Question

I’ve read in a lot of places that a set data structure can be implemented in C++ using a bit array, but I don’t fully understand this and haven’t been able to find a code sample. Does anyone have an example or a detailed explanation?

Answer 1

Using a bit field to implement a set only works if there are only a few possible elements that can go in the set, because you need a bit for each of them. A bit-set of all 32-bit integers, for instance, would need 2^32 bits, or about 500 megabytes.

The good news is, if there are few enough possible elements that space isn’t a problem, it’s really, really fast.

What you do, essentially, is define a bit array such that each bit corresponds to one possible element. Each bit corresponding to an element that’s in the set is 1; the others are 0.

Will post sample C code in a bit (no pun intended). I think C++ may offer direct library support for bit-sets, but unfortunately I don’t speak it.

EDIT: The following sample code, which I just wrote, is for a bit-set which can contain the numbers 0 through 31. Allowing support for an arbitrary number of elements would be significantly more complicated, though certainly useful.

#include <stdint.h>
#include <stdio.h>

const BS_SIZE = 32;
typedef uint32_t bitset32;

/* Takes a pointer to a bit set and an int from 0 to 31,
 * and adds the int to the bit set.
 */
void add_element(bitset32 *bs, int elt)
{
    *bs |= (1 << elt);
}

/* Takes a pointer to a bit set and an int from 0 to 31,
 * and removes the int from the bit set.
 */
void remove_element(bitset32 *bs, int elt)
{
    *bs &= ~(1 << elt);
}

/* Takes a pointer to a bit set and an int from 0 to 31,
 * and returns 1 if the int is in the bit set, 0 otherwise.
 */
int has_element(bitset32 *bs, int elt)
{
    return (*bs >> elt) & 1;
}

/* Takes a pointer to a bit set and prints each element in it. */
void print_all_elements(bitset32 *bs)
{
    bitset32 bits = *bs;
    int i;
    for (i = 0; i < BS_SIZE; i++) {
        if (bits & 1) {
            printf("%d\n", i);
        }
        bits >>= 1;
    }
}

/* Some test code. Prints:
 * 0 in test
 * 0
 * 20
 * 31
 */
int main()
{
    bitset32 test = 0;
    add_element(&test, 0);
    add_element(&test, 13);
    add_element(&test, 13);
    add_element(&test, 20);
    add_element(&test, 28);
    remove_element(&test, 13);
    remove_element(&test, 20);
    remove_element(&test, 28);
    if (has_element(&test, 0)) {
        printf("0 in test\n");
    }
    if (has_element(&test, 20)) {
        printf("20 in test\n");
    }
    add_element(&test, 20);
    add_element(&test, 31);
    print_all_elements(&test);
    return 0;
}