Find All Possible Recipes From Given Supplies
You have information about n
different recipes. You are given a string array recipes
and a 2D string array ingredients
. The ith
recipe has the name recipes[i]
, and you can create it if you have all the needed ingredients from ingredients[i]
. Ingredients to a recipe may need to be created from other recipes, i.e., ingredients[i]
may contain a string that is in recipes
.
You are also given a string array supplies
containing all the ingredients that you initially have, and you have an infinite supply of all of them.
Return a list of all the recipes that you can create. You may return the answer in any order.
Note that two recipes may contain each other in their ingredients.
Example 1:
Input: recipes = ["bread"], ingredients = [["yeast","flour"]], supplies = ["yeast","flour","corn"]
Output: ["bread"]
Explanation:
We can create "bread" since we have the ingredients "yeast" and "flour".
Example 2:
Input: recipes = ["bread","sandwich"], ingredients = [["yeast","flour"],["bread","meat"]], supplies = ["yeast","flour","meat"]
Output: ["bread","sandwich"]
Explanation:
We can create "bread" since we have the ingredients "yeast" and "flour".
We can create "sandwich" since we have the ingredient "meat" and can create the ingredient "bread".
Example 3:
Input: recipes = ["bread","sandwich","burger"], ingredients = [["yeast","flour"],["bread","meat"],["sandwich","meat","bread"]], supplies = ["yeast","flour","meat"]
Output: ["bread","sandwich","burger"]
Explanation:
We can create "bread" since we have the ingredients "yeast" and "flour".
We can create "sandwich" since we have the ingredient "meat" and can create the ingredient "bread".
We can create "burger" since we have the ingredient "meat" and can create the ingredients "bread" and "sandwich".
Constraints:
n == recipes.length == ingredients.length
1 <= n <= 100
1 <= ingredients[i].length, supplies.length <= 100
1 <= recipes[i].length, ingredients[i][j].length, supplies[k].length <= 10
recipes[i], ingredients[i][j]
, andsupplies[k]
consist only of lowercase English letters.- All the values of
recipes
andsupplies
Ā combined are unique. - Each
ingredients[i]
does not contain any duplicate values.
Solution
This is another topological sort problem. Even though we are not asked for an ordering, we need to use the ordering to find out which recipes can be created.
We set up a graph where edges are directed from ingredient
to recipe
representing that a recipe
contains ingredient
.
First, we know that all the supplies
are unlimited so they don't depend on any ingredient nor vice versa, we can start finding the topological order from the ingredients in supplies
.
Then as we remove the in-edges
to a recipe
, we eventually find recipes that are available (with 0 in-degree).
Finally, we iterate through the available
queue to find all recipes that can be created.
Implementation
def findAllRecipes(self, recipes: List[str], ingredients: List[List[str]], supplies: List[str]) -> List[str]:
graph = defaultdict(list)
in_degree = dict() # ingredient count for recipe
for i in range(len(recipes)):
for ingredient in ingredients[i]:
graph[ingredient].append(recipes[i])
in_degree[recipes[i]] = len(ingredients[i])
# Topological sort.
available, output = deque(supplies), []
while available:
ing = available.popleft()
for rcp in graph[ing]:
in_degree[rcp] -= 1
if in_degree[rcp] == 0:
available.append(rcp)
output.append(rcp)
return output
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