← Databricks Interview Insights
This felt like a fresh problem, not something you'd find recycled on a prep site.
Clarify the problem constraints and edge cases, then propose a greedy algorithm that scans the target string and finds the longest possible match in the source string at each step. Discuss time/space complexity and potential optimizations like precomputing a suffix automaton or using dynamic programming for overlapping matches.
Pro tip: Always discuss trade-offs between different approaches (e.g., greedy vs. DP) and mention how you would handle cases where no valid representation exists. This shows you think about robustness and real-world applicability.
Ask questions to understand constraints: Are the index pairs required to be non-overlapping? Can they be in any order? What if multiple representations exist? What if no representation exists? What are the string lengths?
Confirm that the output is a list of index pairs [start, end] (inclusive) from string a that, when concatenated in order, form string b. Ensure the pairs are valid indices and the concatenation exactly matches b.
Propose a greedy approach: iterate through b, and for each position, find the longest substring of b starting at that position that appears in a. Record the corresponding index range and advance. If no match, return failure.
Discuss the time complexity of the greedy approach (e.g., O(n*m) with naive search, or O(n+m) with precomputed data structures like suffix automaton). Mention space complexity and possible optimizations.
Consider empty strings, no valid representation, overlapping matches, and multiple valid representations. Discuss how to modify the algorithm to handle these cases, such as backtracking or dynamic programming if greedy fails.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the original problem: likely partitioning the second string into substrings that are subsequences of the first string, minimizing partitions. Then, analyze how deleting one character from the first string affects the set of possible subsequences and the optimal partition boundaries. Propose an efficient update, such as reusing the original DP table and adjusting only affected states, or recomputing with a modified DP that accounts for the deletion.
Pro tip: Mention that deleting a character can only reduce the set of subsequences, so the minimum number of partitions can only stay the same or increase. This monotonicity can guide pruning or early termination in your algorithm.
Confirm that the task is to partition the second string into the minimum number of contiguous substrings, each of which is a subsequence of the first string. Discuss the baseline DP solution and its complexity.
Determine which subsequences are lost when a character is removed from the first string. Identify how this impacts the feasibility of partitions and the optimal partition boundaries.
Suggest either recomputing the DP with the modified first string, or incrementally updating the original DP by invalidating states that relied on the deleted character. Discuss time/space trade-offs.
Consider cases where the deleted character is not used in any optimal partition, or where deletion makes the second string impossible to partition. Analyze the worst-case time complexity of the update.
Restate the key insight: deletion can only increase or maintain the minimum partitions. Conclude with the recommended approach and its efficiency.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.