1.Have you check the google account? Perhaps you have a backup then you can recover the contact from it.
2.You know, generally ,android phone has a backup and restore feature which is supplied by manufacturer, so you can restore contacts in this app.
3.You should have a official PC companion in your computer which help you upgrade the software and system for you phone, and this PC companion can backup your phone data automatically, thus, you can check whether it makes a backup.
4.If you install app via computer, I think you may install some android phone assistant appliciton in computer, and these applications can automatically make backup when you connect the phone to computer and lauch the application.
5.Anyway, if you do not have any backup, I am afraid that you have to ask recovery software for help, you can learn more here :Android data recovery