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leetcode-problemset/leetcode-cn/originData/minimum-cost-of-buying-candies-with-discount.json
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"categoryTitle": "Algorithms",
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"title": "Minimum Cost of Buying Candies With Discount",
"titleSlug": "minimum-cost-of-buying-candies-with-discount",
"content": "<p>A shop is selling candies at a discount. For <strong>every two</strong> candies sold, the shop gives a <strong>third</strong> candy for <strong>free</strong>.</p>\n\n<p>The customer can choose <strong>any</strong> candy to take away for free as long as the cost of the chosen candy is less than or equal to the <strong>minimum</strong> cost of the two candies bought.</p>\n\n<ul>\n\t<li>For example, if there are <code>4</code> candies with costs <code>1</code>, <code>2</code>, <code>3</code>, and <code>4</code>, and the customer buys candies with costs <code>2</code> and <code>3</code>, they&nbsp;can take the candy with cost <code>1</code> for free, but not the candy with cost <code>4</code>.</li>\n</ul>\n\n<p>Given a <strong>0-indexed</strong> integer array <code>cost</code>, where <code>cost[i]</code> denotes the cost of the <code>i<sup>th</sup></code> candy, return <em>the <strong>minimum cost</strong> of buying <strong>all</strong> the candies</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> cost = [1,2,3]\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> We buy the candies with costs 2 and 3, and take the candy with cost 1 for free.\nThe total cost of buying all candies is 2 + 3 = 5. This is the <strong>only</strong> way we can buy the candies.\nNote that we cannot buy candies with costs 1 and 3, and then take the candy with cost 2 for free.\nThe cost of the free candy has to be less than or equal to the minimum cost of the purchased candies.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> cost = [6,5,7,9,2,2]\n<strong>Output:</strong> 23\n<strong>Explanation:</strong> The way in which we can get the minimum cost is described below:\n- Buy candies with costs 9 and 7\n- Take the candy with cost 6 for free\n- We buy candies with costs 5 and 2\n- Take the last remaining candy with cost 2 for free\nHence, the minimum cost to buy all candies is 9 + 7 + 5 + 2 = 23.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> cost = [5,5]\n<strong>Output:</strong> 10\n<strong>Explanation:</strong> Since there are only 2 candies, we buy both of them. There is not a third candy we can take for free.\nHence, the minimum cost to buy all candies is 5 + 5 = 10.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= cost.length &lt;= 100</code></li>\n\t<li><code>1 &lt;= cost[i] &lt;= 100</code></li>\n</ul>\n",
"translatedTitle": "打折购买糖果的最小开销",
"translatedContent": "<p>一家商店正在打折销售糖果。每购买 <strong>两个</strong>&nbsp;糖果,商店会 <strong>免费</strong>&nbsp;送一个糖果。</p>\n\n<p>免费送的糖果唯一的限制是:它的价格需要小于等于购买的两个糖果价格的 <strong>较小值</strong>&nbsp;。</p>\n\n<ul>\n\t<li>比方说,总共有 <code>4</code>&nbsp;个糖果,价格分别为&nbsp;<code>1</code>&nbsp;<code>2</code>&nbsp;<code>3</code>&nbsp;和&nbsp;<code>4</code>&nbsp;,一位顾客买了价格为&nbsp;<code>2</code> 和&nbsp;<code>3</code>&nbsp;的糖果,那么他可以免费获得价格为 <code>1</code>&nbsp;的糖果,但不能获得价格为&nbsp;<code>4</code>&nbsp;的糖果。</li>\n</ul>\n\n<p>给你一个下标从 <strong>0</strong>&nbsp;开始的整数数组&nbsp;<code>cost</code>&nbsp;,其中&nbsp;<code>cost[i]</code>&nbsp;表示第&nbsp;<code>i</code>&nbsp;个糖果的价格,请你返回获得 <strong>所有</strong>&nbsp;糖果的 <strong>最小</strong>&nbsp;总开销。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre><b>输入:</b>cost = [1,2,3]\n<b>输出:</b>5\n<b>解释:</b>我们购买价格为 2 和 3 的糖果,然后免费获得价格为 1 的糖果。\n总开销为 2 + 3 = 5 。这是开销最小的 <strong>唯一</strong>&nbsp;方案。\n注意我们不能购买价格为 1 和 3 的糖果,并免费获得价格为 2 的糖果。\n这是因为免费糖果的价格必须小于等于购买的 2 个糖果价格的较小值。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre><b>输入:</b>cost = [6,5,7,9,2,2]\n<b>输出:</b>23\n<b>解释:</b>最小总开销购买糖果方案为:\n- 购买价格为 9 和 7 的糖果\n- 免费获得价格为 6 的糖果\n- 购买价格为 5 和 2 的糖果\n- 免费获得价格为 2 的最后一个糖果\n因此最小总开销为 9 + 7 + 5 + 2 = 23 。\n</pre>\n\n<p><strong>示例 3</strong></p>\n\n<pre><b>输入:</b>cost = [5,5]\n<b>输出:</b>10\n<b>解释:</b>由于只有 2 个糖果,我们需要将它们都购买,而且没有免费糖果。\n所以总最小开销为 5 + 5 = 10 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= cost.length &lt;= 100</code></li>\n\t<li><code>1 &lt;= cost[i] &lt;= 100</code></li>\n</ul>\n",
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"How can we generalize this approach to maximize the costs of the candies we get for free?",
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"If we consider costs from high to low, what is the maximum cost of a single candy that we can get for free?",
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