Refactored "recursive algorithm for balls in numbered boxes"

balls_in_numbered_boxes_CVR.py

def balls_in_numbered_boxes(balls, box_sizes):
    if not isinstance(balls, int):
        raise TypeError("balls must be a non-negative integer.")
    if balls < 0:
        raise ValueError("balls must be a non-negative integer.")

    box_sizes = list(box_sizes)
    if not box_sizes:
        raise ValueError("box_sizes must be a non-empty iterable.")

    capacity = 0
    # capacity = sum(box_sizes)
    for size in box_sizes:
        if not isinstance(size, int):
            raise TypeError("box_sizes must contain only positive integers.")
        if size < 1:
            raise ValueError("box_sizes must contain only positive integers.")
        capacity += size

    if capacity < balls:
        raise ValueError("The total capacity of the boxes is less than the "
                            "number of balls to be distributed.")

    return _balls_in_numbered_boxes(balls, box_sizes)


def _balls_in_numbered_boxes(balls, box_sizes):
    if not balls:
        yield len(box_sizes) * (0,)
    
    elif len(box_sizes) == 1:
        if box_sizes[0] >= balls:
            yield (balls,)
    
    else:
        balls_in_first_box = min(balls, box_sizes[0])
        balls_in_other_boxes = balls - balls_in_first_box
        rest_box_sizes = box_sizes[1:]
        
        while True:
            remaining_combos = _balls_in_numbered_boxes(balls_in_other_boxes,
                                                        rest_box_sizes)
            for combo in remaining_combos:
                yield (balls_in_first_box,) + combo
            if not balls_in_first_box:
                break
            balls_in_first_box -= 1
            balls_in_other_boxes += 1