Bitmasking — Pack Many Booleans into an Integer

An integer can encode a subset of labeled items: bit i on means “item i included.”

Try this in Python

def has(mask: int, i: int) -> bool:
    return (mask >> i) & 1 == 1


def set_bit(mask: int, i: int) -> int:
    return mask | (1 << i)


m = 0b101
print(has(m, 0), has(m, 1), bin(set_bit(m, 3)))

Key takeaways

• Test bit with shift-and-1.
• Union of sets is bitwise OR of masks.
• Intersection is AND.