This is the kind of question that feels manageable until they ask you to formally define the state.
Clarify the problem, then define the DP state and recurrence relation before coding. Discuss both memoization and tabulation, and analyze time and space complexity. Walk through a small example to validate your approach.
Pro tip: Start with a brute-force recursive solution, then optimize with memoization. This demonstrates systematic problem-solving and makes the DP transition natural.
Restate the problem in your own words, ask clarifying questions, and define the DP state clearly (e.g., dp[i][j] represents the minimum edit distance between first i characters of word1 and first j characters of word2).
Write the recurrence relation based on the last characters or decisions. For example, if characters match, dp[i][j] = dp[i-1][j-1]; else, take min of insert, delete, replace plus 1.
Define base cases such as dp[0][j] = j (all insertions) and dp[i][0] = i (all deletions). Explain why these are correct.
Decide between memoization (top-down) and tabulation (bottom-up). Discuss trade-offs: memoization is easier to write from recurrence, tabulation avoids recursion overhead and allows space optimization.
State time and space complexity. For edit distance, O(m*n) time and O(m*n) space, with possible O(min(m,n)) space optimization. Explain how you derived it.
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