Compute Total Size of a File System (Tree/Graph)

Given a file system hierarchy, compute the total size starting from a given root directory. Each node is either a directory or a file: A file has a non-negative integer size. A directory has a list of child nodes. During the interview it was clarified as a strict tree: every node has at most one parent, the structure reachable from the root is acyclic. Implement a function that returns the total size of the root directory: the sum of sizes of all reachable files. Input (typical abstraction) root: a reference/ID of the root directory node. You can access children for directories and size for files. Output An integer representing the total size. Follow-ups Analyze time and space complexity. If repeated subtrees can be visited multiple times (e.g., due to shared references / hard-link-like semantics, though the final assumption is a tree), how would you use caching (memoization) to avoid recomputation? Constraints Number of nodes N can be up to 1e5. Example root dir contains file(10) and dirA; dirA contains file(5) and file(7) Output: 22 Example Input root: dir -> [file(10), dirA]; dirA -> [file(5), file(7)] Output 22