Design mkdir and ls for a Basic File System

Design an In-Memory File System

Design an in-memory file system that supports creating directories and listing their contents.

Implement the FileSystem class:

• FileSystem() Initializes the object of the system with a root directory /.
• mkdir(path: str) -> bool: Creates directory nodes along the specified absolute path. If intermediate directories in path do not exist, they should be created automatically (similar to mkdir -p). Returns True if the path was successfully created or already exists as a directory. Returns False if creation fails (for instance, if any component of path already exists as a non-directory, or if the path format is invalid).
• ls(path: str) -> list[str]: Returns a list of the names of all immediate items (directories) located directly inside path, sorted in lexicographical (alphabetical) order. If path does not exist or does not point to a directory, return an empty list [].

Path Format

• Every valid path is an absolute path that starts with /.
• Path components consist of lowercase English letters and digits (a-z, 0-9).
• Consecutive slashes (e.g., //a///b) should be normalized to single delimiters, and trailing slashes should be ignored (e.g., /a/b/ is treated as /a/b).

Examples

fs = FileSystem()

# Listing root initially
fs.ls("/")  # returns []

# Creating nested directories
fs.mkdir("/uber/rides")  # returns True
fs.mkdir("/uber/eats")   # returns True

# Listing contents of /uber
fs.ls("/uber")  # returns ["eats", "rides"]

# Listing root
fs.ls("/")  # returns ["uber"]

# Redundant slashes and trailing slashes
fs.mkdir("//uber///freight/")  # returns True
fs.ls("/uber/")  # returns ["eats", "freight", "rides"]

# Querying a non-existent path
fs.ls("/unknown")  # returns []

Constraints

• 1 <= path.length <= 500
• Directory names contain only lowercase English letters (a-z) and digits (0-9).
• At most 10^4 total calls will be made to mkdir and ls.

Edge Cases

• Querying or creating the root path /.
• Paths containing redundant slashes (e.g., /a//b).
• Querying non-existent paths with ls.