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Went with a dynamic programming table approach.
Start by clarifying the problem (e.g., case sensitivity, empty strings, multiple substrings) and then present a dynamic programming solution with O(m*n) time and space complexity. Explain the DP recurrence and how to reconstruct the substring, and mention potential optimizations like using a rolling array to reduce space to O(min(m,n)).
Pro tip: After presenting the DP solution, briefly discuss how you would handle very large strings or streaming data, showing awareness of scalability and real-world constraints.
Ask about case sensitivity, allowed characters, empty strings, and whether multiple longest common substrings need to be returned. This ensures you understand the problem fully before coding.
Mention that a naive approach would check all substrings of one string against the other, leading to O(m^2 * n) time, which is inefficient for large inputs.
Explain the DP table where dp[i][j] represents the length of the longest common suffix of the substrings ending at i-1 and j-1. Describe the recurrence: if characters match, dp[i][j] = dp[i-1][j-1] + 1; else 0. Track the maximum length and its ending position.
State that time complexity is O(m*n) and space is O(m*n). Then suggest optimizing space to O(min(m,n)) by using a rolling array, since only the previous row is needed.
Using the tracked maximum length and ending index, extract the substring from either input string. If multiple substrings have the same length, clarify which one to return (e.g., the first encountered).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.