Centroid Decomposition for a tree. Given a tree, it can be recursively decomposed into centroids. Then the parent of a centroid `c` is the previous centroid that splitted its connected component into two or more components. It can be shown that in such decomposition, for each path `p` with starting and ending vertices `u`, `v`, the lowest common ancestor of `u` and `v` in centroid tree is a verte
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