Compute total covered interval length

Q: Compute total covered interval length

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Question

Given a list of integer intervals [l, r) (half-open), compute the total length covered by at least one interval. Intervals may overlap or be nested. Return the length and explain time and space complexity. Implement two approaches: (a) sort-and-merge line sweep; (b) a segment tree or interval tree that supports incremental add/remove intervals and querying the total covered length after each update. Discuss handling large coordinate ranges via coordinate compression, treatment of duplicates, and common off-by-one pitfalls.

Compute total covered interval length

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