My first instinct was to just expand every interval and count hits in an array, which works but I knew they'd push back on it if M is huge.
Clarify the problem constraints and edge cases, then propose an efficient sweep-line algorithm using a difference array or event sorting to compute coverage counts in O(N log N) or O(N + M) time. Walk through the algorithm step-by-step, analyze time and space complexity, and discuss potential optimizations or alternative approaches.
Pro tip: Demonstrate awareness of integer overflow and boundary conditions (e.g., intervals extending beyond [-M, M]) and proactively suggest clamping or validation. Also, mention that if multiple integers have the same maximum coverage, returning any is acceptable, showing attention to problem details.
Ask about input size, interval inclusivity, whether intervals can overlap or be invalid, and if the range [-M, M] is guaranteed to contain at least one integer. Confirm that any integer with maximum coverage is acceptable.
Propose a sweep-line approach: create events for interval starts (+1) and ends+1 (-1), sort them, and sweep to track coverage. Alternatively, use a difference array if M is small, or a segment tree for dynamic updates.
Explain how to process events: sort by coordinate, iterate while maintaining a running sum, and record the coordinate with the highest sum. Handle ties by returning the first or any.
State time complexity O(N log N) for sorting events (or O(N + M) with difference array) and space O(N). Discuss edge cases: empty intervals, intervals outside range, all intervals disjoint, and multiple max points.
Mention potential optimizations like coordinate compression if M is large, or using a balanced BST for dynamic intervals. Compare with brute-force O(N*M) approach to highlight efficiency.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The base problem I got through fine, just prune left subtree if node value is below low and right subtree if above high.
Start by explaining the optimal recursive traversal that prunes branches outside the range, achieving O(log n + k) time. Then discuss the follow-up by proposing preprocessing techniques like flattening the BST into a sorted array and using prefix sums for O(log n) per query, or augmenting nodes with subtree sums for O(log n) queries without extra space.
Pro tip: Mention that pruning is key: if the current node's value is less than low, skip its left subtree; if greater than high, skip its right subtree. This shows you understand BST properties deeply.
Ask about the tree size, number of queries, and whether the tree is static or dynamic. This informs the choice of preprocessing.
Describe a recursive function that traverses only nodes within the range, pruning subtrees that cannot contain valid nodes. Analyze time complexity as O(log n + k) where k is the number of nodes in range.
Propose flattening the BST into a sorted array and building a prefix sum array. Then each range query becomes a binary search for indices and a prefix sum difference, O(log n) per query.
Compare the flattening approach (O(n) extra space) with augmenting nodes with subtree sums (O(1) extra space but O(log n) per query). Mention that augmented trees can also handle updates if needed.
Reiterate the best approach based on constraints and highlight the importance of pruning and preprocessing for scalability.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Stack problem, pretty standard once you see it.
Use a stack to track active function calls, recording each function's start time and accumulating child execution time. When a function ends, its exclusive time is the total elapsed time minus the sum of its children's exclusive times. Process events in chronological order, ensuring timestamps are sorted.
Pro tip: Clarify upfront whether timestamps are inclusive or exclusive and whether logs are guaranteed sorted; handling these edge cases demonstrates attention to detail and prevents incorrect assumptions.
Parse the log entries into structured events (function name, start/end, timestamp). If not guaranteed sorted, sort them by timestamp to ensure correct chronological processing.
Use a stack to maintain the current call stack. Also maintain a map from function name to its accumulated exclusive time, and a map to track the start time of each active call.
Iterate through events: on a start event, push the function onto the stack and record its start time. On an end event, pop the function, compute its exclusive time as (end_time - start_time) minus the sum of exclusive times of any nested calls that occurred during this call, and add to its total.
When a nested call ends, its exclusive time is subtracted from the parent's elapsed time. This can be done by maintaining a running total of child exclusive times for each active call or by adjusting the parent's start time to account for child execution.
After processing all events, return the map of function names to their exclusive execution times. Ensure the stack is empty at the end, indicating balanced start/end events.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.