Implement a multi-level digital recipe manager

Implement a RecipeManager class for a digital recipe manager. The task is progressive (Levels 1–4). You can assume a single-process in-memory implementation. Correctness matters; efficiency is not required. Unless otherwise stated, all string comparisons for recipe names and ingredient matching are case-insensitive.

Data model

A recipe has:

• recipe_id: formatted as "recipe" + N, where N is a sequential integer starting from 1 in creation order.
• name: unique across all recipes (case-insensitive).
• ingredients: list of strings (keep original order).
• steps: list of strings (keep original order).

When returning a recipe, represent it as:

• [name, ingredients_as_string, steps_as_string]
• ingredients_as_string is the ingredients joined by "," (comma separator), and similarly for steps_as_string.

If a method returns a list of recipe IDs, they are strings like "recipe1", "recipe2", etc.

Level 1: Basic CRUD (no users)

Implement:

1. add_recipe(self, name: str, ingredients: list[str], steps: list[str]) -> str | None

• Add a new recipe and return its recipe_id.
• If a recipe with the same name already exists (case-insensitive), return None.

1. get_recipe(self, recipe_id: str) -> list[str]

• Return [name, ingredients_as_string, steps_as_string] for the recipe.
• If the recipe does not exist, return an empty array [].
• Ingredients must be returned in the same order they were added.

1. update_recipe(self, recipe_id: str, name: str, ingredients: list[str], steps: list[str]) -> bool

• Update the recipe fields.
• Return True if successful.
• Return False if the recipe does not exist, or if the new name conflicts with another existing recipe name (case-insensitive).

1. delete_recipe(self, recipe_id: str) -> bool

• Delete the recipe.
• Return True if it existed and was deleted; otherwise False.

Level 2: Searching and sorting

Implement:

1. search_recipes_by_ingredient(self, ingredient: str) -> list[str]

• Return recipe IDs for recipes that contain the specified ingredient (case-insensitive match).
• Sort results by:

1. number of ingredients ascending
2. recipe_id ascending (tie-breaker)

1. list_recipes(self, sort_by: str) -> list[str]

• Return all recipe IDs sorted by sort_by, where sort_by is either:
• "name": lexicographic ascending by recipe name; tie-breaker recipe_id ascending
• "ingredient_count": ascending by number of ingredients; tie-breaker recipe_id ascending
• If sort_by is invalid, default to sorting by "name".

Level 3: Users and edits

Introduce users.

1. add_user(self, user_id: str) -> bool

• Add a new user.
• Return True if added; False if the user already exists.

1. edit_recipe(self, user_id: str, recipe_id: str, new_name: str, new_ingredients: list[str], new_steps: list[str]) -> bool

• Any existing user may edit any recipe.
• Enforce recipe-name uniqueness (case-insensitive).
• Return True on success.
• Return False if the user does not exist, the recipe does not exist, or the new name conflicts with another recipe name.

Level 4: Version history and rollback

Add version control for recipes.

Definitions:

• Recipes created by add_recipe have no version history until the first successful edit_recipe or update_recipe.
• Every successful edit_recipe or update_recipe creates a new version entry.
• Version entries are numbered starting at 1 and increase by 1 per entry.
• Each version string format:
• <version>:<name>:<ingredients_as_string>:<steps_as_string>:<last_edited_by>
• For edit_recipe, <last_edited_by> is the user_id.
• For update_recipe, <last_edited_by> is the literal string "system".

Implement:

1. version_recipe(self, recipe_id: str) -> list[str]

• Return all versions for the recipe, sorted by version number ascending.
• Return [] if the recipe does not exist or if it was never edited/updated (i.e., no version history).

1. rollback_recipe(self, recipe_id: str, version: int) -> bool

• Roll back the current recipe state (name/ingredients/steps) to match the specified historical version.
• Rolling back creates a new version entry appended to the history (history is immutable), with editor set to the literal string "rollback".
• Return True if successful.
• Return False if the recipe does not exist, the requested version does not exist, or if rolling back would cause a name conflict with another existing recipe (case-insensitive).