Bloomberg·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Bloomberg SWE interview with a sequence generation problem that looked deceptively simple until I actually had to think about the data structure behind it. One question, pretty focused on implementation and the reasoning around index tracking.

Questions Asked (1)

Given a positive integer n, implement a sequence where each element is either 0 (if the previous value hasn't been seen before) or the gap between the last two occurrences of that value. Return the element at index n-1. The sequence starts: 0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5... How do you efficiently track the last-seen index of each value?

Algorithms & Data Structures

Author's notes

I knew the sequence pattern pretty quickly, the logic clicked after tracing through a few values by hand.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

First, clarify the sequence definition and confirm the indexing (0-based vs 1-based). Then, propose a hash map to store the last-seen index of each value, and simulate the sequence up to n-1, updating the map and computing the next value in O(1) per step. Analyze time and space complexity, and discuss potential optimizations or edge cases.

Pro tip: Mention that the sequence is known as Van Eck's sequence, and that the hash map approach is optimal for a single query; for multiple queries, precomputing up to the maximum n is more efficient.

1. Clarify the problem

Restate the sequence rules and confirm indexing (e.g., n=1 returns the first element 0). Ask if n can be large or if multiple queries are expected.

2. Choose data structures

Use a hash map (dictionary) to map each value to its last-seen index. Use a variable to store the previous value and another for the current index.

3. Simulate the sequence

Iterate from index 0 to n-1. At each step, if the previous value is not in the map, set current value to 0; else set it to the difference between the current index and the last-seen index. Then update the map with the previous value and its index.

4. Return the result

After the loop, return the value at index n-1 (the last computed value).

5. Analyze complexity

Time complexity is O(n) because each step does O(1) map operations. Space complexity is O(n) in the worst case for the map, but often less.

Key Points to Mention

Use a hash map to store the last-seen index of each value for O(1) lookups.
Maintain the previous value and current index to compute the next value.
Handle the base case: the first element is always 0.
Update the map after computing the next value to avoid overwriting the last-seen index prematurely.
Time complexity: O(n) for a single query; space complexity: O(n) worst-case.
For multiple queries, precompute the sequence up to the maximum n and answer in O(1) per query.

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