LeetCode 337 House Robber III - State Design

For each node, compute two values: $\text{rob}[v]$ = max money if you rob $v$, and $\text{skip}[v]$ = max money if you skip $v$.

Transitions: $\text{rob}[v] = v.\text{val} + \text{skip}[\text{left}] + \text{skip}[\text{right}]$, and $\text{skip}[v] = \max(\text{rob}[\text{left}], \text{skip}[\text{left}]) + \max(\text{rob}[\text{right}], \text{skip}[\text{right}])$.

Answer: $\max(\text{rob}[\text{root}], \text{skip}[\text{root}])$.