← Jump Trading Interview Insights

Jump Trading·Machine Learning Engineer·Technical Phone Screen·Senior

Senior
Apr 2026

Summary

Jump Trading MLE interview with two pretty dense algorithmic problems. Both had tight complexity requirements and the second one had a tricky correctness argument I wasn't fully prepared for. No behavioral stuff at all, just code and think-out-loud.

Questions Asked (2)

Q1

Given an array of daily stock prices and two patterns (buy and sell), where each pattern is a sequence of +1/-1 values representing day-over-day price direction, simulate a trading strategy: on each day, check if the tail of the price series matches the sell pattern (sell one share if you hold any) and/or the buy pattern (buy one share), processing sell before buy. Return the holdings array after each day. Aim for O(n) time and O(1) extra space.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

The pattern matching part seems straightforward until you realize zeros in the sign function break any match since the patterns only use -1 and 1.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Clarify the problem constraints and edge cases, then propose an O(n) time and O(1) space solution using a rolling hash or direct comparison of the last k price differences. Simulate the trading day by day, checking sell before buy, and update holdings accordingly.

Pro tip: Mention that the patterns are based on price differences, not absolute prices, so you can precompute the differences array once and then match patterns efficiently. Also, emphasize the importance of handling edge cases like empty patterns or insufficient data.

1. Understand the problem

Restate the problem in your own words, confirm the input/output format, and clarify any ambiguities (e.g., pattern length, initial holdings, what happens if both patterns match).

2. Design the algorithm

Propose an O(n) time and O(1) extra space approach. For each day, compute the price difference from the previous day, then check if the recent differences match the sell pattern (and sell if holding) and then the buy pattern (and buy).

3. Handle pattern matching efficiently

Use a rolling hash or direct comparison of the last k differences to check pattern matches in O(1) per day. Precompute the pattern hashes or use a simple loop if pattern length is small.

4. Simulate and record holdings

Iterate through the days, process sell before buy, update holdings, and record the holdings after each day. Ensure the simulation respects the order of operations.

5. Test and validate

Walk through a small example, test edge cases (e.g., empty patterns, patterns longer than available data, no matches), and verify time and space complexity.

Key Points to Mention

  • Time complexity: O(n) by processing each day once and using O(1) pattern matching.
  • Space complexity: O(1) extra space by storing only necessary variables (e.g., holdings, rolling hash).
  • Pattern matching based on price differences, not absolute prices.
  • Order of operations: sell before buy on each day.
  • Edge cases: empty patterns, insufficient data, multiple matches, initial holdings.
  • Potential use of rolling hash for efficient pattern matching.

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

Q2

Given a string and a set of disallowed 2-character substrings, repeatedly remove any occurrence of any disallowed pair until none remain. Return the final string length, and also discuss how you'd return the actual final string. Design an O(n) solution with minimal extra space and argue correctness.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

Stack-based approach is the natural move here and I got there quickly.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Use a stack to simulate the removal process in a single pass, checking if the current character and the top of the stack form a disallowed pair. For the length, simply return the stack size; for the actual string, join the stack characters. This achieves O(n) time and O(n) space, which is minimal for the string reconstruction case.

Pro tip: Emphasize that the stack approach is optimal because it processes each character once and avoids repeated scans; for the length-only case, you can sometimes reduce space by using a two-pointer technique if the disallowed set has special structure, but the stack is generally the cleanest solution.

1. Clarify the problem and constraints

Confirm that removals are applied repeatedly until no disallowed pairs remain, and that the order of removals does not affect the final result. Ask about input size and whether the disallowed set is given as a set for O(1) lookups.

2. Design the stack-based algorithm

Iterate through the string, pushing each character onto a stack. Before pushing, check if the top of the stack and the current character form a disallowed pair; if so, pop the stack instead of pushing. After processing, the stack contains the final string.

3. Argue correctness

Prove that the stack simulates the removals correctly by induction: after processing each prefix, the stack equals the final string for that prefix. Show that any disallowed pair formed later will be caught when the second character is processed.

4. Analyze time and space complexity

Time is O(n) because each character is pushed and popped at most once. Space is O(n) for the stack in the worst case, which is minimal for returning the actual string; for length-only, space can be O(1) if we only track the stack size and the last few characters, but O(n) is still acceptable.

5. Discuss returning the actual string

To return the final string, simply join the characters in the stack. This takes O(n) time and space. If only the length is needed, return the stack size, which is O(1) extra space beyond the input.

Key Points to Mention

  • Stack-based simulation for O(n) time complexity
  • Correctness proof by induction on the processed prefix
  • Space complexity: O(n) for string reconstruction, O(1) for length-only if optimized
  • Handling of overlapping removals and order independence
  • Use of a hash set for O(1) disallowed pair lookups
  • Trade-off between returning length vs. actual string

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