stateindex for MDP without CartesianIndices

[dmteams]

Hello,

I am currently struggling with the function stateindex at the moment of solving a simple MDP with value iteration.

Basically, my problem is the following:
I have taxis traveling around locations to serve riders. There can be a maximum of n_cars in the network. Thus, the state is described by two vectors. One for the number of cars in each node (I have two transit and two pick-up nodes) and one for the number of riders waiting in each location (max_wait is the max number of riders waiting).

I define:

function POMDPs.states(mdp::RideHailingEnv)
    s = RideHailingState[] # initialize an array of RideHailingStates

    #loop over all our states
    for i = 0:mdp.n_cars, j = 0:mdp.n_cars, k = 0:mdp.n_cars, l = 0:mdp.n_cars, m = 0:mdp.max_wait, n = 0:mdp.max_wait

        if i+j+k+l==mdp.n_cars
            push!(s, RideHailingState([i,j,k,l],[m,n]))
        end
    end
    return s
end;

At the moment of indexing my states, I do not exactly know how to do it efficiently. Using a typical function as CartesianIndices would not work as the number of states would be way too large.

For instance, state index would create me n_cars^4*max_wait^2 possible indexes while I only need factorial(n_cars+n_locations-1)/factorial(n_locations-1)*(n_cars) indexes. Another example: if I have 5 cars, RideHailingState([3,1,2,0],[1,0]) would be indexed with CartesianIndices while actually not valid

I am not particularly an expert in programming. Therefore, I was wondering if there would exist a way to index the states efficiently for the problem I just described.

Thanks in advance for the reply!