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BM25 Search

In the last chapter we implemented TF-IDF, and in this chapter we've made the key improvements needed for BM25 search:

More stable IDF calculation
Term frequency saturation
Document length normalization

Now we're ready to put it all together to implement BM25.

BM25 Search Algorithm

The BM25 formula multiplies TF by IDF, like TF-IDF, but it uses the improved versions we've built in the last few lessons:

BM25 = bm25_tf * bm25_idf

This gives us a score for one document and one term. To calculate the full BM25 score for a query, we sum the scores for each query term:

Tokenize the query.
Calculate the BM25 score for each query token in a given document, and sum them.
Do this for every document.
Sort documents by score (highest first).
Return the top N documents.

Assignment

Add a new bm25(self, doc_id, term) method to the InvertedIndex class in lib/keyword_search.py.
1. Use your get_bm25_tf and get_bm25_idf methods to get the score components.
2. Return the full BM25 score, i.e. bm25_tf * bm25_idf.
Add a new bm25_search(self, query, limit) method to the InvertedIndex class.
1. Tokenize the query.
2. Initialize a scores dictionary to map document IDs to their total BM25 scores.
3. For each document in the index, calculate the total BM25 score:
  1. For each query token, add its BM25 score to the document's running total.
  2. Store the total score in the scores dictionary.
4. Sort the documents by score in descending order.
5. Return the top limit documents along with their scores.
Add a bm25search command to your CLI in keyword_search_cli.py. It should accept, at minimum, a query as a positional argument. You may also like to add an optional --limit argument (defaulting to 5).
```
bm25search_parser = subparsers.add_parser(
    "bm25search", help="Search movies using full BM25 scoring"
)
bm25search_parser.add_argument("query", type=str, help="Search query")
```
The command should use the InvertedIndex to load the movie data and perform the BM25 search.

Print the results in this format:

1. (15) The Adventures of Mowgli - Score: 7.79
2. (11342) Gakuen Alice - Score: 7.42
3. (30) Day of the Animals - Score: 7.21
4. (5542) Candy - Score: 7.07
5. (3395) Life of Pi - Score: 7.05

The number in parentheses is the document ID.

Run and submit the CLI tests.