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Start by clarifying the requirements and edge cases, then propose a sweep-line algorithm that processes events in order of position, using a priority queue to manage active spans. Explain how to resolve overlaps by priority, length, and input order, and how to split losing spans while preserving metadata. Finally, analyze time and space complexity and discuss potential optimizations.
Pro tip: Emphasize that splitting a span must preserve its original metadata (priority, type, input order) so that future comparisons remain consistent; this shows attention to detail and understanding of the problem's invariants.
Ask about input constraints (e.g., number of spans, index range), expected output format, and how to handle invalid spans (e.g., start >= end). Confirm that splitting should retain original metadata.
Propose a sweep-line approach: create events for span starts and ends, sort them by position, and use a priority queue to track active spans. Alternatively, consider interval tree or divide-and-conquer if appropriate.
Specify the comparator for spans: higher priority wins; if equal, shorter original length wins; if still equal, earlier input order wins. Explain how to handle partial overlaps by splitting the losing span.
Walk through the algorithm: at each event, update active set, determine the winning span for the current segment, and if a span is partially overlapped, split it into surviving fragments, each retaining the original span's metadata.
State time complexity (e.g., O(n log n) for sorting and heap operations) and space complexity. Discuss test cases: no overlaps, full overlaps, partial overlaps, ties, and edge cases like zero-length spans.
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