gistfile1.py

from math import floor, ceil

def distribute(z, *args):
    """
    returns distribution of z over args with natural numbers
    and each arg >= 1
    :param z: z >= len(args)
    :param args: len(args) >= 2
    :return: distribution of z overs args ratio
    """
    original_z = z  # for ratio comparsion

    n_sum = sum(*args)
    sorted_args = sorted(*args)
    solution = []

    for i, arg in enumerate(sorted_args):
        solution.append(floor(original_z * (arg / n_sum)))
        z -= solution[i]

    print(solution)

    z_2 = z # for second ratio comparison
    for i, arg in enumerate(solution):
        if arg == 0:
            solution[i] += 1
            z -= 1
        solution[i] += floor(z_2 * (sorted_args[i]) / n_sum)
        z -= floor(z_2 * (sorted_args[i]) / n_sum)

    solution[-1] += z
    return solution
  

if __name__ == '__main__':
    print(distribute(10000, [1, 2, 3, 4, 6, 10])) # prints [86, 172, 258, 344, 517, 8623]