Problem Description

You are tasked with implementing two core functions related to text similarity and then optimizing their usage for ranking.

Function 1: jaccard_similarity(s1, s2)

Implement a function jaccard_similarity that takes two strings, s1 and s2, as input. This function should:

• Tokenize each string by splitting on any non-alphanumeric character.
• Convert all tokens to lowercase.
• Treat the resulting tokens for each string as a set, ignoring duplicate tokens.
• Calculate the Jaccard Similarity, defined as |A ∩ B| / |A ∪ B|, where A and B are the sets of tokens from s1 and s2 respectively.
• Return 0.0 if the union of the token sets is empty.

Function 2: rank_by_jaccard(reviews, target)

Implement a function rank_by_jaccard that takes a list of reviews (strings) and a target string as input. This function should:

• Calculate the Jaccard Similarity between the target string and each review in the reviews list using the jaccard_similarity function.
• Return the reviews list sorted in descending order based on their similarity to the target string.
• Maintain stability on ties, meaning if two reviews have the same similarity score, their original relative order in the input reviews list should be preserved.

Discussion and Optimization

Beyond the core implementation, discuss the following considerations and optimizations:

• Long Inputs: How would you handle very long input strings or large lists of reviews, potentially using streaming or iterators, to avoid excessive memory usage?
• Unicode and Punctuation: Address edge cases related to Unicode characters and various punctuation marks during tokenization.
• Time Complexity: Explain how to achieve an expected time complexity of O(T) for the rank_by_jaccard function, where T is the total number of tokens across all reviews and the target string.
• Top-K Optimization: Extend the rank_by_jaccard function to efficiently return only the top-k most similar reviews, where k is significantly smaller than n (the total number of reviews). Justify your choice of data structures and analyze the complexity of this optimized approach.