You are at a fruit market with different types of exotic fruits on display.
\n\nYou are given a 1-indexed array prices, where prices[i] denotes the number of coins needed to purchase the ith fruit.
The fruit market has the following offer:
\n\nith fruit at prices[i] coins, you can get the next i 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 a new offer.
Return the minimum number of coins needed to acquire all the fruits.
\n\n\n
Example 1:
\n\n\nInput: prices = [3,1,2]\nOutput: 4\nExplanation: You can acquire the fruits as follows:\n- Purchase the 1st fruit with 3 coins, you are allowed to take the 2nd fruit for free.\n- Purchase the 2nd fruit with 1 coin, you are allowed to take the 3rd fruit for free.\n- Take the 3rd fruit for free.\nNote that even though you were allowed to take the 2nd fruit for free, you purchased it because it is more optimal.\nIt can be proven that 4 is the minimum number of coins needed to acquire all the fruits.\n\n\n
Example 2:
\n\n\nInput: prices = [1,10,1,1]\nOutput: 2\nExplanation: You can acquire the fruits as follows:\n- Purchase the 1st fruit with 1 coin, you are allowed to take the 2nd fruit for free.\n- Take the 2nd fruit for free.\n- Purchase the 3rd fruit for 1 coin, you are allowed to take the 4th fruit for free.\n- Take the 4th fruit for free.\nIt can be proven that 2 is the minimum number of coins needed to acquire all the fruits.\n\n\n
\n
Constraints:
\n\n1 <= prices.length <= 10001 <= prices[i] <= 105你在一个水果超市里，货架上摆满了玲琅满目的奇珍异果。
\n\n给你一个下标从 1 开始的数组 prices ，其中 prices[i] 表示你购买第 i 个水果需要花费的金币数目。
水果超市有如下促销活动：
\n\nprice[i] 购买了水果 i ，那么接下来的 i 个水果你都可以免费获得。注意 ，即使你 可以 免费获得水果 j ，你仍然可以花费 prices[j] 个金币去购买它以便能免费获得接下来的 j 个水果。
请你返回获得所有水果所需要的 最少 金币数。
\n\n\n\n
示例 1：
\n\n\n输入：prices = [3,1,2]\n输出：4\n解释：你可以按如下方法获得所有水果：\n- 花 3 个金币购买水果 1 ，然后免费获得水果 2 。\n- 花 1 个金币购买水果 2 ，然后免费获得水果 3 。\n- 免费获得水果 3 。\n注意，虽然你可以免费获得水果 2 ，但你还是花 1 个金币去购买它，因为这样的总花费最少。\n购买所有水果需要最少花费 4 个金币。\n\n\n
示例 2：
\n\n\n输入：prices = [1,10,1,1]\n输出：2\n解释：你可以按如下方法获得所有水果：\n- 花 1 个金币购买水果 1 ，然后免费获得水果 2 。\n- 免费获得水果 2 。\n- 花 1 个金币购买水果 3 ，然后免费获得水果 4 。\n- 免费获得水果 4 。\n购买所有水果需要最少花费 2 个金币。\n\n\n
\n\n
提示：
\n\n1 <= prices.length <= 10001 <= prices[i] <= 105dp[i] denote the minimum number of coins, such that we bought ith fruit and acquired all the fruits in the range [i...n].",
"dp[i] = min(dp[i], dp[j] + prices[i]) , where j is in the range [i + 1, i + 1 + i]."
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