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`. 2) `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. 3) `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). 4) `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: 5) `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) 6) `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. 7) `add_user(self, user_id: str) -> bool` - Add a new user. - Return `True` if added; `False` if the user already exists. 8) `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: 9) `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). 10) `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).