Division of time periods

I will be working with periods in time. Each period has a start and end date (along with other data..but for the help I need only the start/end are relevant). I have a list of default periods. The default periods are arranged perfectly so the start of one is exactly one day greater than the end of the previous..etc.
Now the fun part.
I need to be able to add new periods to the existing group (defaults). The new period being added may span more than one "existing" period. Existing periods need to adjust their start/end as needed to fit in the incomming period.
Here is an example showing 2 default periods and one custom period being added:
period - start=1000 end=2000
period - start=2001 end=3000
..new incomming period: period - start=1500 end=2300
After the addtion of the new period I would have the following:
period - start=1000 end=1499
period - start=1500 end=2000
period - start=2001 end=2299
period - start-2300 end=3000
Any help/pointers in the right direction would be helpful.
One last note: I realize as dates the values will be nothing like "2300". I'm not looking for a date specific answer. I am looking for the core concepts behind being able to take a group of objects which have start and end values and adding new objects to that group such that the final result is a sorted group of objects (by start value) which have been diveded up correctly to accomadate any new incomming objects.

Find the last period whose start attribute is earlier than the new start attribute. Find the first period whose end attribute is greater than the new end indicator. Adjust these periods to fit around your new period, delete any periods in between these periods, then insert your new period between.

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Division of time periods

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