Bitmasks for Subsets

You can represent a subset of $n$ elements using an integer. Each bit position corresponds to one element: bit $i$ is 1 if element $i$ is in the subset, 0 otherwise.

For example, with 4 elements $\{0, 1, 2, 3\}$, the number $5 = 0101$ represents the subset $\{0, 2\}$ (bits 0 and 2 are set).

With $n$ elements, there are $2^n$ possible subsets (each element is either in or out). You can iterate through all subsets by looping from $0$ to $2^n - 1$ and treating each number as a bitmask.