The most robust way would be to start the program as the root user, loop through the passwd file with getpwent, switch to each of the UIDs, and try to open the file or opendir the directory. That will work with all kinds of ACLs and other oddities your version of Unix may include.
If you know your system only uses standard Unix stuff, you can just open the bottommost directory, make a hash of users who have access to it, then remove one directory component at a time with File::Basename's dirname function. Make sure all of the users in your hash have at least execute permission on that parent directory, and if not delete them from the hash. When you've checked the root filesystem, you're done, and whoever is in the hash can access that directory.
You may also have to deal with symlinks. For some help on that, see 346747.
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