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There are N date ranges which include check-in date and check-out date. How can I find out the busiest day?

Example:

2016-10-12 to 2016-10-18
2016-10-11 to 2016-10-15
2016-10-13 to 2016-10-14
2016-10-12 to 2016-10-13

From these dates, it is obvious that 2016-10-12 was booked on all 4 times. How can I mathematically solve this?

Using two dates we can find out overlaps like this.

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    You can solve this easily computationally - You sort by check in and then keep a rolling counters for eqch date. – 2017-02-23

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Hint -

I think you can create 4 sets for given 4 date range's. Then you can find intersection of these 4 sets.

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    these dates can be more than 5 – 2017-02-23