The Tree DP Pattern

Here's the core pattern: $dp[v]$ = some combination of $dp[\text{child}]$ for all children of $v$. For leaves (nodes with no children), $dp[\text{leaf}]$ comes directly from the node's properties.

For internal nodes, you combine children's dp values according to the problem's logic. The answer is usually $dp[\text{root}]$, representing the solution for the entire tree. Sometimes you track a global maximum across all nodes instead.