Find the Length of the Longest Common Prefix

lcpy gen -n 3043   # by problem number
lcpy gen -s find_the_length_of_the_longest_common_prefix   # by problem name

Input: arr1 = [1,10,100], arr2 = [1000]
Output: 3
Explanation: There are 3 pairs (arr1[i], arr2[j]):
- The longest common prefix of (1, 1000) is 1.
- The longest common prefix of (10, 1000) is 10.
- The longest common prefix of (100, 1000) is 100.
The longest common prefix is 100 with a length of 3.

Input: arr1 = [1,2,3], arr2 = [4,4,4]
Output: 0
Explanation: There exists no common prefix for any pair (arr1[i], arr2[j]), hence we return 0.
Note that common prefixes between elements of the same array do not count.

class Solution:
    # Time: O((n + m) * d) where d is the max digit count
    # Space: O(n * d)
    def longest_common_prefix(self, arr1: list[int], arr2: list[int]) -> int:
        prefixes: set[str] = set()
        for x in arr1:
            s = str(x)
            for i in range(1, len(s) + 1):
                prefixes.add(s[:i])

        best = 0
        for y in arr2:
            s = str(y)
            for i in range(best + 1, len(s) + 1):
                if s[:i] in prefixes:
                    best = i
        return best