Difficulty: Medium
Tags: LeetCode, Medium, Queue, Array, Dynamic Programming, Monotonic Queue, Heap (Priority Queue), leetcode-2944, O(n), DP, Sorted List, BST, Mono Deque

Problem

You are given an integer array prices where prices[i] denotes the number of coins needed to purchase the i^th fruit.

The fruit market has the following reward for each fruit:

If you purchase the i^th fruit at prices[i] coins, you can get any number of the next (i + 1) fruits for free.

Note that even if you can take fruit j for free, you can still purchase it for prices[j] coins to receive its reward.

Return the minimum number of coins needed to acquire all the fruits.

Example 1:

Input: prices = [3,1,2]

Output: 4

Explanation:

Purchase the 1^st fruit with prices[0] = 3 coins, you are allowed to take the 2^nd fruit for free.
Purchase the 2^nd fruit with prices[1] = 1 coin, you are allowed to take the 3^rd fruit for free.
Take the 3^rd fruit for free.

Note that even though you could take the 2^nd fruit for free as a reward of buying 1^st fruit, you purchase it to receive its reward, which is more optimal.

Example 2:

Input: prices = [1,10,1,1]

Output: 2

Explanation:

Purchase the 1^st fruit with prices[0] = 1 coin, you are allowed to take the 2^nd fruit for free.
Take the 2^nd fruit for free.
Purchase the 3^rd fruit for prices[2] = 1 coin, you are allowed to take the 4^th fruit for free.
Take the 4^t^h fruit for free.

Example 3:

Input: prices = [26,18,6,12,49,7,45,45]

Output: 39

Explanation:

Purchase the 1^st fruit with prices[0] = 26 coin, you are allowed to take the 2^nd fruit for free.
Take the 2^nd fruit for free.
Purchase the 3^rd fruit for prices[2] = 6 coin, you are allowed to take the 4^th, 5^th and 6^th (the next three) fruits for free.
Take the 4^t^h fruit for free.
Take the 5^t^h fruit for free.
Purchase the 6^th fruit with prices[5] = 7 coin, you are allowed to take the 8^th and 9^th fruit for free.
Take the 7^t^h fruit for free.
Take the 8^t^h fruit for free.

Note that even though you could take the 6^th fruit for free as a reward of buying 3^rd fruit, you purchase it to receive its reward, which is more optimal.

Constraints:

1 <= prices.length <= 1000
1 <= prices[i] <= 10⁵