What happens when you download an app that was free for a limited time?

I downloaded a bunch of apps that were free for a "limited" time, but not anymore.

Now I have to restore my iphone.

Will the apps be registered to my Apple ID as purchased, or will they charge me if I try to download it again?

I don't want to mistakenly purchase an app.

Yeah I know your problem. When you downloaded an app that was free for a limited time. The next time when you want to download again. You will found the app in itunes show "install" but not "purchase".Last time I downloaded the Fruit Ninjia free for a limited time. Now even is not free, I can download for free. Hope it can help you.

_I would like to TravleChina.HK