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The core scan isn't bad once you think monotonic stack, but I got snagged on the output format.
Clarify the problem and edge cases, then propose an efficient monotonic stack solution that finds the next smaller or equal element for each price in O(n) time. Explain how to compute the final prices and identify full-price items, and discuss the total sum and indices.
Pro tip: Mention that a monotonic stack is ideal for 'next smaller or equal element' problems, and that using a stack of indices allows you to update the result array in place while preserving original order.
Restate the problem in your own words and confirm details: discount is the first later item with price <= current, final price = current - discount (or current if none), output total sum and indices of items sold at full price.
Acknowledge the O(n^2) brute force approach, then propose an O(n) solution using a monotonic stack to efficiently find the next smaller or equal element for each price.
Iterate through prices, maintaining a stack of indices with non-decreasing prices. For each price, pop indices where the current price is <= the price at that index, and set the discount for those indices to the current price.
After processing, any indices left in the stack have no discount (full price). Compute the total sum of final prices and collect the indices of items sold at full price.
State time and space complexity: O(n) time, O(n) space. Discuss edge cases: empty array, single item, all increasing, all decreasing, duplicates.
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