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Recognize this as the edit distance (Levenshtein distance) problem and propose a dynamic programming solution. Define dp[i][j] as the minimum operations to convert the first i characters of string1 to the first j characters of string2, then derive the recurrence relation based on whether the current characters match. Analyze time and space complexity, and mention potential optimizations.
Pro tip: Emphasize that this is a classic DP problem and that you can optimize space to O(min(m,n)) by using two rows. Also, relate it to real-world applications like spell checking or DNA sequence alignment to show practical understanding.
Confirm that operations are single-character insertions, deletions, or replacements, and that each operation costs 1. Ask if there are any constraints on string lengths or character sets.
Let dp[i][j] be the minimum edit distance between the first i characters of string1 and the first j characters of string2. Initialize dp[0][j] = j and dp[i][0] = i.
If characters match, dp[i][j] = dp[i-1][j-1]. Else, dp[i][j] = 1 + min(dp[i-1][j] (deletion), dp[i][j-1] (insertion), dp[i-1][j-1] (replacement)).
Fill the DP table iteratively and return dp[m][n]. Discuss time complexity O(m*n) and space complexity O(m*n), then mention space optimization to O(min(m,n)).
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