Several weeks ago, I reinstalled my PC. I’ve made some mistakes in saving my data on my laptop and my iPhone. I shall deauthorized the PC and make a little backup first for my downloaded and purchased apps. Yesterday, after I sync my device and iTunes, I didn’t see all my apps there, it just 30, it should be more than 50. I didn’t understand how could this happen. Google is always be the answer, and I found this: http://support.apple.com/kb/HT2519
The great iTunes System stored all our activities, including download, purchase, or updating data. So, when we lost our apps on our device, iTunes will allows us to download them again for free. We don’t need to repurchase them. This really helps. Thank you Apple!