Trees as Recursive Structures

Think of a tree with root $r$. It has children $c_1, c_2, \ldots, c_k$. Each child $c_i$ is itself the root of a tree.

The subtree rooted at $c_i$ contains $c_i$ and all nodes you can reach by going down from $c_i$. This recursive structure matters. To compute something about $r$, first compute it for each child, then combine those results.

The tree breaks into smaller trees. You solve small cases, then build up to the full answer.