Add the child item IDs for one item object and their children.

def _get_id2children(id2children, item_id, item_obj):
    """Add the child item IDs for one item object and their children."""
    if item_id in id2children:
        return id2children[item_id]
    child_ids = set()
    for child_obj in item_obj.children:
        child_id = child_obj.item_id
        child_ids.add(child_id)
        child_ids |= _get_id2children(id2children, child_id, child_obj)
    id2children[item_id] = child_ids
    return child_ids