I knew this one but still managed to overcomplicate it at first.
Start by clarifying the problem constraints (e.g., array size, price range) and then propose an efficient one-pass solution that tracks the minimum price seen so far and computes the maximum profit at each step. Explain the algorithm clearly, analyze its time and space complexity, and test with edge cases like decreasing prices or single-element arrays.
Pro tip: Demonstrate Amazon's Leadership Principles by proactively discussing trade-offs (e.g., simplicity vs. optimality) and by writing clean, production-ready code with meaningful variable names and error handling.
Ask about input size, price range, and whether the array can be empty or contain negative values. Confirm that only one transaction is allowed and that buying and selling on the same day is not permitted.
Mention the O(n^2) brute-force method, then explain the O(n) one-pass solution that tracks the minimum price and maximum profit. Highlight why the optimal approach is better for large datasets.
Use a small example like [7,1,5,3,6,4] to illustrate how the minimum price updates and profit is calculated. Show how the algorithm handles a decreasing array like [7,6,4,3,1] to return 0 profit.
State that time complexity is O(n) and space is O(1). Discuss edge cases: empty array, single element, all decreasing, all increasing, and duplicate prices.
Implement the solution in a language of your choice (e.g., Python) with clear variable names and comments. Test with the example and edge cases to ensure correctness.
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