If you're looking for a free C/C++ compiler for Linux, there's gcc (which IS by Gnu folks.. unlike the kernel...). Non-miniature distributions usually include gcc as compiler, plus GNU make, various binary utilities such as an assembler, GNU's C library, and a linker. There's gdb, the GNU debugger, and ddd, a GUI front-end to gdb. Various text editors, such as Emacs and vim, typically have support such as syntax highlighting, parentheses matching, and allowing a separate frame with compiler output.
gcc happens to be common on many Unices, although in general if there's a vendor compiler it may be MUCH better in terms of optimizations and so forth.
I've no experience with Linux IDEs, however; am strictly a text-editor / CLI compiler guy, never having liked even IDEs for DOS and Windows. There are some available, IIRC, but I can't comment on 'em.
Incidentally, gcc came out with a recent 3.0 release. I wouldn't touch it with a 10-ft pole yet, because of all the non-trivial stuff that's been changed. Oh, and Linux, and its GNU Public License, is definitely not public domain. Mr. Stallman would probably go berserk if told it was.
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-- The thing that goes bump in the night