Introduction to Bitmask DP

You need to assign $n$ workers to $n$ tasks. Each worker has different costs for different tasks. Find the minimum total cost. There are $n!$ possible assignments. For $n = 20$, that's over $2 \times 10^{18}$ possibilities. So... impossible.

But you don't need to track the order of assignments, just which workers are used. That's $2^n$ states. For $n = 20$, that's about a million. Bitmasks let you represent "which elements are chosen" as a single integer. I'll show you how to think in subsets.