LeetCode 337 House Robber III - Key Observation

If you rob node $v$, you get $v$'s money but cannot rob $v$'s children. You can still rob grandchildren. If you skip node $v$, you get no money from $v$, but you're free to rob or skip each child independently.

This creates a dependency: your choice at $v$ constrains your choices at $v$'s children. You need to track both possibilities. For each node, store $2$ values: the best result when you rob it and the best when you skip it.