# Implement an In-Memory File System The source reports an in-memory file-system exercise but not its exact error serialization or current-directory removal policy. The error codes, driver, and busy-directory rule below are deterministic practice assumptions. Implement: ```python class FileSystemError(Exception): code: str class FileSystem: def ls(self, path: str = ".") -> list[str]: ... def cd(self, path: str) -> None: ... def add(self, path: str, is_directory: bool) -> None: ... def remove(self, path: str, recursive: bool = False) -> None: ... def run_file_system(operations: list[list[object]]) -> list[object]: ... ``` The file system starts with an empty root `/` and current working directory `/`. Directories contain named children; files contain no data. ## Paths and Successful Results - Support absolute and relative paths, repeated `/`, `.`, `..`, and trailing separators. Traversal above root stays at root. An empty path string is invalid. - `ls(path)` returns sorted child names for a directory and `[basename]` for a file. - `cd(path)` changes the working directory only when the resolved target is a directory and returns `None`. - `add(path, is_directory)` creates exactly one file or directory. The resolved parent must already be a directory, and the target must not exist. Success returns `None`. - `remove(path, recursive=False)` removes a file or empty directory. A nonempty directory requires `recursive=True`. Success returns `None`. Resolve the complete path before mutating anything. A file may be the final target of `ls` or `remove`, but no operation may traverse through a file. ## Deterministic Errors Class methods raise `FileSystemError` with exactly one of these codes: - `"invalid_path"`: the path is not a nonempty string. - `"not_found"`: a required component or target is absent. - `"not_directory"`: traversal would continue through a file, or `cd` targets a file. - `"already_exists"`: `add` resolves to an existing node. - `"root"`: `remove` targets `/`. - `"busy"`: `remove` targets the current working directory or any of its ancestors, even with `recursive=True`. - `"directory_not_empty"`: a non-busy, non-root directory has children and `recursive=False`. For `remove`, resolve first, then apply error precedence `root`, `busy`, and `directory_not_empty`. Resolution errors occur before those checks. Every failed class operation is atomic: the tree and current working directory remain unchanged. The driver uses these commands: - `["LS"]` or `["LS", path]` - `["CD", path]` - `["ADD", path, is_directory]` - `["REMOVE", path]` or `["REMOVE", path, recursive]` It returns one result per operation. On a successful command, append the method's result. On `FileSystemError`, append `["ERROR", code]` and continue. A malformed command, unknown command, or non-Boolean flag appends `["ERROR", "invalid_operation"]` without calling a class method. ## Performance and Tests Aim for time proportional to normalized path components plus returned output, except that recursive deletion is proportional to the removed subtree. Test above-root traversal, repeated separators, traversal through files, duplicate adds, failed `cd`, removing root, removing the current directory and each ancestor, recursive removal of an unrelated subtree, failure atomicity, and error precedence.