How can I build a search filter ([something like this](http://tvpedia.org/gen/actiune)) with WordPress?

I have a custom post type name: "Locatii". It is a custom post type with categories.

Ex: Cat 1 , Cat 2 ... and so on.

How can I implement AJAX so that when I click Cat 1 ( checkbox) and Cat 2 I should retrieve the posts that are in that categories, without having a search button.