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"categoryTitle": "Algorithms",
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"title": "Minimum Operations to Halve Array Sum",
"titleSlug": "minimum-operations-to-halve-array-sum",
"content": "<p>You are given an array <code>nums</code> of positive integers. In one operation, you can choose <strong>any</strong> number from <code>nums</code> and reduce it to <strong>exactly</strong> half the number. (Note that you may choose this reduced number in future operations.)</p>\n\n<p>Return<em> the <strong>minimum</strong> number of operations to reduce the sum of </em><code>nums</code><em> by <strong>at least</strong> half.</em></p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,19,8,1]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> The initial sum of nums is equal to 5 + 19 + 8 + 1 = 33.\nThe following is one of the ways to reduce the sum by at least half:\nPick the number 19 and reduce it to 9.5.\nPick the number 9.5 and reduce it to 4.75.\nPick the number 8 and reduce it to 4.\nThe final array is [5, 4.75, 4, 1] with a total sum of 5 + 4.75 + 4 + 1 = 14.75. \nThe sum of nums has been reduced by 33 - 14.75 = 18.25, which is at least half of the initial sum, 18.25 &gt;= 33/2 = 16.5.\nOverall, 3 operations were used so we return 3.\nIt can be shown that we cannot reduce the sum by at least half in less than 3 operations.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [3,8,20]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> The initial sum of nums is equal to 3 + 8 + 20 = 31.\nThe following is one of the ways to reduce the sum by at least half:\nPick the number 20 and reduce it to 10.\nPick the number 10 and reduce it to 5.\nPick the number 3 and reduce it to 1.5.\nThe final array is [1.5, 8, 5] with a total sum of 1.5 + 8 + 5 = 14.5. \nThe sum of nums has been reduced by 31 - 14.5 = 16.5, which is at least half of the initial sum, 16.5 &gt;= 31/2 = 16.5.\nOverall, 3 operations were used so we return 3.\nIt can be shown that we cannot reduce the sum by at least half in less than 3 operations.\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;= nums[i] &lt;= 10<sup>7</sup></code></li>\n</ul>\n",
"translatedTitle": "将数组和减半的最少操作次数",
"translatedContent": "<p>给你一个正整数数组&nbsp;<code>nums</code>&nbsp;。每一次操作中,你可以从&nbsp;<code>nums</code>&nbsp;中选择 <strong>任意</strong>&nbsp;一个数并将它减小到 <strong>恰好</strong>&nbsp;一半。(注意,在后续操作中你可以对减半过的数继续执行操作)</p>\n\n<p>请你返回将 <code>nums</code>&nbsp;数组和 <strong>至少</strong>&nbsp;减少一半的 <strong>最少</strong>&nbsp;操作数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre><b>输入:</b>nums = [5,19,8,1]\n<b>输出:</b>3\n<b>解释:</b>初始 nums 的和为 5 + 19 + 8 + 1 = 33 。\n以下是将数组和减少至少一半的一种方法\n选择数字 19 并减小为 9.5 。\n选择数字 9.5 并减小为 4.75 。\n选择数字 8 并减小为 4 。\n最终数组为 [5, 4.75, 4, 1] ,和为 5 + 4.75 + 4 + 1 = 14.75 。\nnums 的和减小了 33 - 14.75 = 18.25 减小的部分超过了初始数组和的一半18.25 &gt;= 33/2 = 16.5 。\n我们需要 3 个操作实现题目要求,所以返回 3 。\n可以证明无法通过少于 3 个操作使数组和减少至少一半。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre><b>输入:</b>nums = [3,8,20]\n<b>输出:</b>3\n<strong>解释:</strong>初始 nums 的和为 3 + 8 + 20 = 31 。\n以下是将数组和减少至少一半的一种方法\n选择数字 20 并减小为 10 。\n选择数字 10 并减小为 5 。\n选择数字 3 并减小为 1.5 。\n最终数组为 [1.5, 8, 5] ,和为 1.5 + 8 + 5 = 14.5 。\nnums 的和减小了 31 - 14.5 = 16.5 ,减小的部分超过了初始数组和的一半, 16.5 &gt;= 31/2 = 16.5 。\n我们需要 3 个操作实现题目要求,所以返回 3 。\n可以证明无法通过少于 3 个操作使数组和减少至少一半。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</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;= nums[i] &lt;= 10<sup>7</sup></code></li>\n</ul>\n",
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