Spent way too long overthinking the data structure here.
Start by clarifying the problem and edge cases, then propose an efficient solution using prefix and suffix frequency arrays to track distinct characters. Explain how to compute the intersection count for each split in O(1) after O(n) preprocessing, and analyze time and space complexity.
Pro tip: Mention that you can optimize space by using bitmasks if the character set is small (e.g., lowercase English letters), and discuss trade-offs between different approaches to show depth.
Confirm the definition of 'distinct characters shared by both parts' and ask about constraints (e.g., string length, character set).
Describe a naive O(n^2) solution: for each split, compute the distinct characters in prefix and suffix, then count the intersection.
Precompute prefix and suffix frequency arrays (or sets) to get distinct characters for any split in O(1). Then iterate through all splits and count those with intersection size > k.
State that preprocessing takes O(n * alphabet_size) time and O(n * alphabet_size) space, and the final iteration is O(n * alphabet_size) or O(n) with bitmasks.
Discuss cases like k >= alphabet_size, empty string, or when no valid split exists, and ensure the solution handles them correctly.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the problem constraints and edge cases, then propose an efficient algorithm. A good strategy is to sort the costs and use binary search on the target package cost, checking feasibility with a greedy two-pointer approach. Explain the time and space complexity and discuss potential optimizations.
Pro tip: Demonstrate Amazon's leadership principles by discussing trade-offs between different approaches and considering scalability for large inputs. Also, mention how you would test the solution with edge cases like duplicate costs and odd-length arrays.
Ask clarifying questions to ensure you understand the constraints: Can packages have one or two items? Is the array sorted? What are the possible values of costs? Can we assume all costs are positive integers?
Recognize that the goal is to maximize the number of packages with a fixed total cost per package, using each item at most once. This is a combinatorial optimization problem that can be solved by checking feasibility for a given target cost.
Sort the array. For a candidate target cost, use a two-pointer technique to greedily form as many packages as possible: pair the smallest with the largest if their sum equals the target, otherwise adjust pointers. Also consider single-item packages if an item's cost equals the target.
The number of packages is monotonic with respect to the target cost: if a target cost is feasible, any smaller target cost is also feasible. Use binary search over the possible target costs (from min to max sum of two items) to find the maximum feasible target cost.
State the time complexity: O(n log n) for sorting plus O(n log M) for binary search, where M is the range of possible costs. Discuss space complexity O(1) or O(n) depending on implementation. Walk through edge cases and test with examples.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.