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Peak number of concurrent live orders

Asked at IMC, Flow Traders

Each order is live over an interval [start, end]. Find the largest number of orders that are simultaneously live at any instant.

orders = [[1, 4], [2, 5], [7, 8]]
-> 2            # [1,4] and [2,5] overlap

Return the peak concurrency. Aim for O(nlogn)O(n \log n).

Your answer

This one is open-ended. Work it through, then check your reasoning against the full solution.

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