Iterating Through Subsets

To generate all subsets of $n$ elements, loop through all integers from $0$ to $2^n - 1$. For each integer $mask$, check which bits are set to determine which elements are in that subset.

For $n=3$ elements $\{0, 1, 2\}$, loop through masks $0$ to $7$: $000, 001, 010, 011, 100, 101, 110, 111$. Each mask corresponds to one subset.

To extract which elements are in subset represented by mask $m$, loop through bits $i$ from $0$ to $n-1$ and check if bit $i$ is set: $(m \& (1 << i)) \neq 0$.