Pick a unique random subset from a set of unique values

Question

C++. Visual Studio 2010.

I have a std::vector V of N unique elements (heavy structs). How can efficiently pick M random, unique, elemen

Answer 1

Since you wanted it to be efficient, I think you can get an amortised O(M), assuming you have to perform that operation a lot of times. However, this approach is not reentrant.

First of all create a local (i.e. static) vector of std::vector<...>::size_type (i.e. unsigned will do) values.

If you enter your function, resize the vector to match N and fill it with values from the old size to N-1:

static std::vector indices;
if (indices.size() < N) {
  indices.reserve(N);
  for (unsigned i = indices.size(); i < N; i++) {
    indices.push_back(i);
  }
}

Then, randomly pick M unique numbers from that vector:

std::vector result;
result.reserver(M);
for (unsigned i = 0; i < M; i++) {
  unsigned const r = getRandomNumber(0,N-i); // random number < N-i
  result.push_back(indices[r]);
  indices[r] = indices[N-i-1];
  indices[N-i-1] = r;
}

Now, your result is sitting in the result vector.

However, you still have to repair your changes to indices for the next run, so that indices is monotonic again:

for (unsigned i = N-M; i < N; i++) {
  // restore previously changed values
  indices[indices[i]] = indices[i];
  indices[i] = i;
}

But this approach is only useful, if you have to run that algorithm a lot and N doesn't grow so big that you cannot live with indices eating up RAM all the the time.