← Jump Trading Interview Insights
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.
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.
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).
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).
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.
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.
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.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Stack-based approach is the natural move here and I got there quickly.
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.
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.
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.
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.
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.
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.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.