Classic DP problem and I still fumbled the base case initialization for like two minutes.
Start by clarifying the problem and edge cases, then propose a dynamic programming solution using a 2D table where dp[i][j] represents the edit distance between the first i characters of string1 and first j characters of string2. Explain the recurrence relation and discuss time and space complexity, mentioning possible optimizations like using two rows instead of the full matrix.
Pro tip: Demonstrate awareness of space optimization by mentioning that you can reduce space complexity from O(mn) to O(min(m,n)) using two rows, and discuss how this might be implemented in a real interview setting. Also, briefly mention that if the strings are very large, you might consider approximate algorithms or using a threshold for early termination.
Ask about input constraints (string lengths, character set), whether case sensitivity matters, and if there are any memory or time limits. Discuss edge cases like empty strings, identical strings, and very long strings.
Define dp[i][j] as the edit distance between the first i characters of word1 and first j characters of word2. Explain the recurrence: if characters match, dp[i][j] = dp[i-1][j-1]; else dp[i][j] = 1 + min(dp[i-1][j], dp[i][j-1], dp[i-1][j-1]).
Initialize the first row and column to represent transformations from empty string (dp[i][0] = i, dp[0][j] = j). Then iterate through the table, filling each cell according to the recurrence.
State that time complexity is O(mn) and space complexity is O(mn). Then propose optimizing space to O(min(m,n)) by keeping only the previous and current rows, since each cell depends only on the current and previous row.
Walk through a small example (e.g., 'kitten' to 'sitting') to verify correctness. Mention possible extensions like weighted edit distance or using the algorithm for spell checking.
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