My first instinct was to just iterate from 1 upward and count misses, which works fine for small inputs but falls apart when nums[i] can go up to a billion.
Clarify that the array contains distinct positive integers and we need the k-th missing positive integer. Use a set for O(1) lookups and iterate from 1 upward, counting missing numbers until reaching k. Alternatively, use a boolean array of size n+k+1 to mark present numbers and scan for the k-th missing.
Pro tip: Mention that the answer is at most n+k, so you can bound your search space and avoid infinite loops. Also, discuss trade-offs: set approach uses O(n) space but is simple; boolean array is more memory-efficient for dense ranges.
Confirm that the array has distinct positive integers and we need the k-th smallest positive integer not in the array. Ask about constraints (e.g., array size, k range) to determine optimal approach.
Decide between using a hash set for O(1) membership checks or a boolean array of size n+k+1 to mark presence. Consider space-time trade-offs.
Iterate through the array and mark each number as present in the chosen data structure. Ignore numbers greater than n+k as they don't affect the first k missing numbers.
Iterate from 1 upward, counting numbers not marked as present. When the count reaches k, return that number.
State time complexity O(n + k) and space complexity O(n) or O(n+k) depending on approach. Discuss potential optimizations like using the array itself for marking if modification is allowed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Sliding window with a per-operation deque tracking the last two timestamps.
Clarify the problem definition and edge cases, then propose an efficient algorithm using a hash map to track the last occurrence of each operation. Iterate through the events in chronological order, and for each event, check if the same operation occurred within the previous W seconds; if so, increment the redundant count and update the last occurrence time.
Pro tip: Emphasize that the solution should handle large datasets efficiently, ideally O(n) time and O(k) space where k is the number of unique operations. Also, discuss how to handle ties or out-of-order timestamps if the input isn't sorted.
Ask questions to confirm the definition of 'redundant', whether the arrays are sorted by timestamp, and what to do if multiple events occur at the same timestamp.
Select a hash map to store the most recent timestamp for each operation, enabling O(1) lookups. If timestamps are not sorted, consider sorting first or using a sliding window approach.
Iterate through the events, and for each event, check if the operation's last occurrence is within W seconds. If yes, mark as redundant; then update the last occurrence to the current timestamp.
State the time complexity (O(n) if sorted, O(n log n) if sorting needed) and space complexity (O(k) for k unique operations).
Walk through a small example to verify correctness, including edge cases like no redundancies, all redundancies, and boundary conditions (exactly W seconds apart).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.