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Design a data structure that maintains a dynamic set of intervals (possibly with associated weights) supporting updates like add/remove/modify and answering range queries such as covered length, overlap counts, or maximum/minimum value over a range. The challenge is to handle interval merging/splitting and aggregations efficiently, typically using ordered maps, segment trees, or binary indexed trees to achieve logarithmic-time updates and queries.
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Leetcode 2805. Custom Interval
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