Algorithm to detect overlapping periods

I've to detect if two time periods are overlapping.
Every period has a start date and an end date.
I need to detect if my first time period (A) is overlapping with another one(B/C).
In my case, if the start of B is equal to the end of A, they are not overlapping(the inverse too)
I found the following cases:

So actually I'm doing this like this:

tStartA < tStartB && tStartB < tEndA //For case 1
OR
tStartA < tEndB && tEndB <= tEndA //For case 2
OR
tStartB < tStartA  && tEndB > tEndA //For case 3

(The case 4 is taken in the account either in case 1 or in case 2)

It works , but it seems not very efficient.

So, first is there an existing class in c# that can modelize this(a time period), something like a timespan, but with a fixed start date.

Secondly: Is there already ac# code(like in the DateTime class) which can handle this?

Third: if no, what would be your approach to make this comparison the most fast?

---

Simple check to see if two time periods overlap:

bool overlap = a.start < b.end && b.start < a.end;

or in your code:

bool overlap = tStartA < tEndB && tStartB < tEndA;

(Use <= instead of < if you change your mind about wanting to say that two periods that just touch each other overlap.)

---

There is a wonderful library with good reviews on CodeProject: http://www.codeproject.com/Articles/168662/Time-Period-Library-for-NET

That library does a lot of work concerning overlap, intersecting them, etc. It's too big to copy/paste all of it, but I'll see which specific parts which can be useful to you.

---

You can create a reusable Range pattern class :

public class Range<T> where T : IComparable
{
    readonly T min;
    readonly T max;

    public Range(T min, T max)
    {
        this.min = min;
        this.max = max;
    }

    public bool IsOverlapped(Range<T> other)
    {
        return Min.CompareTo(other.Max) < 0 && other.Min.CompareTo(Max) < 0;
    }

    public T Min { get { return min; } }
    public T Max { get { return max; } }
}

You can add all methods you need to merge ranges, get intersections and so on...

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