##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
The core idea
Three phases in a single pass:
Add all intervals that end before new interval starts (no overlap, completely before).
Merge all intervals that overlap with new interval. Track the merged interval's min start and max end.
Add all intervals that start after new interval ends (no overlap, completely after).
This exploits the sorted order to process in time.
