The mixture of genre influence here is complex enough to make it unique for its' time. There's some older 60's influences (I think of more "Songwriter" oriented musicians over genre, such as The Beatles), Disco vibes ("I Would Die 4 U" in particular), Funk vocal stylings (Prince pulls some James Brown stuff here, especially towards the end of "When Doves Cry"), love for guitar solos (I'm sure there's a whole list of influences there) and Glam aesthetic mixed in with a punk attitude. It's undeniably what made Prince "Prince"; He didn't limit himself strictly to one thing, but took all of his inspirations and mixed them together into a melting pot of glittery, goopy, stick-to-your-teeth sugar-pop amazingness.
Overall, it's a classic with its' own atmosphere. And everyone should at least once in their life listen to the title track on a warm Summer night while driving with the windows rolled down.