Encode an N-ary tree as a string and decode it back to the identical tree

A rooted N-ary tree is a tree in which each node can have any number of children, kept in a fixed order. Design a string format for such trees and implement both directions: - `serialize(root)` turns a tree into a string. - `deserialize(data)` rebuilds the tree from that string. Deserializing the output of `serialize` must reproduce the original tree exactly: the same values, the same shape and the same order of children under every node. The format is yours to choose, but `deserialize` must work from the string alone, with no state kept between calls. ```python class Node: def __init__(self, val, children=None): self.val = val self.children = children if children is not None else [] def serialize(root: Node | None) -> str: ... def deserialize(data: str) -> Node | None: ... ``` ```hint Where do the children stop? In a binary tree every node has exactly two child slots, so writing a marker for each empty slot is enough to recover the shape. Here the number of children varies. Decide what the decoder must learn from the string to know where one node's children end. ``` ```hint Decode in one left-to-right pass Choose a node order and a token layout that let the decoder consume tokens strictly from left to right, building nodes as it goes, without backtracking. ``` ### Constraints and Clarifications - Assume node values are integers, possibly negative, unless the interviewer says otherwise. - The tree may be empty (`root` is `None`) or consist of a single node. - Child order matters: two trees that differ only in the order of some node's children are different trees. ### Clarifying Questions - Are values always integers, or can they be arbitrary strings that may contain the characters your format uses as delimiters? - How many nodes, how many children per node, and how deep can the tree be? - Does the size of the string matter, for example because it is stored or sent over a network, or should it stay human-readable? - Should `deserialize` detect malformed input, or may it assume the string came from `serialize`? ### What a Strong Answer Covers - A format that makes each node's number of children, or the end of its child list, unambiguous - Correct encoding and decoding, including the empty tree, a single node, and leaves at different depths - Linear time and space in the number of nodes, without quadratic string building - Correct handling of multi-digit and negative values, and a plan for values that contain delimiter characters - Behavior on very deep trees and on truncated or malformed strings ### Follow-up Questions - Values become arbitrary strings that may contain spaces, commas and brackets. How does your format change? - How would you make the encoded form as compact as possible? - How would you decode a tree whose depth is one million without exceeding the recursion limit? - How would you detect a truncated or corrupted string instead of returning a wrong tree?