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Complexity Breakdown

Given that the input intervals are already sorted, our solution exhibits a linear time complexity of (O(n)) and linear space complexity. This is because we iterate through each of the (n) intervals exactly once.

The Final Logic: A Code Snapshot

The final logic could be understood as below (actual code not shown here). While iterating through the sorted array:

  • Check for overlap with the last interval.
  • Extend last if there's an overlap.
  • Append to result in case of a clear separation.

By following this systematic approach, merging time intervals becomes a straightforward task, completely doable within reasonable time and space constraints.