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Bloomberg·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Bloomberg SWE interview with a binary search problem that sounds straightforward until the follow-up hits you. The core question was clean but the floating-point extension added a layer I wasn't fully prepared for.

Questions Asked (2)

Q1

You have N cables with integer lengths and a target K. Find the maximum integer length L such that cutting all cables into pieces of length L produces at least K pieces total. Return 0 if it's not possible. Walk through a binary search approach and analyze the time complexity.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

The binary search framing clicked pretty fast for me.

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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 [1, max(cables)]. For each candidate L, compute total pieces by summing floor(cable/L) and compare to K. Return the largest feasible L, or 0 if even L=1 yields fewer than K pieces.

Pro tip: Mention that the search space is bounded by max(cables) and that using 64-bit integers for the piece count avoids overflow when N and cable lengths are large. Also, clarify that the answer is the maximum L, so the binary search should favor the upper bound when feasible.

1. Define feasibility check

Write a helper function that, given L, returns true if the total number of pieces (sum of floor(cable/L)) is at least K. This is the core operation repeated during binary search.

2. Set binary search bounds

Initialize low = 1 and high = max(cables). If the feasibility check fails for low, return 0 immediately. Otherwise, binary search for the maximum feasible L.

3. Perform binary search

While low <= high, compute mid = low + (high - low) / 2. If feasible(mid), record mid as a potential answer and set low = mid + 1; else set high = mid - 1.

4. Return result

After the loop, return the last recorded feasible L, or 0 if none was found. This yields the maximum integer length.

5. Analyze complexity

Time complexity is O(N log(max(cables))) because each feasibility check takes O(N) and binary search performs O(log(max(cables))) iterations. Space complexity is O(1) beyond the input.

Key Points to Mention

  • Monotonicity: if L is feasible, any smaller L is also feasible, enabling binary search.
  • Feasibility check: sum of floor(cable/L) >= K, computed in O(N) time.
  • Binary search bounds: low=1, high=max(cables); handle the case where even L=1 is infeasible by returning 0.
  • Integer division and potential overflow: use 64-bit integers for the sum to avoid overflow.
  • Time complexity: O(N log(max(cables))), space O(1).
  • Edge cases: K=0 (return 0 or max? clarify), N=0, cables with length 0, and very large K.

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

Q2

Follow-up: how would you modify your solution to support non-integer cable lengths, with a precision requirement of 1e-3?

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

This tripped me up more than I expected.

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AI HintsAI Generated

Suggested Approach

First, clarify the original solution's assumptions and identify where integer constraints are used. Then, propose converting to floating-point or fixed-point arithmetic, using binary search with a precision threshold, and handling floating-point comparisons carefully. Finally, discuss trade-offs like performance and numerical stability.

Pro tip: Mention that you would use binary search with a precision of 1e-3, but also consider scaling to integers to avoid floating-point errors, showing awareness of numerical stability in financial systems.

1. Clarify the original solution

Briefly restate the original approach and identify where integer assumptions are made, such as array indices or loop bounds.

2. Adapt data types and operations

Change integer variables to floating-point (e.g., double) and adjust comparisons to use an epsilon tolerance (1e-3).

3. Modify algorithm for continuous search

If the original used binary search on integers, switch to binary search on real numbers, terminating when the interval is smaller than 1e-3.

4. Address precision and performance

Discuss potential floating-point errors and suggest scaling to integers (e.g., multiply by 1000) to maintain precision, and analyze time complexity.

5. Test and validate

Outline how to test with non-integer inputs, ensuring results are within 1e-3 of the true value, and consider edge cases like very small or large values.

Key Points to Mention

  • Binary search on real numbers with termination condition based on precision (1e-3).
  • Use of epsilon for floating-point comparisons to avoid precision issues.
  • Alternative: scale lengths to integers (e.g., multiply by 1000) to use integer arithmetic.
  • Time complexity remains O(log(range/precision)) for binary search.
  • Consideration of numerical stability and potential overflow/underflow.
  • Impact on data structures: may need to store floating-point values or scaled integers.

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