The Bitmask DP Pattern

The core idea: $dp[\text{mask}]$ = answer for the subset represented by mask. Your DP (dynamic programming) table has $2^n$ entries, one per subset. Transitions typically add or remove one element, connecting $dp[\text{mask}]$ to $dp[\text{mask with one bit changed}]$.

You build larger subsets from smaller ones, or vice versa. Time complexity is typically $O(n \cdot 2^n)$ if each state checks $n$ transitions, or $O(n^2 \cdot 2^n)$ if transitions involve pairs. For $n = 20$, that's $20$ million or $400$ million operations, both feasible.