Generate all combinations in bit version - c++

Question

I'd like to generate all possible combination (without repetitions) in bit representation. I can't use any library like boost or stl::next_combination - it has to be my own code (computation time is very important).
Here's my code (modified from ones StackOverflow user):
int combination = (1 << k) - 1;
int new_combination = 0;
int change = 0;
while (true)
{
// return next combination
cout << combination << endl;
// find first index to update
int indexToUpdate = k;
while (indexToUpdate > 0 && GetBitPositionByNr(combination, indexToUpdate)>= n - k + indexToUpdate)
indexToUpdate--;
if (indexToUpdate == 1) change = 1; // move all bites to the left by one position
if (indexToUpdate <= 0) break; // done
// update combination indices
new_combination = 0;
for (int combIndex = GetBitPositionByNr(combination, indexToUpdate) - 1; indexToUpdate <= k; indexToUpdate++, combIndex++)
{
if(change)
{
new_combination |= (1 << (combIndex + 1));
}
else
{
combination = combination & (~(1 << combIndex));
combination |= (1 << (combIndex + 1));
}
}
if(change) combination = new_combination;
change = 0;
}
where n - all elements, k - number of elements in combination.
GetBitPositionByNr - return position of k-th bit.
GetBitPositionByNr(13,2) = 3 cause 13 is 1101 and second bit is on third position.
It gives me correct output for n=4, k=2 which is:
0011 (3 - decimal representation - printed value)
0101 (5)
1001 (9)
0110 (6)
1010 (10)
1100 (12)
Also it gives me correct output for k=1 and k=4, but gives me wrong outpu for k=3 which is:
0111 (7)
1011 (11)
1011 (9) - wrong, should be 13
1110 (14)
I guess the problem is in inner while condition (second) but I don't know how to fix this.
Maybe some of you know better (faster) algorithm to do want I want to achieve? It can't use additional memory (arrays).
Here is code to run on ideone: IDEONE

Answer 1

When in doubt, use brute force. Alas, generate all variations with repetition, then filter out the unnecessary patterns:
unsigned bit_count(unsigned n)
{
unsigned i = 0;
while (n) {
i += n & 1;
n >>= 1;
}
return i;
}
int main()
{
std::vector<unsigned> combs;
const unsigned N = 4;
const unsigned K = 3;
for (int i = 0; i < (1 << N); i++) {
if (bit_count(i) == K) {
combs.push_back(i);
}
}
// and print 'combs' here
}
Edit: Someone else already pointed out a solution without filtering and brute force, but I'm still going to give you a few hints about this algorithm:
most compilers offer some sort of intrinsic population count function. I know of GCC and Clang which have __builtin_popcount(). Using this intrinsic function, I was able to double the speed of the code.
Since you seem to be working on GPUs, you can parallelize the code. I have done it using C++11's standard threading facilities, and I've managed to compute all 32-bit repetitions for arbitrarily-chosen popcounts 1, 16 and 19 in 7.1 seconds on my 8-core Intel machine.
Here's the final code I've written:
#include <vector>
#include <cstdio>
#include <thread>
#include <utility>
#include <future>
unsigned popcount_range(unsigned popcount, unsigned long min, unsigned long max)
{
unsigned n = 0;
for (unsigned long i = min; i < max; i++) {
n += __builtin_popcount(i) == popcount;
}
return n;
}
int main()
{
const unsigned N = 32;
const unsigned K = 16;
const unsigned N_cores = 8;
const unsigned long Max = 1ul << N;
const unsigned long N_per_core = Max / N_cores;
std::vector<std::future<unsigned>> v;
for (unsigned core = 0; core < N_cores; core++) {
unsigned long core_min = N_per_core * core;
unsigned long core_max = core_min + N_per_core;
auto fut = std::async(
std::launch::async,
popcount_range,
K,
core_min,
core_max
);
v.push_back(std::move(fut));
}
unsigned final_count = 0;
for (auto &fut : v) {
final_count += fut.get();
}
printf("%u\n", final_count);
return 0;
}