I’m working on a problem involving string matching where I need to compute the similarity scores for each prefix of a string C against another string S. The similarity score for a prefix P of C and S is defined as the product of two metrics:

1. Hit Count (H): The number of occurrences of P in S.

2. Plagiarism Likelihood (L): The number of times a substring is both a prefix and a suffix of P.

Given the constraints that both C and S can be up to 5*10^6 characters long, I am looking for an efficient way to perform these calculations, and time limit is 3 sec (ideally aiming for a time complexity of O(|S| + |C|)).

I initially considered using the KMP (Knuth-Morris-Pratt) algorithm for counting the occurrences of each prefix in S, but I am unsure how to efficiently compute L for each prefix without excessive recomputation.

Specific Questions:
1. Is there an efficient algorithm or a combination of algorithms that can help achieve this complexity for both computing H and L?
2. How can dynamic programming be applied to compute the L values efficiently for each prefix?

Any insights or suggestions on how to tackle this problem would be greatly appreciated!