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Given two lists of strings, A and B, count how many pairs (a, b) can be formed such that a is a prefix of b and a is in list A, and b is in list B.

• A and B are lists of non-empty strings consisting of only lowercase English letters.
• We need to count pairs where strings from A are prefixes of strings from B.

Clarifying Questions

1. What is the expected length of lists A and B?
   • This helps determine if the brute-force solution will be efficient enough.
2. Are there any constraints on the length of individual strings within the lists?
   • Understanding the length constraints helps in determining an efficient approach.
3. Are there any repetitive strings within the lists A and B?
   • Clarifying this can help optimize the solution if necessary.
4. Do we need to consider case sensitivity?
   • Ensuring that all comparisons are done in a consistent manner.

Strategy

1. Brute-Force Approach:
   • Iterate over each string a in list A and each string b in list B.
   • Check if a is a prefix of b.
   • Increment the count if a is a prefix of b.
2. Optimized Approach:
   • Since this problem primarily involves prefix checking, we can pre-sort lists to potentially reduce unnecessary comparisons.
   • However, in this problem, each string needs to be checked individually, making sorting and dictionary approaches relatively complex for minor gains in efficiency.

Code

Here’s the implementation of the brute-force method to solve the problem:

def count_prefix_suffix_pairs(A, B):
    count = 0
    for a in A:
        for b in B:
            if b.startswith(a):
                count += 1
    return count

# Example usage
A = ["a", "b", "ab"]
B = ["ab", "bc", "abc"]
print(count_prefix_suffix_pairs(A, B))  # Output should be 4

Time Complexity

• Time Complexity: (O(n \times m \times l))
  • (n) is the length of list A
  • (m) is the length of list B
  • (l) is the average length of strings in B (for prefix checking)
• Space Complexity: (O(1))
  • We are using a constant amount of extra space.

This brute-force solution should be efficient enough for moderate-sized lists. If the input lists are extremely large, further optimizations would be warranted.

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