Delete Operation for Two Strings
Given two strings `word1` and `word2`, find the minimum number of steps required to make `word1` and `word2` the same. A step is deleting exactly one character. This relates to LCS.
Why Interviewers Ask This
Microsoft asks this problem to evaluate a candidate's ability to transform a complex deletion task into a classic dynamic programming subproblem. They specifically look for the insight that minimizing deletions is mathematically equivalent to maximizing the Longest Common Subsequence (LCS). This tests your pattern recognition skills and your capacity to reduce an O(N*M) brute force scenario into an optimized solution.
How to Answer This Question
1. Clarify the Goal: Immediately restate that deleting characters from both strings to match them is equivalent to finding the longest shared sequence of characters. 2. Define the Relationship: Explain that Total Steps = (Length of word1 - LCS) + (Length of word2 - LCS). 3. Choose the Algorithm: Propose Dynamic Programming as the standard approach for LCS, defining dp[i][j] as the LCS length for prefixes word1[0..i] and word2[0..j]. 4. Walk Through Logic: Detail the recurrence relation: if characters match, take diagonal + 1; otherwise, take max of left or top cell. 5. Optimize Space: Mention that while a 2D table works, you can optimize to O(min(N,M)) space using two rows, showing attention to resource efficiency valued at Microsoft.
Key Points to Cover
- Recognizing the reduction from deletion problem to Longest Common Subsequence
- Explicitly stating the mathematical relationship: Total Lengths - 2 * LCS
- Defining clear DP state transitions for matching and non-matching characters
- Discussing Time Complexity O(N*M) and Space Optimization techniques
- Walking through a concrete small example like 'sea' and 'eat' to validate logic
Sample Answer
To solve this efficiently, I first realized that the minimum number of steps to make two strings identical by only deleting characters is directly tied to their Longest Common Subsequence. Instead of trying every possible combination of deletions, which would be exponential, we want to keep the maximum number of characters that are already in the correct relative order. The formula becomes straightforward: the total deletions needed equal the sum of the lengths of both strings minus twice the length of their LCS. I would implement this using Dynamic Programming. I'd create a 2D array where dp[i][j] represents the length of the LCS between the first i characters of word1 and the first j characters of word2. If the current characters match, we extend the previous LCS by one. If they don't match, we carry forward the best result found so far by either ignoring the character in word1 or word2. For example, with 'sea' and 'eat', the LCS is 'ea' with length 2. We delete 's' from 'sea' and 't' from 'eat', resulting in 2 steps. Finally, I would consider space optimization, noting that we only need the previous row to calculate the current one, reducing space complexity from O(N*M) to O(min(N,M)).
Common Mistakes to Avoid
- Attempting a recursive brute-force solution without memoization, leading to Time Limit Exceeded errors
- Confusing Longest Common Substring (contiguous) with Longest Common Subsequence (non-contiguous)
- Failing to account for deletions required from both strings simultaneously in the final calculation
- Overlooking edge cases where one string is empty or both strings are already identical
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