find best match between two sets of sub strings in python

There are several algorithms and techniques that can be used to find the best match between two sets of sub strings in Python, depending on the specific requirements of the problem. One of the most common and efficient methods is dynamic programming, which can be used to calculate the longest common subsequence (LCS) between two strings.

To implement this algorithm in Python, you can use the built-in lru_cache function to store the results of previously calculated function calls and avoid redundant computations:

main.py
from functools import lru_cache

@lru_cache(maxsize=None)
def lcs(s1, s2):
    if len(s1) == 0 or len(s2) == 0:
        return ''
    elif s1[0] == s2[0]:
        return s1[0] + lcs(s1[1:], s2[1:])
    else:
        result1 = lcs(s1[1:], s2)
        result2 = lcs(s1, s2[1:])
        if len(result1) > len(result2):
            return result1
        else:
            return result2
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This function takes two input strings s1 and s2 and returns their LCS as a string. It uses memoization to avoid repeating the same calculations for overlapping subproblems, which significantly improves the running time for longer strings.

To apply this algorithm to two sets of sub strings, you can first generate all possible pairs of substrings from each set, and then compute the LCS for each pair using the lcs function. Finally, you can select the pair with the maximum LCS length as the best match:

main.py
def find_best_match(set1, set2):
    best_pair = None
    best_length = -1
    for s1 in set1:
        for s2 in set2:
            l = len(lcs(s1, s2))
            if l > best_length:
                best_pair = (s1, s2)
                best_length = l
    return best_pair
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This function takes two lists of strings set1 and set2 as input and returns the pair of substrings (one from each set) with the maximum LCS length as a tuple. If no match is found, it returns None. Note that this implementation has a worst-case running time of O(N^3), where N is the total number of substrings in both sets, due to the nested loop over all possible pairs of substrings. However, for practical purposes, it performs very well on small to medium-sized inputs.