Start by clarifying the problem and walking through a simple example to confirm understanding. Then propose a straightforward solution using sets, analyze its time complexity, and optimize to O(n) by leveraging hash sets for O(1) lookups. Finally, generalize to multiple lists by maintaining a combined set of forbidden values from the previous d lists.
Pro tip: Explicitly discuss trade-offs between time and space, and mention edge cases like k larger than list length or d larger than the number of previous lists. This shows thoroughness and practical engineering judgment.
Restate the problem in your own words, ask clarifying questions about constraints (e.g., list sizes, value ranges, k and d bounds), and walk through a small example to ensure alignment.
Propose a naive approach: for each element in the second list's first k, check against the first list's first k using nested loops. Analyze its O(k^2) time complexity.
Improve by converting the first list's first k elements into a hash set, then iterate through the second list, removing any element found in the set. This achieves O(n) time where n is the length of the second list.
For a list of lists, process each list in order. Maintain a set of forbidden values from the first k elements of the previous d lists. For the current list, remove any of its first k elements that are in the forbidden set, then update the forbidden set with the remaining first k elements.
Analyze time and space complexity of the generalized solution. Discuss potential optimizations, such as using a sliding window for the forbidden set when d is small, and consider edge cases.
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