How does this algorithm corresponds to the roulette wheel selection?

Question

I am trying to implement a roulette wheel selection. I have understood this algorithm:

1. Calculate the sum S of all chromosome fitnesses in population
2. Generate a random number, r, from interval (0,S)
3. Loop through the population and sum fitnesses from 0 till S, this is the partial sum, call it P.
4. When the P > S: stop and return the corresponding chromosome.

What I don't understand is how this corresponds to doing this instead: Roulette wheel selection algorithm (the answer with 44 votes). This makes sense to me, but not the one above.

Answer 1

The following is done using the sum

def choose_parent_using_RWS(genes, S, points):
    P = randint(0, int(S))
    for x in genes:
        P += evaluate(x, points)
        if P > S:
            return x
    return genes[-1]

the following is done by normalizing between 0 and 1

def choose_parent_using_RWS(genes, S, points):
    P = randint(0, int(S))/S
    for x in genes:
        P += evaluate(x, points)/S
        if P > S/S:
            return x
    return genes[-1]