Are memory requirements O(entities * component types)?

Reading the code, it seems to me like components share the index of their Entity, e.g. the Position Component for Entity #1,000,000 will the 1,000,000th Position Component in the Position Component Pool.

Am I understanding this correctly? If I have 1,000,000 entities, and there is one instance of the Foobar component, but it happens to be on entity 999,999, then we'll have to eat the memory of unused 999,998 unused components in the Foobar pool?

Am I reading the code correctly? If I'm wrong, can you help me understand how?

I'm mainly looking at EntityManager::assign to make this determination, specifically in the placement new:

::new(pool->get(id.index())) C(std::forward(args) ...);

where `pool` is the component pool, and `id` is the entity id.