Any way to speedup itertool.product

Question

I am using itertools.product to find the possible weights an asset can take given that the sum of all weights adds up to 100.

min_wt = 10
max_wt = 50
step = 10
nb_Assets = 5

weight_mat = []
for i in itertools.product(range(min_wt, (max_wt+1), step), repeat = nb_Assets):
    if sum(i) == 100:
        weight = [i]
        if np.shape(weight_mat)[0] == 0:
            weight_mat = weight
        else:
            weight_mat = np.concatenate((weight_mat, weight), axis = 0)

The above code works, but it is too slow as it goes through the combinations that are not acceptable, example [50,50,50,50,50] eventually testing 3125 combinations instead of 121 possible combinations. Is there any way we can add the 'sum' condition within the loop to speed things up?

Answer 1

Many improvements are possible.

For starters, the search space can be reduced using itertools.combinations_with_replacement() because summation is commutative.

Also, the last addend should be computed rather than tested. For example if t[:4] was (10, 20, 30, 35), you could compute t[4] as 1 - sum(t), giving a value of 5. This will give a 100-fold speed-up over trying one-hundred values of x in (10, 20, 30, 35, x).