Date Range Overlap with Nullable Dates

I'm looking for an extended answer to the question asked here:

Determine Whether Two Date Ranges Overlap

where any of the dates in either date range can be null. I've come up with the following solution, but I'm not sure if it can be simplified further.

(StartA == NULL || StartA <= EndB) &&
(EndA == NULL || EndA >= StartB) &&
(StartB == NULL || StartB <= EndA) &&
(EndB == NULL || EndB >= StartA)

Assuming:

DateTime ranges of StartA to EndA and StartB to EndB

EDIT: Sorry I quickly threw the above logic together, which seems to fail when either range's start and end dates are NULL. See David's solution below for a better & well-explained approach.

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This case can be handled by a slight generalization of Charles Bretana's excellent answer to that question.

Let CondA Mean DateRange A Completely After DateRange B (True if StartA > EndB) Let CondB Mean DateRange A Completely Before DateRange B (True if EndA < StartB)

In this case, assuming you want a null date to represent "no starting/ending bound," the conditions are modified. For CondA , for instance, in order for DateRange A to be completely after DateRange B, DateRange A must have a defined starting time, DateRange B must have a defined ending time, and the starting time of A must be after the ending time of B:

CondA := (StartA != null) && (EndB != null) && (StartA > EndB)

CondB is the same with A and B switched:

CondB := (StartB != null) && (EndA != null) && (StartB > EndA)

Continuing,

Then Overlap exists if Neither A Nor B is true

Overlap := !(CondA || CondB)

and

Now deMorgan's law, I think it is, says that

Not (A Or B) <=> Not A And Not B

Overlap == !CondA && !CondB
        == ![(StartA != null) && (EndB != null) && (StartA > EndB)] &&
           ![(StartB != null) && (EndA != null) && (StartB > EndA)]
        == [(StartA == null) || (EndB == null) || (StartA <= EndB)] &&
           [(StartB == null) || (EndA == null) || (StartB <= EndA)]

I think this is actually a bit more robust than the solution you developed, because if EndB == NULL but StartA is not null, your first condition will wind up comparing StartA <= NULL . In most languages I'm familiar with, that's an error condition.

---

That is probably as 'simple' as you can get it, although I haven't actually proven it.

It probably isn't worth it to simplify further, since that block ends up being about 8 operations in the worst case (4 on average thanks to short-circuit evaluation).

---

All answers are based if the condition is true. I'would like to add some note here.

1- The DateTime variable type is a struct and you can not set it to null unless that you are using nullable type like "DateTime?"

2- To find the overlap range follow the following steps

DateTime? StartOverLap = null,EndOverLap = null;
            if (StartA != null && StartB != null)
            {
                StartOverLap = StartA > StartB ? StartA : StartB;
            }
            else if (StartA == null && StartB != null)
            {
                StartOverLap = StartB;
            }
            else if (StartA != null && StartB == null)
            {
                StartOverLap = StartA;
            }
            if (EndA != null && EndB != null)
            {
                EndOverLap = EndA < EndB ? EndA : EndB;
            }
            else if (EndA == null && EndB != null)
            {
                EndOverLap = EndB;
            }
            else if (EndA != null && EndB == null)
            {
                EndOverLap = EndA;
            }
            if (StartOverLap != null && EndOverLap == null)
            {
                if (EndOverLap < StartOverLap)
                {
                    StartOverLap = null;
                    EndOverLap = null;
                }
            }

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