Implement a nested key-value store

Design and implement a nested key–value store that supports set(path, value), get(path), and delete(path), where path is dot-delimited (e.g., "a.b.c"). Support creating intermediate nodes, overwriting existing values, and returning clear errors for missing paths. Add: (

1. an iterator to list immediate children under a prefix; (
2. a method to flatten the structure into a single-level map using dot paths; (
3. optional type checking to prevent incompatible overwrites. Provide expected time and space complexity for each operation and explain how you would serialize/deserialize the structure.