Problem Description
You are given an 0-indexed integer array prices where prices[i] denotes the number of coins needed to purchase the (i + 1)th fruit. The fruit market has the following reward for each fruit: If you purchase the (i + 1)th fruit at prices[i] coins, you can get any number of the next i fruits for free. Return the minimum number of coins needed to acquire all the fruits.
Key Insights
- You can purchase a fruit and get subsequent fruits for free, which allows for strategic purchasing.
- The goal is to minimize total coin expenditure while taking advantage of free fruits.
- A greedy approach is effective where you always choose to buy the cheapest available fruit that allows you to maximize free fruits.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
The solution involves iterating through the prices array while maintaining a running total of the minimum coins spent. For each fruit, you decide whether to buy it or to take advantage of the free fruits allowed by a previous purchase. By always opting for the minimum price that allows you to take further fruits for free, you minimize the total cost effectively.