That depends on the details of what your web host makes available to you and allows you to do on your own. Do they allow you to compile c programs? Do they have a policy against you compiling your own code? If they don't provide a c compiler, but don't mind what you install in your own space, you might find a precompiled copy of gcc somewhere and copy it to your account (assuming you have enough space to do so). You might even be lucky enough to find a precompiled version of Compress::ZLib somewhere and save yourself the hassle.
--DrWhy
"If God had meant for us to think for ourselves he would have given us brains. Oh, wait..."