Recommendation System Optimization

You are required to implement a recommendation system that analyzes user review sentiments and real‐time trend data to produce a list of recommended items. The system will adjust the popularity of items based on provided trend scores and then rank the items by a computed score – the product of the (adjusted) popularity and the overall sentiment score, with a secondary sort by rating. The final recommendation list must include at most 10 items and contain recommendations from at least three different genres. All formulas used in the computations should be written in LaTeX format. For example, the computed score for an item is given by:

$$score = (popularity + trend\_score) \times sentiment\_score $$

Implement the class methods to satisfy these requirements.

inputFormat

The input is provided as a single JSON object via standard input. It contains the following fields:

1. "user_reviews": an array of objects. Each object has a key "sentiment" with an integer value.
2. "possible_recommendations": an array of objects. Each object has the following keys:
   • "id" (integer)
   • "title" (string)
   • "genre" (string)
   • "popularity" (integer)
   • "rating" (float)
3. "trend_data": an array of objects. Each object has:
   • "id" (integer)
   • "trend_score" (integer)

You can assume that the input JSON is correctly formatted.

outputFormat

Output a JSON array to standard output. Each element of the array should be an object representing a recommended item with the following keys:

• "id"
• "title"
• "genre"
• "popularity" (after applying trend adjustments)
• "rating"

The final list must contain at most 10 items and include recommendations that cover at least three different genres.## sample

{"user_reviews": [{"sentiment": 1}, {"sentiment": -1}, {"sentiment": 1}, {"sentiment": 1}, {"sentiment": 0}],
 "possible_recommendations": [
   {"id": 1, "title": "Movie1", "genre": "Action", "popularity": 5, "rating": 4.5},
   {"id": 2, "title": "Movie2", "genre": "Drama", "popularity": 3, "rating": 4.8},
   {"id": 3, "title": "Movie3", "genre": "Romance", "popularity": 6, "rating": 4.2}
 ],
 "trend_data": [
   {"id": 1, "trend_score": 2},
   {"id": 2, "trend_score": 3},
   {"id": 3, "trend_score": -1}
 ]}

[{"id":1,"title":"Movie1","genre":"Action","popularity":7,"rating":4.5}, {"id":2,"title":"Movie2","genre":"Drama","popularity":6,"rating":4.8}, {"id":3,"title":"Movie3","genre":"Romance","popularity":5,"rating":4.2}]