As always, some code may help to visualize. For lack of anything more inspired we'll put the source data in an array structure:

@array = (
  [ '03:30', '05:45' ],
  [ '05:45', '09:15' ],
  [ '10:00', '11:35' ],
  [ '11:00', '15:40' ]
);
[download]

Some assumptions about the data that will always be true:

• Start times will always be less than end times and will never be identical
• All times are going to be in a 24 hour HH:MM format
• Ranges may overlap
• Ranges are listed in a random and arbitrary order
• Range times may be repeated in the list and ranges may be completely identical to other ranges
• All times will be between 00:00 and 24:00 inclusive

(I feel that last one needs explaining: while 24:00 is not a real time, it's needed to indicate a "full" ending range. If a user wants to specify "11:00pm until Midnight" I can't use 00:00 since that's technically last midnight, and I don't want to force the user into specifying something like 23:59 since that leaves a small gap. So 24 is a way to indicate the full range of time up until midnight, whether that's 23:59 or 23:59.99999.)

The specific results I need from these are the ranges of time not included in any of the pairs in the list. In the example code from above, it would be nice to see a result set that looks like:

(
  [ '00:00', '03:30' ],
  [ '09:15', '10:00' ],
  [ '15:40', '24:00' ]
);
[download]

Note that having two ranges back to back does NOT result in a "gap": the 3:30-5:45 and 5:45-9:15 ranges should be considered contiguous.

I just have no idea how to get this result from the previous sample data. I'd really like to avoid hacks like testing each minute in a 24 hour period, as that would probably not be performance-effective...

Any suggestions would be very much appreciated! I'm also open to changes on how the data is structured and formatted, if changes will help with possible solutions. Thanks!