Find min and max range with a combination of column values in PySpark

I have a pyspark dataframe like this,

+----------+--------+----------+----------+
|id_       | p      |d1        |  d2      |
+----------+--------+----------+----------+
|  1       | A      |2018-09-26|2018-10-26|
|  2       | B      |2018-06-21|2018-07-19|
|  2       | C      |2018-07-13|2018-10-07|
|  2       | B      |2018-12-31|2019-02-27|
|  2       | A      |2019-01-28|2019-06-25|
-------------------------------------------

From this dataframe I have to make a dataframe like this,

+----------+--------+----------+----------+
|id_       | q      |d1        |  d2      |
+----------+--------+----------+----------+
|  1       | A      |2018-09-26|2018-10-26|
|  2       | B      |2018-06-21|2018-07-12|
|  2       | B C    |2018-07-13|2018-07-19|
|  2       | C      |2018-07-20|2019-10-07|
|  2       | B      |2018-12-31|2019-01-27|
|  2       | B A    |2019-01-28|2019-02-27|
|  2       | A      |2019-02-28|2019-06-25|
-------------------------------------------

It is something like, finding which values of p are present in the data for a particular id_ from when to when. If there are multiple p in a same day then both should be present in the data, seperated by a space.

I tried to do this is by creating each and every dates in the range min(d1) and max(d2) and filling them accordingly. From that dataframe, after some melting and grouping I can get the desired result.

But the process takes very long time and is very inefficient.

I am looking for an efficient method for performing this task.

I can also have more complex cases of overlap, ie overlap among more than two p-values.

See a sample data below,

+----------+--------+----------+----------+
|id_       | p      |d1        |  d2      |
+----------+--------+----------+----------+
|  1       | A      |2018-09-26|2018-10-26|
|  2       | B      |2018-06-21|2018-07-19|
|  2       | C      |2018-06-27|2018-07-07|
|  2       | A      |2018-07-02|2019-02-27|
|  2       | A      |2019-03-28|2019-06-25|
-------------------------------------------

This must be converted to,

+----------+--------+----------+----------+
|id_       | q      |d1        |  d2      |
+----------+--------+----------+----------+
|  1       | A      |2018-09-26|2018-10-26|
|  2       | B      |2018-06-21|2018-06-26|
|  2       | B C    |2018-06-27|2018-07-01|
|  2       | B C A  |2018-07-02|2018-07-07|
|  2       | A B    |2018-07-08|2018-07-19|
|  2       | A      |2018-07-20|2019-02-27|
|  2       | A      |2019-03-28|2019-06-25|
-------------------------------------------

Order of individual items in the q doesn't matter. ie either if A, B and C are in overlap. It can either be shown as A B C, or B C A or A C B so on.

from Find min and max range with a combination of column values in PySpark