如何合并有交集的集合(连通分量算法)? [英] How to merge sets which have intersections (connected components algorithm)?

问题描述

是否有任何有效的方法来合并具有交集的集合.例如:

Is there any effective way to merge sets which have intersections. For example:

l = [{1, 3}, {2, 3}, {4, 5}, {6, 5}, {7, 5}, {8, 9}]

预期结果是:

r = [{1, 2, 3}, {4, 5, 6, 7}, {8, 9}]

所有具有交集(公共分量)的集合都应合并.例如:

All sets which have intersection (common components) should be merged. For example:

{1, 3} & {2, 3}
# {3}

因此这两个集合应该合并:

So these two sets should be merged:

{1, 3} | {2, 3}
# {1, 2, 3}

不幸的是，我没有任何有效的解决方案.

Unfortunately I don't have any working solution.

更新:结果中集的顺序并不重要.

UPDATE: The order of sets in the result is not important.

推荐答案

一种有效的方法来实现是将集合列表转换为可散列的冻结集的集合，以便在迭代过程中找到与当前集合相交的冻结集.从池中将其删除:

An efficient way to implement the connected components algorithm as mentioned by @mkrieger1 in the comments is to convert the list of sets to a set of hashable frozensets so that as you iterate through it and find a frozenset that intersects with the current one you can easily remove it from the pool:

pool = set(map(frozenset, l))
groups = []
while pool:
    groups.append(set(pool.pop()))
    while True:
        for candidate in pool:
            if groups[-1] & candidate:
                groups[-1] |= candidate
                pool.remove(candidate)
                break
        else:
            break

给出l = [{1, 3}, {2, 3}, {4, 5}, {6, 5}, {7, 5}, {8, 9}]，groups将变为:

[{1, 2, 3}, {4, 5, 6, 7}, {8, 9}]

给定l = [{1, 2}, {3, 4}, {2, 3}]，groups将变为:

[{1, 2, 3, 4}]

给定l = [{1}, {2}, {1, 2}]，groups将变为:

[{1, 2}]

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