Delete Operation for Two Strings

Delete Operation for Two Strings

1. What is this problem about?

The Delete Operation for Two Strings interview question asks for the minimum number of steps required to make two strings, word1 and word2, identical. In each step, you can delete one character from either string. This Delete Operation for Two Strings coding problem is effectively a variation of finding the Longest Common Subsequence (LCS) between the two inputs.

2. Why is this asked in interviews?

Companies like Google and Bloomberg ask this to evaluate your knowledge of Dynamic Programming interview patterns. It tests your ability to break a string similarity problem into smaller, overlapping sub-problems and find an optimal mathematical relationship between the lengths of the strings and their shared characters.

3. Algorithmic pattern used

The core pattern is Longest Common Subsequence (LCS).

• The characters you don't delete must form the longest shared subsequence.
• The formula is: $Cost = (length(word1) - LCS) + (length(word2) - LCS)$.
• You can use a 2D DP table where dp[i][j] stores the LCS of word1[0...i] and word2[0...j].

4. Example explanation

word1 = "sea", word2 = "eat"

1. The Longest Common Subsequence is "ea" (length 2).
2. Deletions from "sea" to get "ea": 1 ('s').
3. Deletions from "eat" to get "ea": 1 ('t'). Total steps = $1 + 1 = 2$.

5. Common mistakes candidates make

• Confusion with Edit Distance: Trying to use the Levenshtein distance (which includes replacement) instead of just deletions.
• $O(2^N)$ Recursion: Writing a simple recursive solution without memoization, which will fail for strings longer than 20 characters.
• Space Inefficiency: Using a full 2D array when only two rows are needed to calculate the next state.

6. Interview preparation tip

Master the LCS pattern. Many string optimization problems (like "Shortest Common Supersequence" or "Minimum Deletions to make a Palindrome") are actually LCS problems in disguise. Learning to reduce a new problem to a known pattern like LCS is a high-signal interview skill.