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I believe O(n) is possible since they are sorted by start time.
Keep auxiliary variables storing the current maximum end time of the processes seen so far and the time the current set of consecutive processes started.
Go through the entries in the log in order. If the current process starts at a time larger than the previous maximum time the processor was busy, then this is a break (it was idle) and update the current start time.
- Miguel Oliveira December 05, 2013