generate random numbers of which the sum is constant

Question

I am thinking if there is anyway to generate a set of random numbers of which the sum is always a constant. For example, 20 can be divided into 5 numbers ( 1, 2,3,4,10) I don't care what each of the 5 numbers is as long as their sum is equal to 20. Is there anyway to do so programmatically?

Answer 1

To get a uniform distribution, the trick is to think of your sum as a number line, and rather than generating random numbers for the segments, generate n-1 numbers as points along the line, and subtract to get the segments. Here's the function from ojrandlib:

static int compare(const void *a, const void *b) {
    return *(int*)a - *(int*)b;
}
void ojr_array_with_sum(ojr_generator *g, int *a, int count, int sum) {
    int i;
    for (i = 0; i < count-1; ++i) { a[i] = ojr_rand(g, sum+1); }
    qsort(a, count-1, sizeof(int), compare);
    a[count-1] = sum;
    for (i = count-1; i > 0; --i) { a[i] -= a[i-1]; }
}

ojr_rand(g, limit) generates a uniform random integer from 0 to limit-1. This function then fills the array a with count random integers that add to sum. Shouldn't be too hard to adapt this to any other RNG.