leetcode-problemset/leetcode-cn/originData/minimum-number-of-coins-for-fruits.json

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        "question": {
            "questionId": "3209",
            "questionFrontendId": "2944",
            "categoryTitle": "Algorithms",
            "boundTopicId": 2539684,
            "title": "Minimum Number of Coins for Fruits",
            "titleSlug": "minimum-number-of-coins-for-fruits",
            "content": "<p>You are given an <strong>1-indexed</strong> integer array <code>prices</code> where <code>prices[i]</code> denotes the number of coins needed to purchase the <code>i<sup>th</sup></code> fruit.</p>\n\n<p>The fruit market has the following reward for each fruit:</p>\n\n<ul>\n\t<li>If you purchase the <code>i<sup>th</sup></code> fruit at <code>prices[i]</code> coins, you can get any number of the next <code>i</code> fruits for free.</li>\n</ul>\n\n<p><strong>Note</strong> that even if you <strong>can</strong> take fruit <code>j</code> for free, you can still purchase it for <code>prices[j]</code> coins to receive its reward.</p>\n\n<p>Return the <strong>minimum</strong> number of coins needed to acquire all the fruits.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">prices = [3,1,2]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<ul>\n\t<li>Purchase the 1<sup>st</sup> fruit with <code>prices[0] = 3</code> coins, you are allowed to take the 2<sup>nd</sup> fruit for free.</li>\n\t<li>Purchase the 2<sup>nd</sup> fruit with <code>prices[1] = 1</code> coin, you are allowed to take the 3<sup>rd</sup> fruit for free.</li>\n\t<li>Take the 3<sup>rd</sup> fruit for free.</li>\n</ul>\n\n<p>Note that even though you could take the 2<sup>nd</sup> fruit for free as a reward of buying 1<sup>st</sup> fruit, you purchase it to receive its reward, which is more optimal.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">prices = [1,10,1,1]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<ul>\n\t<li>Purchase the 1<sup>st</sup> fruit with <code>prices[0] = 1</code> coin, you are allowed to take the 2<sup>nd</sup> fruit for free.</li>\n\t<li>Take the 2<sup>nd</sup> fruit for free.</li>\n\t<li>Purchase the 3<sup>rd</sup> fruit for <code>prices[2] = 1</code> coin, you are allowed to take the 4<sup>th</sup> fruit for free.</li>\n\t<li>Take the 4<sup>t</sup><sup>h</sup> fruit for free.</li>\n</ul>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">prices = [26,18,6,12,49,7,45,45]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">39</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<ul>\n\t<li>Purchase the 1<sup>st</sup> fruit with <code>prices[0] = 26</code> coin, you are allowed to take the 2<sup>nd</sup> fruit for free.</li>\n\t<li>Take the 2<sup>nd</sup> fruit for free.</li>\n\t<li>Purchase the 3<sup>rd</sup> fruit for <code>prices[2] = 6</code> coin, you are allowed to take the 4<sup>th</sup>, 5<sup>th</sup> and 6<sup>th</sup> (the next three) fruits for free.</li>\n\t<li>Take the 4<sup>t</sup><sup>h</sup> fruit for free.</li>\n\t<li>Take the 5<sup>t</sup><sup>h</sup> fruit for free.