Vocabulary - Bitmask

A bitmask is an integer where each bit represents whether an element is included. With $n$ elements labeled $0$ to $n-1$, bit $i$ being $1$ means element $i$ is in the subset.

Example with $n=4$: mask $= 11$ in decimal $= 1011$ in binary. Bits $0$, $1$, and $3$ are set, so this represents $\{0, 1, 3\}$. The empty set is $0$. The full set is $2^n - 1$ (all bits set). This mapping is one-to-one: every subset has exactly one integer in $[0, 2^n)$, and vice versa. This lets us use integers as array indices for DP (dynamic programming).