Centroid Decomposition — Divide-and-Conquer on Trees

Why it matters

Centroid decomp enables O(n log n) tree algorithms.

The architecture

Centroid: node whose removal leaves subtrees ≤ n/2.

Recursively decompose each subtree.

How it works end to end

Applications: path counting, distance queries.

Implementation: recursively find + process.

Combines with other techniques (BFS from centroid).