LeetCode 337 House Robber III - Walkthrough

Tree: root $3$, left $2$ (left $3$), right $3$ (right $1$). DFS leaf $3$ (left of $2$): returns $(0, 3)$. DFS node $2$: exclude $= 3$, include $= 2$. Returns $(3, 2)$. DFS leaf $1$ (right of $3$): returns $(0, 1)$. DFS node $3$ (right): exclude $= 1$, include $= 3$.

Returns $(1, 3)$. DFS root: exclude $= max(3, 2) + max(1, 3) = 6$, include $= 3 + 3 + 1 = 7$. Answer: $7$. Taking the root and both grandchildren gives the maximum.