Bloomberg·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026

Summary

Bloomberg SWE interview with a sequence generation problem that looks deceptively simple until you realize the naive approach is going to time out. The core challenge is figuring out how to track previously seen values without rescanning the whole sequence each step.

Questions Asked (1)

Given an integer n >= 1, compute the (n-1)th element of a sequence where a[0] = 0, and each subsequent element is either 0 (if the previous value hasn't appeared before) or the distance back to its most recent prior occurrence. Design an efficient algorithm to do this.

Algorithms & Data Structures

Author's notes

I stared at the example for longer than I'd like to admit.

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AI HintsAI Generated

Suggested Approach

Clarify the sequence definition and confirm the indexing (0-based) with the interviewer. Then propose a hash map solution that tracks the last occurrence of each value, allowing O(1) lookup per step and O(n) time overall. Walk through a small example to validate the logic before coding.

Pro tip: Mention that the sequence is known as Van Eck's sequence, and note that while the problem asks for the (n-1)th element, you can compute it iteratively without storing the entire sequence, saving memory.

1. Clarify the problem

Restate the sequence rules and confirm the indexing (a[0] = 0, compute a[n-1]). Ask if n can be large and if memory is a concern.

2. Choose data structures

Use a hash map to store the last index where each value appeared. Keep only the previous value and current index to compute the next value.

3. Design the algorithm

Iterate from i=1 to n-1. If the previous value has been seen before, set current = i-1 - last_seen[prev]; else current = 0. Update last_seen[prev] = i-1.

4. Analyze complexity

Time complexity is O(n) because each step does constant work. Space complexity is O(n) in the worst case for the hash map, but often less.

5. Test and optimize

Walk through a small example (e.g., n=5) to verify. Discuss potential optimizations like using an array if values are bounded, or early termination if n is small.

Key Points to Mention

Hash map for O(1) last occurrence lookup
Iterative computation with O(n) time and O(n) space
Handling the base case a[0] = 0
Updating the last occurrence after computing each new value
Edge cases: n=1 returns 0, large n performance
Van Eck's sequence as the known name (optional but impressive)

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