best L found, or 0 if none.

5. Analyze complexity and test edge cases

Time complexity is O(n log(max_log)), space O(1). Test with cases like k=0, empty array, logs smaller than k, and large values.

Key Points to Mention

Monotonicity of the piece count with respect to L, enabling binary search.
Binary search bounds: low=1, high=max(logs) (or sum(logs)//k as an optimization).
Feasibility check: sum of floor(log_i / L) >= k, using integer division.
Handling edge cases: return 0 if k=0, array empty, or no valid L.
Time and space complexity: O(n log(max_log)) time, O(1) space.
Potential overflow: use 64-bit integers for the sum.

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