# Merge and Serialize N-ary Trees You are asked to merge two N-ary trees and then serialize the result, but no merge key, value-conflict rule, child-order rule, or wire format has been specified. Explain the questions you must resolve. Then choose one coherent contract, outline an implementation, and design a deterministic serialization and parser for that contract. ### Constraints & Assumptions - Input trees are finite and acyclic. - Node values alone may not be unique. - Children may be ordered or unordered depending on the chosen contract. - The serialized representation must distinguish structure unambiguously. - Inputs must not be mutated unless explicitly agreed. ### Clarifying Questions to Ask - Do nodes merge by stable ID, path position, or value? - What happens when matching nodes have different payloads? - Are duplicate children valid, and is child order meaningful? - Must serialization support arbitrary text, schema evolution, and malformed-input detection? ### Part 1 - Define merge semantics State node identity, value-conflict, child-order, duplicate, and ownership rules. #### What This Part Should Cover - Why several reasonable contracts yield different trees - Stable keys or a positional alternative - Deterministic conflict resolution - Deep-copy versus structural sharing ### Part 2 - Merge under the chosen contract Give an algorithm, correctness argument, complexity, and behavior for malformed inputs. #### What This Part Should Cover - Matching and unmatched children - Duplicate-key validation - Iterative handling of deep trees - Input immutability ### Part 3 - Serialize and parse Specify a versioned, length-safe format with a canonical child order and validation rules. #### What This Part Should Cover - Unambiguous boundaries - Round-trip and canonicalization guarantees - Resource limits and invalid data - Schema evolution ```hint Contract precedes code Two implementations cannot be compared until node identity, conflict handling, and child order define one expected merged tree. ``` ### What a Strong Answer Covers - Recognition that the source prompt lacks a canonical executable result - One explicit, internally consistent merge contract - A correct algorithm with ownership and complexity analysis - Deterministic, validated round-trip serialization ### Follow-up Questions 1. How would the algorithm change if child order were semantically meaningful? 2. Can structural sharing be safe when callers may mutate nodes? 3. How would you stream a tree too large to hold in memory?