Question

I have three sets:

s0 = [set([16,9,2,10]), set([16,14,22,15]), set([14,7])]   # true, 16 and 14
s1 = [set([16,9,2,10]), set([16,14,22,15]), set([7,8])]    # false

I want a function that will return True if every set in the list intersects with at least one other set in the list. Is there a built-in for this or a simple list comprehension?

Answer 1

It’s a little verbose but I think it’s a pretty efficient solution. It takes advantage of the fact that when two sets intersect, we can mark them both as connected. It does this by keeping a list of flags as long as the list of sets. when set i and set j intersect, it sets the flag for both of them. It then loops over the list of sets and only tries to find a intersection for sets that haven’t already been intersected. After reading the comments, I think this is what @Victor was talking about.

s0 = [set([16,9,2,10]), set([16,14,22,15]), set([14,7])]   # true, 16 and 14
s1 = [set([16,9,2,10]), set([16,14,22,15]), set([7,8])]    # false


def connected(sets):
    L = len(sets)

    if not L: return True
    if L == 1: return False

    passed = [False] * L
    i = 0
    while True:
        while passed[i]: 
            i += 1
            if i == L: 
                return True

        for j, s in enumerate(sets):
            if j == i: continue
            if sets[i] & s: 
                passed[i] = passed[j] = True
                break
        else:
            return False


print connected(s0)
print connected(s1)

I decided that an empty list of sets is connected (If you produce an element of the list, I can produce an element that it intersects ;). A list with only one element is dis-connected trivially. It’s one line to change in either case if you disagree.