The example they gave was [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] with answer 5.
First clarify the problem: given an array, you can perform operations (e.g., increment elements) to maximize the median. Then, sort the array and use a greedy approach to increment the smallest elements in the upper half until they reach the next distinct value, ensuring the median is as large as possible. Finally, analyze the time complexity and edge cases.
Pro tip: Amazon interviewers value candidates who ask clarifying questions about constraints and operation costs before diving into a solution. Explicitly state your assumptions and walk through a small example to validate your greedy strategy.
Ask about the allowed operations (e.g., increment any element by 1), the definition of median (for even-sized arrays), and constraints on the array size and values.
Sort the array in non-decreasing order. For an array of size n, the median is at index n//2 (0-indexed) for odd n, or the average of indices n//2 - 1 and n//2 for even n.
To maximize the median, focus on the upper half of the sorted array. Increment the smallest elements in that half to match the next larger element, effectively raising the median. Repeat until the operation budget is exhausted or all elements in the upper half are equal.
Calculate the maximum median value after optimally distributing the increments. If the budget is large enough, the median can be increased further by incrementing all elements in the upper half equally.
Discuss time complexity (dominated by sorting, O(n log n)) and space complexity (O(1) if in-place). Mention edge cases like n=1, even n, and zero budget.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.