I need some Relationship Advice.?

I need some advice on my relationship. So there's this girl that likes me and I like her back and we been talkin and hangin with each other for quite awhile. She says that she's gotten over her last boyfriend and that she only likes me now, but I've seen her give him hugs and my friends have told me that she still hangs out with him. It seems to me that she still likes him and cannot get over him even tho has had made her cry many times. Is this a lost cause for me? Or should I keep pushin on?I need some Relationship Advice.?
Just keep pushin on, but keep your eyes and ears open. If you don't see improvement, she may be one of those women who likes to keep guys on a string. Not good if that's the case.