This is the one that actually made me think.
This is a weighted interval scheduling problem. Sort intervals by end time, then use dynamic programming where dp[i] is the maximum cost using intervals up to i, and for each interval find the latest non-overlapping interval via binary search.
Pro tip: Clarify edge cases upfront: empty input, zero durations, negative costs, and whether intervals touching at endpoints are considered overlapping. This shows attention to detail and avoids incorrect assumptions.
Confirm input format, whether intervals are inclusive/exclusive at endpoints, and if costs can be negative. Define non-overlapping precisely.
Combine start, duration, and cost into interval objects. Sort intervals by end time (or start time) to enable efficient DP.
Define dp[i] as max cost using first i intervals. Recurrence: dp[i] = max(dp[i-1], cost[i] + dp[p(i)]) where p(i) is the latest interval that doesn't overlap with i.
For each interval, use binary search on sorted end times to find p(i) in O(log n), achieving O(n log n) overall.
State time and space complexity. Walk through a small example and edge cases to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Came up in both full-time and intern rounds apparently.
Clarify the definition of 'overlapping time' (e.g., total duration covered by at least two intervals, or sum of pairwise overlaps) and edge cases. Then propose an efficient algorithm: sort intervals by start time, sweep through while tracking the maximum end seen so far, and accumulate overlap lengths. Discuss time/space complexity and potential optimizations.
Pro tip: Explicitly state your assumptions about what 'overlapping time' means and confirm with the interviewer before coding; this shows attention to detail and avoids solving the wrong problem. Also, mention how you would handle large inputs or streaming data, as Amazon values scalability.
Ask the interviewer to define 'overlapping time' precisely: is it the total duration covered by at least two intervals, or the sum of all pairwise overlaps? Also clarify input format, interval inclusivity, and whether intervals are sorted.
Briefly describe a naive O(n^2) method: for each pair of intervals, compute their overlap and sum. This establishes a baseline and shows you can think simply before optimizing.
Sort intervals by start time. Sweep through them while maintaining the maximum end time seen so far. When the current interval's start is less than the max end, there is overlap; compute the overlapping length and update the max end.
State that sorting takes O(n log n) and the sweep is O(n), so overall O(n log n) time and O(1) extra space (if sorting in place). Discuss edge cases: no overlaps, all intervals overlapping, touching intervals, zero-length intervals.
Walk through a small example (e.g., [[1,4],[2,5],[7,9]]) to verify the algorithm and demonstrate correctness. Mention potential pitfalls like double-counting overlaps.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem constraints (e.g., whether intervals are sorted, inclusive/exclusive boundaries, and expected output format). Then propose sorting intervals by start time and iterating through them to merge overlapping ones, analyzing time and space complexity. Finally, discuss edge cases and potential optimizations.
Pro tip: At Amazon, emphasize scalability and real-world applications (e.g., merging meeting rooms or resource allocations). Mention that sorting is often acceptable but consider if input is already sorted or if a streaming approach is needed.
Ask about input format, whether intervals are sorted, boundary conditions (inclusive/exclusive), and expected output. Confirm if intervals can be empty or have invalid ranges.
Propose sorting intervals by start time, then iterating and merging when the current interval overlaps with the last merged interval. Explain how to detect overlap (current.start <= last.end).
State that sorting takes O(n log n) time and merging takes O(n) time, resulting in O(n log n) overall. Space complexity is O(n) for the output (or O(1) extra if sorted in-place and output is not counted).
Cover cases like empty input, single interval, all overlapping, none overlapping, and intervals with same start. Mention if input is already sorted, we can skip sorting and achieve O(n) time.
If asked, write clean code with meaningful variable names, handling edge cases. For example, sort, initialize result with first interval, then iterate and merge.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The frequency-based greedy solution trips people up if they haven't seen it.
Start by clarifying the problem constraints (e.g., cooldown n, task types, idle slots). Then explain the greedy approach: always execute the most frequent remaining task, using a max-heap and a cooldown queue to track when tasks become available. Derive the formula max((maxFreq-1)*(n+1)+numMaxFreq, totalTasks) and discuss its intuition.
Pro tip: Mention that the formula works because the most frequent tasks dictate the schedule, and idle slots can be filled by other tasks; if not, the answer is simply the total number of tasks. This shows you understand both the greedy simulation and the mathematical shortcut.
Ask about the range of n, task list size, and whether tasks are represented as characters or integers. Confirm that cooldown applies between same tasks and that idle slots are allowed.
Use a hash map to count how many times each task appears. Identify the maximum frequency and how many tasks share that maximum.
Compute the minimum time using the formula: max((maxFreq - 1) * (n + 1) + numMaxFreq, totalTasks). Explain why this works: the most frequent tasks create a skeleton schedule with gaps that can be filled by other tasks.
If time permits, describe how a max-heap and a cooldown queue can simulate the process to verify the formula, especially for cases where idle slots are unavoidable.
State that the formula approach runs in O(N) time and O(1) space (since there are at most 26 tasks if characters). Mention that the simulation approach is O(N log N) but more intuitive.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This one was vague in how it was described and honestly I'm still not 100% sure what the exact problem statement was.
Start by clarifying the problem: what exactly is the 'optimal difference' (e.g., minimize maximum gap, maximize minimum gap), what are the intervals (points, ranges), and what constraints exist (e.g., must choose k intervals, non-overlapping, within bounds). Then propose an algorithmic approach such as sorting, greedy, dynamic programming, or binary search on the answer, and analyze time/space complexity. Finally, discuss edge cases and test with examples.
Pro tip: Amazon values customer obsession and ownership: frame your solution in terms of real-world impact, such as optimizing delivery windows or resource allocation, and proactively discuss trade-offs and scalability.
Ask questions to understand the exact definition of 'optimal difference', the nature of intervals, and all constraints. Confirm input/output format and edge cases.
Brainstorm algorithms: sorting, greedy, dynamic programming, binary search on answer, or graph-based methods. Consider which fits the constraints best.
Choose the most efficient algorithm, explain why it works, and outline steps with pseudocode. Justify correctness and analyze time/space complexity.
Identify edge cases (e.g., empty input, single interval, all intervals overlapping) and walk through a small example to validate the solution.
Mention how the solution scales with input size, potential optimizations, and any trade-offs between time and space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.