</li>\n\t<li>Purchase the 6<sup>th</sup> fruit with <code>prices[5] = 7</code> coin, you are allowed to take the 8<sup>th</sup> and 9<sup>th</sup> fruit for free.</li>\n\t<li>Take the 7<sup>t</sup><sup>h</sup> fruit for free.</li>\n\t<li>Take the 8<sup>t</sup><sup>h</sup> fruit for free.</li>\n</ul>\n\n<p>Note that even though you could take the 6<sup>th</sup> fruit for free as a reward of buying 3<sup>rd</sup> fruit, you purchase it to receive its reward, which is more optimal.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= prices.length &lt;= 1000</code></li>\n\t<li><code>1 &lt;= prices[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "购买水果需要的最少金币数",
            "translatedContent": "<p>给你一个 <strong>下标从 1 开始的</strong> 整数数组&nbsp;<code>prices</code>&nbsp;，其中&nbsp;<code>prices[i]</code>&nbsp;表示你购买第 <code>i</code>&nbsp;个水果需要花费的金币数目。</p>\n\n<p>水果超市有如下促销活动：</p>\n\n<ul>\n\t<li>如果你花费 <code>prices[i]</code>&nbsp;购买了下标为&nbsp;<code>i</code>&nbsp;的水果，那么你可以免费获得下标范围在&nbsp;<code>[i + 1, i + i]</code>&nbsp;的水果。</li>\n</ul>\n\n<p><strong>注意</strong>&nbsp;，即使你&nbsp;<strong>可以</strong>&nbsp;免费获得水果&nbsp;<code>j</code>&nbsp;，你仍然可以花费&nbsp;<code>prices[j]</code>&nbsp;个金币去购买它以获得它的奖励。</p>\n\n<p>请你返回获得所有水果所需要的 <strong>最少</strong>&nbsp;金币数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">prices = [3,1,2]</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">4</span></p>\n\n<p><strong>解释：</strong></p>\n\n<ul>\n\t<li>用&nbsp;<code>prices[0] = 3</code>&nbsp;个金币购买第 1 个水果，你可以免费获得第 2 个水果。</li>\n\t<li>用&nbsp;<code>prices[1] = 1</code>&nbsp;个金币购买第 2 个水果，你可以免费获得第 3 个水果。</li>\n\t<li>免费获得第 3 个水果。</li>\n</ul>\n\n<p>请注意，即使您可以免费获得第 2 个水果作为购买第 1 个水果的奖励，但您购买它是为了获得其奖励，这是更优化的。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">prices = [1,10,1,1]</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">2</span></p>\n\n<p><strong>解释：</strong></p>\n\n<ul>\n\t<li>用&nbsp;<code>prices[0] = 1</code> 个金币购买第 1 个水果，你可以免费获得第 2 个水果。</li>\n\t<li>免费获得第 2 个水果。</li>\n\t<li>用&nbsp;<code>prices[2] = 1</code> 个金币购买第 3 个水果，你可以免费获得第 4 个水果。</li>\n\t<li>免费获得第 4 个水果。</li>\n</ul>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">prices = [26,18,6,12,49,7,45,45]</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">39</span></p>\n\n<p><strong>解释：</strong></p>\n\n<ul>\n\t<li>用&nbsp;<code>prices[0] = 26</code> 个金币购买第 1 个水果，你可以免费获得第 2 个水果。</li>\n\t<li>免费获得第 2 个水果。</li>\n\t<li>用&nbsp;<code>prices[2] = 6</code> 个金币购买第 3 个水果，你可以免费获得第 4，5，6（接下来的三个）水果。</li>\n\t<li>免费获得第 4 个水果。</li>\n\t<li>免费获得第 5&nbsp;个水果。</li>\n\t<li>用&nbsp;<code>prices[5] = 7</code>&nbsp;个金币购买第 6 个水果，你可以免费获得第 7 和 第 8 个水果。</li>\n\t<li>免费获得第 7&nbsp;个水果。</li>\n\t<li>免费获得第 8&nbsp;个水果。</li>\n</ul>\n\n<p>请注意，即使您可以免费获得第 6 个水果作为购买第 3 个水果的奖励，但您购买它是为了获得其奖励，这是更优化的。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= prices.length &lt;= 1000</code></li>\n\t<li><code>1 &lt;= prices[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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                "Let <code>dp[i]</code> denote the minimum number of coins, such that we bought <code>i<sup>th</sup></code> fruit and acquired all the fruits in the range <code>[i...n]</code>.",
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