Quiz: Decomposition Tree Depth

A centroid decomposition tree of $n$ nodes has depth $O(\log n)$. Why?

1. A.Because each centroid splits the tree into exactly $2$ equal halves
2. B.Because removing a centroid leaves subtrees of at most $\lfloor n/2 \rfloor$ nodes, so sizes halve at each level
3. C.Because the tree is always balanced after decomposition
4. D.Because centroid decomposition applies binary search on the tree