Problem Description
You are given an integer array prices where prices[i] is the price of the ith item in a shop. There is a special discount for items in the shop. If you buy the ith item, then you will receive a discount equivalent to prices[j] where j is the minimum index such that j > i and prices[j] <= prices[i]. Otherwise, you will not receive any discount at all. Return an integer array answer where answer[i] is the final price you will pay for the ith item of the shop, considering the special discount.
Key Insights
- Each item may have a discount based on future items in the list.
- The discount is applied based on the first subsequent item that has a price less than or equal to the current item's price.
- A stack can be utilized to keep track of indices of prices as we iterate through the list, allowing us to efficiently find discounts.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(n)
Solution
To solve this problem, we can use a stack to keep track of the indices of the prices. We iterate through the prices array. For each price, we check if it can receive a discount from a previously processed price (using the stack). If the current price is less than or equal to the price at the index stored on the top of the stack, we pop the index from the stack and apply the discount. The final price for each item is calculated by subtracting the discount from the original price. This approach ensures that each price is processed only once, leading to an efficient solution.