I am trying to compute the number of intersecting array elements for multiple arrays (essentially elements belonging to separate parts of venn diagrams). Initially and naively I thought this should be an easy thing to do and for 2 arrays it is:

1. Make a hash table for one array with keys being its elements
2. Loop through another array and count if an element exists in the previously created hash table
3. Subtract the number of shared elements from the total number of elements of each array.

But when the number of arrays increases the number of possible intersections between respective arrays increases (for A,B,C arrays we have A/B, A/C, B/C, A/B/C). So the problem I am having is how to scale the above algorithm.

Does anyone know a solution to this problem even if a limited number of sets can only be included (I think this is an NP problem thus any algorithm that can produce a solution for more than 7 arrays would be acceptable)

Thank you