As a Review.

Typora even cannot deal with $\LaTeX$ in sudo mode?

# Des.

Giving a undirected graph of $N$ nodes and $M$ edges. And you are given $Q$ operations, they might be deleting an edge or ask if there’re at least 2 paths without intersection between 2 nodes.

# Sol.

The situation in description is exactly what a biconnected-component of a graph is, as what we called BCC.

However deleting operation is difficult to execute, so we reverse the operation sequence and answer questions off-line.

When edges on the tree form a loop, a BCC is generated, and we shrink all nodes on that loop into a specific node, this can be maintained with a UFS.

When answering, just check if the two nodes are in the same component.

Notice that as we shrink nodes, operation with $f[x]$ in LCT should be modified to $bel[f[i]]$, which is the representing node of one component.