Design an In-Memory Unix File System and Implement Basic Commands

Problem: Design an In-Memory Unix File System and Implement Basic Commands Design and implement a simplified Unix-like file system that lives entirely in memory. The file system stores directories and files in a tree structure and supports the commands below. Data Model There are two node types: directory and file. Every node has: name (string) parent (reference to parent directory; root’s parent is null) A directory node also contains a collection/map of children indexed by name. A file node only needs existence (no content/permissions/timestamps required). The root directory is /. Path Rules Input paths are Unix style: /a/b/c. Assume no empty segments (e.g., //) and no invalid characters. Part 1 Commands 1) touch <path> Create a file at the given path. If the parent directory does not exist: return an error. If the target already exists: If it is a file: treat as success (no-op). If it is a directory: return an error. 2) mkdir <path> Create a directory at the given path. If the parent directory does not exist: return an error. If the target already exists: If it is a directory: treat as success (no-op). If it is a file: return an error. 3) ls <path> List the contents of the given path. If path is a directory: return the names of its direct children. If path is a file: return a list containing only that file name. If the path does not exist: return an error. Output requirement: Return names sorted in lexicographic ascending order (if unspecified, state this assumption). Part 2 Commands 4) rm <path> Remove a file. Only files can be removed; if path points to a directory: return an error. If the file does not exist: return an error. 5) rmdir <path> Remove a directory. Only directories can be removed. The directory must be empty (no children) or return an error. If the directory does not exist: return an error. You must not remove the root directory /. Interface Suggestion class FileSystem: touch(path) -> void/Result mkdir(path) -> void/Result ls(path) -> List[str]/Result rm(path) -> void/Result rmdir(path) -> void/Result Error Handling You may throw exceptions, return error codes, or return (success, message). Errors should distinguish: path not found, type mismatch, directory not empty, etc. Example (for semantics) mkdir /a success touch /a/f success ls /a returns ["f"] rm /a/f success rmdir /a success Example Input mkdir /a ls / Output [a]