LeetCode 337 House Robber III - Recurrence

If you rob $v$ (state $1$): you get value[v] plus the sum of not robbing any child. dp[v][1] = value[v] + dp[left][0] + dp[right][0].

If you do not rob $v$ (state $0$): pick the best option for each child. dp[v][0] = max(dp[left][0], dp[left][1]) + max(dp[right][0], dp[right][1]).