Ask HN: Projects which build up chops in algorithms / data structures

I have been trying to brush up my knowledge on algorithms and data structures, which is a bit lacking. I have always found it easier to work on projects along with reading from books. While I understand that reading from books is necessary in this case (I am using Adam Drozdek's book on algorithms), I feel the progress would be better if I had a project where I could apply the newly learned algorithms and data structures as I went.

I have thought some about this and the two ideas I have so far are writing a game and writing a media player. Please let me know if someone has good ideas on this sort of a project.

My languages of choice are java and python but please feel free to let me know of projects in other areas as well.

Thank you