In a Unix$-$like operating system, file permissions are often represented using octal numbers. For example, the octal number

$0755$

$0755$ represents read, write, and execute permissions for the owner and read and execute permissions for the group and others $($

$-$rwxr$-$xr$-$x

$-$rwxr$-$xr$-$x in symbolic notation$).$

Imagine you are a system administrator tasked with auditing a large number of files and directories on a server. Each file and directory has its permissions encoded as a three$-$digit octal number $($ranging from

$000$

$000$ to

$777$

$777).$

Your task is to devise an algorithm to sort these octal permission numbers in linear time. The sorted list will help you quickly identify files with specific permission sets for further auditing and management.

Question $3\mathrm{.}1$

Q$3\mathrm{.}13$ Points

Grading comment:

Explain why a linear$-$time sorting algorithm is possible for this specific scenario.