Solution Explanation

This problem requires designing an in-memory file system. The solution uses a Trie data structure to efficiently store and retrieve file and directory information. A Trie is a tree-like data structure where each node represents a part of a path (e.g., directory or file name). This allows for quick lookups and insertions based on paths.

Data Structure (Trie):

Each Trie node contains:

• name: The name of the file (only for file nodes).
• isFile: A boolean indicating whether the node represents a file or a directory.
• content: A string builder (or equivalent) to store the file content (only for file nodes).
• children: A map (dictionary) to store child nodes (subdirectories or files within this directory).

Methods:

• FileSystem(): Initializes the file system with an empty root Trie node.

• ls(path):

  1. Searches for the given path in the Trie. If the path doesn't exist, it returns an empty list.
  2. If the path points to a file, it returns a list containing only the file's name.
  3. If the path points to a directory, it returns a lexicographically sorted list of all file and directory names within that directory (obtained from the children map of the directory node).

• mkdir(path):

  1. Inserts the given path into the Trie as a directory (isFile = False). If intermediate directories along the path don't exist, they are also created.

• addContentToFile(filePath, content):

  1. Inserts the filePath into the Trie as a file (isFile = True). If the file already exists, the new content is appended to its existing content.

• readContentFromFile(filePath):

  1. Searches for the given filePath in the Trie. It returns the content of the file if found.

Time Complexity Analysis:

• ls(path): O(P log P), where P is the length of the path. The search operation in the Trie takes O(P) time. Sorting the directory contents takes O(P log P) time in the worst case (where P is the number of files/directories in the directory).

• mkdir(path): O(P), where P is the length of the path. The Trie insertion operation takes O(P) time in the worst case.

• addContentToFile(filePath, content): O(F), where F is the length of the filePath. Trie insertion and appending content takes O(F) time.

• readContentFromFile(filePath): O(F), where F is the length of the filePath. Trie search operation takes O(F) time.

Space Complexity Analysis:

The space complexity is O(N), where N is the total number of files and directories in the file system. This is because the Trie structure stores all the file and directory information.

Example Code (Python):

The Python code provided above implements the FileSystem class using a Trie data structure as described. The Java and Go code offer equivalent implementations in their respective languages. All implementations follow the same Trie-based approach to handle file system operations efficiently.