How to form overlapping periods?

Question

PHP

Greetings!
I apologize for the appeal, I have a headache with working with dates.
I need to do the following thing: if the periods intersect, then I need to separate them.
Incoming data (for example, in reality datetime objects)

[
    0 => ['openDate' => "2018-05-15", 'closeeDate' => "2018-05-30", "item" => 77],
    1 => ['openDate' => "2018-05-20", 'closeeDate' => "2018-05-25", "item" => 60]
]

In this example, the first period should be divided into two (key: 0, 2).
Those. get the output

[
    0 => ['openDate' => "2018-05-15", 'closeeDate' => "2018-05-19", "item" => 77]
    1 => ['openDate' => "2018-05-20", 'closeeDate' => "2018-05-25", "item" => 60],
    2 => ['openDate' => "2018-05-26", 'closeeDate' => "2018-05-30", "item" => 77],
]

Can you post the algorithm?
Thank you.
UPD
Breaking periods for each day is not an option. Dozens of arrays can come, in which the periods are for a year or two.
I still see the option to look for the intersection (it's simple). And how to form the required periods further. Those. detail.

Answer 1

As far as I understand it goes like this

Answer 2

another option is to collect everything in one array
initial data
$days = [2018-05-15, 2018-05-30, 2018-05-20, 2018-05-25];
then we sort in ascending order,
after which we take the first element and the second -1 day, then the second and 3-1 days, etc.