LeetCode 337 House Robber III - Implementation

Write a DFS function that returns a pair $( ext{exclude}, ext{include})$ for each node. Pseudocode:

function dfs(v)
    if v is null then
        return (0, 0)
    (left0, left1) := dfs(v.left)
    (right0, right1) := dfs(v.right)
    rob := v.val + left0 + right0
    skip := max(left0, left1) + max(right0, right1)
    return (skip, rob)

Return max of both states at root. Time $O(n)$, space $O(h)$ where $h$ is tree height.