Stable Marrage algorithm

I am developing an app which holds students names in a list and their group number each student can transfer to another group so there is another field carries there wishes

I want the program to carry matching group number with students wishes and getting the best result with 0 conflict and doing the update to SQLite database

someone has told me to use the stable marrage algorithm it would be perfect to this type of programs

the problem is that i don't know much about this last one and how it would be looks like in android so if you can offer me a simple explanation and an example which have SQLite , java code it would be perfect