How do I kill all a user's processes using their UID

Use pkill -U UID or pkill -u UID or username instead of UID. Sometimes skill -u USERNAME may work, another tool is killall -u USERNAME.

Skill was a linux-specific and is now outdated, and pkill is more portable (Linux, Solaris, BSD).

pkill allow both numberic and symbolic UIDs, effective and real http://man7.org/linux/man-pages/man1/pkill.1.html

pkill - ... signal processes based on name and other attributes

    -u, --euid euid,...
         Only match processes whose effective user ID is listed.
         Either the numerical or symbolical value may be used.
    -U, --uid uid,...
         Only match processes whose real user ID is listed.  Either the
         numerical or symbolical value may be used.

Man page of skill says is it allowed only to use username, not user id: http://man7.org/linux/man-pages/man1/skill.1.html

skill, snice ... These tools are obsolete and unportable. The command syntax is poorly defined. Consider using the killall, pkill

  -u, --user user
         The next expression is a username.

killall is not marked as outdated in Linux, but it also will not work with numberic UID; only username: http://man7.org/linux/man-pages/man1/killall.1.html

killall - kill processes by name

   -u, --user
         Kill only processes the specified user owns.  Command names
         are optional.

I think, any utility used to find process in Linux/Solaris style /proc (procfs) will use full list of processes (doing some readdir of /proc). I think, they will iterate over /proc digital subfolders and check every found process for match.

To get list of users, use getpwent (it will get one user per call).

skill (procps & procps-ng) and killall (psmisc) tools both uses getpwnam library call to parse argument of -u option, and only username will be parsed. pkill (procps & procps-ng) uses both atol and getpwnam to parse -u/-U argument and allow both numeric and textual user specifier.

If you pass -1 as the process ID argument to either the kill shell command or the kill C function, then the signal is sent to all the processes it can reach, which in practice means all the processes of the user running the kill command or syscall.

su -c 'kill -TERM -1' bob

In C (error checking omitted):

if (fork() == 0) {
    setuid(uid);
    signal(SIGTERM, SIG_DFL);
    kill(-1, SIGTERM);
}

If the pkill function is unavailable on your UNIX / Linux distribution you could run the following command as the root user:

ps -ef | grep username | grep -v grep | awk '{print $2}' | xargs kill

where username is the user who's processes you want to delete