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leetcode-problemset/leetcode-cn/originData/minimum-number-of-coins-for-fruits.json
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{
"data": {
"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 at a fruit market with different types of exotic fruits on display.</p>\n\n<p>You are given a <strong>1-indexed</strong> 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 offer:</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 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 a new offer.</p>\n\n<p>Return <em>the <strong>minimum</strong> number of coins needed to acquire all the fruits</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> prices = [3,1,2]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> You can acquire the fruits as follows:\n- Purchase the 1<sup>st</sup> fruit with 3 coins, you are allowed to take the 2<sup>nd</sup> fruit for free.\n- Purchase the 2<sup>nd</sup> fruit with 1 coin, you are allowed to take the 3<sup>rd</sup> fruit for free.\n- Take the 3<sup>rd</sup> fruit for free.\nNote that even though you were allowed to take the 2<sup>nd</sup> 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</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> prices = [1,10,1,1]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> You can acquire the fruits as follows:\n- Purchase the 1<sup>st</sup> fruit with 1 coin, you are allowed to take the 2<sup>nd</sup> fruit for free.\n- Take the 2<sup>nd</sup> fruit for free.\n- Purchase the 3<sup>rd</sup> fruit for 1 coin, you are allowed to take the 4<sup>th</sup> fruit for free.\n- Take the 4<sup>t</sup><sup>h</sup> fruit for free.\nIt can be proven that 2 is the minimum number of coins needed to acquire all the fruits.\n</pre>\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>你在一个水果超市里,货架上摆满了玲琅满目的奇珍异果。</p>\n\n<p>给你一个下标从 <strong>1</strong>&nbsp;开始的数组&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>price[i]</code>&nbsp;购买了水果&nbsp;<code>i</code>&nbsp;,那么接下来的 <code>i</code>&nbsp;个水果你都可以免费获得。</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;个金币去购买它以便能免费获得接下来的 <code>j</code>&nbsp;个水果。</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<pre>\n<b>输入:</b>prices = [3,1,2]\n<b>输出:</b>4\n<b>解释</b><strong></strong>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</pre>\n\n<p><strong class=\"example\">示例 2</strong></p>\n\n<pre>\n<b>输入:</b>prices = [1,10,1,1]\n<b>输出:</b>2\n<b>解释:</b>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</pre>\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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"The intended solution uses Dynamic Programming.",
"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>.",
"<code>dp[i] = min(dp[i], dp[j] + prices[i]) </code>, where <code>j</code> is in the range <code>[i + 1, i + 1 + i]</code>."
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