I recognized this was a stack problem pretty fast, which felt good.
Clarify the problem and edge cases, then propose a monotonic stack solution that processes the array from right to left to efficiently find the next smaller or equal element. Explain the algorithm, analyze its O(n) time and space complexity, and optionally discuss a brute-force alternative for comparison.
Pro tip: Emphasize the monotonic stack pattern as a reusable technique for 'next smaller element' problems, and mention that you'd validate with edge cases like strictly increasing/decreasing arrays and duplicates.
Confirm the discount rule: find the first later item with price <= current price, subtract it; if none, price unchanged. Discuss edge cases: empty array, single item, all increasing, all decreasing, duplicates.
Use a monotonic stack to track indices of items with increasing prices from right to left. For each item, pop stack elements with price > current price, then the top (if any) is the next smaller or equal element.
Iterate from right to left, maintain a stack of indices with non-decreasing prices. For each index i, while stack not empty and prices[stack.top] > prices[i], pop. If stack not empty, discount = prices[stack.top]; else discount = 0. Push i onto stack.
Each element is pushed and popped at most once, so time complexity is O(n). Space complexity is O(n) for the stack in the worst case.
Mention brute-force O(n^2) approach for small inputs or as a baseline. Highlight that the stack solution is optimal and can be adapted for similar problems.
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