Is there a efficient way to find only the combinations of interest from V exciting in P

Question

Is there a efficient way to find only the combinations of interest from V exciting in P

I have a list of something like this.

V = [2,3,5,7,9,12] 

Size of V can be anywhere from 0 to 50  based on my input. V has no duplicates.

I have another list P something like this 

P = [ [1],[1,2],[2,3] [3,4], [3,5,7], [3,5,8] ...]

P is constant with size 1000.

P has no duplicates and within P, each element is sorted in ascending order. 

What would be an efficient way to find the combinations from V existing in P.

For example

When V = [2,3,5,7,9,12] combination of interest would be [[2,3],[3,5,7]].

I have already tried generating all possible arrangements from V and then filter by P.  This is not very efficient. Just wondering if there is a better way to do what I asked for. 

Since I already know P is any form of Tree a better option for this ?

Answer 1

Using set.issuperset is probably the fastest method in practice:

v = set(V)
[c for c in P if v.issuperset(c)]

It is also possible to use two pointers, gradually advancing along each list. It will probably be slower in Python, but faster in C/C++:

def is_subset(V, combination):
    # both V and combination are assumed sorted
    v = iter(V)
    for element in combination:
        for el in v:
            if el >= element:
                break
        if el != element:
            return False
    return True

[c for c in P if is_subset(V, c)]