Bloomberg·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Bloomberg SWE interview that came down to a single algorithmic problem. The question had more edge cases than it looked like at first glance, and I spent a good chunk of time just getting the structure right before even touching the backtracking logic.

Questions Asked (1)

Given n football teams, generate a complete round-robin schedule where every team plays every other team exactly once. For even n there are n-1 rounds with n/2 simultaneous matches per round; for odd n there are n rounds with one team sitting out each round. Output all valid schedules for n=4.

Algorithms & Data Structures

Author's notes

I knew round-robin scheduling as a concept but generating ALL valid schedules via backtracking is a different beast.

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AI HintsAI Generated

Suggested Approach

Use the circle method (polygon method) to generate a round-robin schedule efficiently. For n=4, enumerate all valid schedules by considering team permutations and round orderings, then eliminate duplicates. Explain the algorithm and verify the output meets the constraints.

Pro tip: Mention that the circle method naturally handles odd n by adding a dummy team; also note that for n=4, there are 6 matches total, and the number of distinct schedules is small, so brute-force enumeration is feasible.

1. Understand the problem and constraints

Clarify that a complete round-robin requires each pair of teams to play exactly once, with rounds having simultaneous matches. For n=4, there are 3 rounds with 2 matches each.

2. Choose a generation method

Select the circle method for efficiency, or brute-force for small n. Explain how the circle method fixes one team and rotates others to generate rounds.

3. Generate schedules for n=4

Apply the method to produce all distinct schedules. Consider symmetries (team relabeling, round order) to avoid duplicates.

4. Verify and output

Check that each schedule has 3 rounds, each team plays once per round, and all 6 unique pairings occur exactly once. Present the schedules clearly.

Key Points to Mention

Circle method (polygon method) for round-robin scheduling
Handling odd n by adding a bye (dummy team)
Symmetry and deduplication of schedules
Time complexity: O(n^2) for generating one schedule
Verification: each team plays n-1 matches, total matches n(n-1)/2
For n=4, there are 6 matches and 3 rounds; number of distinct schedules is 6 (up to relabeling and round order)

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