Question

You’re given an array of size n, containing arbitrary boolean values.

What is the fastest way to return the index of a random TRUE value.

The algorithm should randomly return any one of the indices containing a TRUE.

Answer 1

Something like this:

int count = 0;
int index = -1;
for (int i = 0; i != n; ++i)
{
    if (values[i])
    {
        ++count;
        if (unit_random <= 1.0f / count)
        {
            index = i;
        }
    }
}

So for 4 values for example you get the following probabilities for their indices:

1: (1 / 1) * (1 / 2) * (2 / 3) * (3 / 4) = 1 / 4 
2: (1 / 2) * (2 / 3) * (3 / 4) = 1 / 4
3: (1 / 3) * (3 / 4) = 1 / 4
4: 1 / 4 = 1 / 4

EDIT: As Steve Jessop pointed out the floating point comparision will eventually lead to a very non uniform selection. Assuming unit_random is defined as rand() / RAND_MAX the comparision can be changed to:

typedef unsigned long long u64;
u64 product = u64(count) * rand();
if (product <= u64(RAND_MAX))

This won’t give perfect distribution due to the discrete nature of rand but it will be better.