Design a food rating system that can do the following:

• Modify the rating of a food item listed in the system.
• Return the highest-rated food item for a type of cuisine in the system.

Implement the FoodRatings class:

• FoodRatings(String[] foods, String[] cuisines, int[] ratings) Initializes the system. The food items are described by foods, cuisines and ratings, all of which have a length of n.
  • foods[i] is the name of the ith food,
  • cuisines[i] is the type of cuisine of the ith food, and
  • ratings[i] is the initial rating of the ith food.
• void changeRating(String food, int newRating) Changes the rating of the food item with the name food.
• String highestRated(String cuisine) Returns the name of the food item that has the highest rating for the given type of cuisine. If there is a tie, return the item with the lexicographically smaller name.

Note that a string x is lexicographically smaller than string y if x comes before y in dictionary order, that is, either x is a prefix of y, or if i is the first position such that x[i] != y[i], then x[i] comes before y[i] in alphabetic order.

 

Example 1:

Input
["FoodRatings", "highestRated", "highestRated", "changeRating", "highestRated", "changeRating", "highestRated"]
[[["kimchi", "miso", "sushi", "moussaka", "ramen", "bulgogi"], ["korean", "japanese", "japanese", "greek", "japanese", "korean"], [9, 12, 8, 15, 14, 7]], ["korean"], ["japanese"], ["sushi", 16], ["japanese"], ["ramen", 16], ["japanese"]]
Output
[null, "kimchi", "ramen", null, "sushi", null, "ramen"]

Explanation
FoodRatings foodRatings = new FoodRatings(["kimchi", "miso", "sushi", "moussaka", "ramen", "bulgogi"], ["korean", "japanese", "japanese", "greek", "japanese", "korean"], [9, 12, 8, 15, 14, 7]);
foodRatings.highestRated("korean"); // return "kimchi"
                                    // "kimchi" is the highest rated korean food with a rating of 9.
foodRatings.highestRated("japanese"); // return "ramen"
                                      // "ramen" is the highest rated japanese food with a rating of 14.
foodRatings.changeRating("sushi", 16); // "sushi" now has a rating of 16.
foodRatings.highestRated("japanese"); // return "sushi"
                                      // "sushi" is the highest rated japanese food with a rating of 16.
foodRatings.changeRating("ramen", 16); // "ramen" now has a rating of 16.
foodRatings.highestRated("japanese"); // return "ramen"
                                      // Both "sushi" and "ramen" have a rating of 16.
                                      // However, "ramen" is lexicographically smaller than "sushi".

 

Constraints:

• 1 <= n <= 2 * 104
• n == foods.length == cuisines.length == ratings.length
• 1 <= foods[i].length, cuisines[i].length <= 10
• foods[i], cuisines[i] consist of lowercase English letters.
• 1 <= ratings[i] <= 108
• All the strings in foods are distinct.
• food will be the name of a food item in the system across all calls to changeRating.
• cuisine will be a type of cuisine of at least one food item in the system across all calls to highestRated.
• At most 2 * 104 calls in total will be made to changeRating and highestRated.