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

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            "title": "Minimum Limit of Balls in a Bag",
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            "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&nbsp;after performing the operations</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong>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>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 an you should return 2.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [7,17], maxOperations = 2\n<strong>Output:</strong> 7\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",
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            "hints": [
                "Let's change the question if we know the maximum size of a bag what is the minimum number of bags you can make",
                "note that as the maximum size increases the minimum number of bags decreases so we can binary search the maximum size"
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