Bitmask DP

Bitmasks represent sets: bit $i$ indicates element $i$ membership.

TSP example: dp[mask][i] = min cost visiting cities in mask, ending at $i$.

for mask from 0 to 2^n - 1:
    for last in mask:
        for next not in mask:
            newMask = mask | (1 << next)
            dp[newMask][next] = min(dp[newMask][next],
                                    dp[mask][last] + dist[last][next])

Time: $O(n^2 \cdot 2^n)$. Space: $O(n \cdot 2^n)$. Feasible for $n \leq 20$.