UnionFind

It can be viewed as adding an edge to the graph and checking whether two vertices are connected or not is fast.

For a relation between N objects, if it can be decomposed into iffs, it can be described as a graph edge

For example, "x beats y" when there is a target that is either goo or chokiper is equivalent to adding 3 edges to the 3N vertex set because it can be decomposed into 3 iff "x is goo iff y is chokiper".

The connected component corresponds to a solution that satisfies the condition

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