Shock first, then algaecide.

No.

Pouring pool shock and algaecide in at the same time is a waste of money. The chlorine in shock will just break down most algaecides before they can do their job. You’re basically canceling out the algaecide.

If you want to use both, shock the pool first. Let the chlorine levels drop back to normal (usually 24-48 hours), then add the algaecide. That way each chemical gets a chance to work.

Honestly though, if you’re keeping your chlorine at the right level, you probably don’t need algaecide at all. It’s more of a backup for when things go wrong. Most green pools just need a good shock and filtration.