Find the root of the largest tree

Ask what root means before coding. In a directed rooted forest, the root of a component is the node with indegree zero; find components and choose the root belonging to the largest one. If edges are undirected and root is arbitrary, traverse each component, count nodes, and return a specified representative only after agreeing on tie-breaking. If the task means the centroid root that minimizes height, it needs subtree sizes and rerooting logic, which is a different problem. A disjoint-set union is useful for streaming undirected edges: union endpoints, maintain component sizes, and retain a representative, but it cannot infer a directed tree root by itself. Test one-node trees, multiple equal-size components, invalid cycles, and missing parent links. Traversal is O(V+E) time and O(V) space; DSU is near O(E alpha(V)) time with O(V) space. Do not silently equate a DSU leader with a semantic tree root.