Question

How do I generate all possible combinations of n-bit strings? I need to generate all combinations of 20-bit strings in a fastest way possible. (my current implementation is done with bitwise AND and right shift operation, but I am looking for a faster technique).

I need to store the bit-strings in an array (or list) for the corresponding decimal numbers, like —

0 --> 0 0 0

1 --> 0 0 1

2 --> 0 1 0 … etc.

any idea?

Answer 1

for (unsigned long i = 0; i < (1<<20); ++i) {
    // do something with it
}

An unsigned long is a sequence of bits.

If what you want is a string of characters '0' and '1', then you could convert i to that format each time. You might be able to get a speed-up taking advantage of the fact that consecutive numbers normally share a long initial substring. So you could do something like this:

char bitstring[21];
for (unsigned int i = 0; i < (1<<10); ++i) {
    write_bitstring10(i, bitstring);
    for (unsigned int j = 0; j < (1<<10); ++j) {
        write_bitstring10(j, bitstring + 10);
        // do something with bitstring
    }
}

I’ve only increased from 1 loop to 2 there, but I do a little over 50% as much converting from bits to chars as before. You could experiment with the following:

• use even more loops
• split the loops unevenly, maybe 15-5 instead of 10-10
• write a function that takes a string of zeros and ones, and adds 1 to it. It’s pretty easy: find the last '0', change it to a '1', and change all the '1's after it to '0'.

To fiendishly optimize write_bitstring, multiples of 4 are good because on most architectures you can blit 4 characters at a time in a word write:

To start:

assert(CHAR_BIT == 8);
uint32_t bitstring[21 / 4]; // not char array, we need to ensure alignment
((char*)bitstring)[20] = 0; // nul terminate

Function definition:

const uint32_t little_endian_lookup = {
    ('0' << 24) | ('0' << 16) | ('0' << 8) | ('0' << 0),
    ('1' << 24) | ('0' << 16) | ('0' << 8) | ('0' << 0),
    ('1' << 24) | ('1' << 16) | ('0' << 8) | ('0' << 0),
    // etc.
};
// might need big-endian version too

#define lookup little_endian_lookup // example of configuration

void write_bitstring20(unsigned long value, uint32_t *dst) {
    dst[0] = lookup[(value & 0xF0000) >> 16];
    dst[1] = lookup[(value & 0x0F000) >> 12];
    dst[2] = lookup[(value & 0x00F00) >> 8];
    dst[3] = lookup[(value & 0x000F0) >> 4];
    dst[4] = lookup[(value & 0x0000F)];
}

I haven’t tested any of this: obviously you’re responsible for writing a benchmark that you can use to experiment.