leetcode-problemset/leetcode-cn/originData/minimum-limit-of-balls-in-a-bag.json

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        "question": {
            "questionId": "1886",
            "questionFrontendId": "1760",
            "categoryTitle": "Algorithms",
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            "title": "Minimum Limit of Balls in a Bag",
            "titleSlug": "minimum-limit-of-balls-in-a-bag",
            "content": "<p>You are given an integer array <code>nums</code> where the <code>i<sup>th</sup></code> bag contains <code>nums[i]</code> balls. You are also given an integer <code>maxOperations</code>.</p>\n\n<p>You can perform the following operation at most <code>maxOperations</code> times:</p>\n\n<ul>\n\t<li>Take any bag of balls and divide it into two new bags with a <strong>positive </strong>number of balls.\n\n\t<ul>\n\t\t<li>For example, a bag of <code>5</code> balls can become two new bags of <code>1</code> and <code>4</code> balls, or two new bags of <code>2</code> and <code>3</code> balls.</li>\n\t</ul>\n\t</li>\n</ul>\n\n<p>Your penalty is the <strong>maximum</strong> number of balls in a bag. You want to <strong>minimize</strong> your penalty after the operations.</p>\n\n<p>Return <em>the minimum possible penalty after performing the operations</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [9], maxOperations = 2\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> \n- Divide the bag with 9 balls into two bags of sizes 6 and 3. [<strong><u>9</u></strong>] -&gt; [6,3].\n- Divide the bag with 6 balls into two bags of sizes 3 and 3. [<strong><u>6</u></strong>,3] -&gt; [3,3,3].\nThe bag with the most number of balls has 3 balls, so your penalty is 3 and you should return 3.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,4,8,2], maxOperations = 4\n<strong>Output:</strong> 2\n<strong>Explanation:</strong>\n- Divide the bag with 8 balls into two bags of sizes 4 and 4. [2,4,<strong><u>8</u></strong>,2] -&gt; [2,4,4,4,2].\n- Divide the bag with 4 balls into two bags of sizes 2 and 2. [2,<strong><u>4</u></strong>,4,4,2] -&gt; [2,2,2,4,4,2].\n- Divide the bag with 4 balls into two bags of sizes 2 and 2. [2,2,2,<strong><u>4</u></strong>,4,2] -&gt; [2,2,2,2,2,4,2].\n- Divide the bag with 4 balls into two bags of sizes 2 and 2. [2,2,2,2,2,<strong><u>4</u></strong>,2] -&gt; [2,2,2,2,2,2,2,2].\nThe bag with the most number of balls has 2 balls, so your penalty is 2, and you should return 2.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= maxOperations, nums[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "袋子里最少数目的球",
            "translatedContent": "<p>给你一个整数数组 <code>nums</code> ，其中 <code>nums[i]</code> 表示第 <code>i</code> 个袋子里球的数目。同时给你一个整数 <code>maxOperations</code> 。</p>\n\n<p>你可以进行如下操作至多 <code>maxOperations</code> 次：</p>\n\n<ul>\n\t<li>选择任意一个袋子，并将袋子里的球分到 2 个新的袋子中，每个袋子里都有 <strong>正整数</strong> 个球。\n\n\t<ul>\n\t\t<li>比方说，一个袋子里有 <code>5</code> 个球，你可以把它们分到两个新袋子里，分别有 <code>1</code> 个和 <code>4</code> 个球，或者分别有 <code>2</code> 个和 <code>3</code> 个球。</li>\n\t</ul>\n\t</li>\n</ul>\n\n<p>你的开销是单个袋子里球数目的 <strong>最大值</strong> ，你想要 <strong>最小化</strong> 开销。</p>\n\n<p>请你返回进行上述操作后的最小开销。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [9], maxOperations = 2\n<b>输出：</b>3\n<b>解释：</b>\n- 将装有 9 个球的袋子分成装有 6 个和 3 个球的袋子。[<strong>9</strong>] -> [6,3] 。\n- 将装有 6 个球的袋子分成装有 3 个和 3 个球的袋子。[<strong>6</strong>,3] -> [3,3,3] 。\n装有最多球的袋子里装有 3 个球，所以开销为 3 并返回 3 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [2,4,8,2], maxOperations = 4\n<b>输出：</b>2\n<strong>解释：</strong>\n- 将装有 8 个球的袋子分成装有 4 个和 4 个球的袋子。[2,4,<strong>8</strong>,2] -> [2,4,4,4,2] 。\n- 将装有 4 个球的袋子分成装有 2 个和 2 个球的袋子。[2,<strong>4</strong>,4,4,2] -> [2,2,2,4,4,2] 。\n- 将装有 4 个球的袋子分成装有 2 个和 2 个球的袋子。[2,2,2,<strong>4</strong>,4,2] -> [2,2,2,2,2,4,2] 。\n- 将装有 4 个球的袋子分成装有 2 个和 2 个球的袋子。[2,2,2,2,2,<strong>4</strong>,2] -> [2,2,2,2,2,2,2,2] 。\n装有最多球的袋子里装有 2 个球，所以开销为 2 并返回 2 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [7,17], maxOperations = 2\n<b>输出：</b>7\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= maxOperations, nums[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
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                "Let's change the question if we know the maximum size of a bag what is the minimum number of bags you can make",
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