leetcode-problemset/leetcode-cn/originData/maximum-split-of-positive-even-integers.json

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            "title": "Maximum Split of Positive Even Integers",
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            "content": "<p>You are given an integer <code>finalSum</code>. Split it into a sum of a <strong>maximum</strong> number of <strong>unique</strong> positive even integers.</p>\n\n<ul>\n\t<li>For example, given <code>finalSum = 12</code>, the following splits are <strong>valid</strong> (unique positive even integers summing up to <code>finalSum</code>): <code>(12)</code>, <code>(2 + 10)</code>, <code>(2 + 4 + 6)</code>, and <code>(4 + 8)</code>. Among them, <code>(2 + 4 + 6)</code> contains the maximum number of integers. Note that <code>finalSum</code> cannot be split into <code>(2 + 2 + 4 + 4)</code> as all the numbers should be unique.</li>\n</ul>\n\n<p>Return <em>a list of integers that represent a valid split containing a <strong>maximum</strong> number of integers</em>. If no valid split exists for <code>finalSum</code>, return <em>an <strong>empty</strong> list</em>. You may return the integers in <strong>any</strong> order.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> finalSum = 12\n<strong>Output:</strong> [2,4,6]\n<strong>Explanation:</strong> The following are valid splits: <code>(12)</code>, <code>(2 + 10)</code>, <code>(2 + 4 + 6)</code>, and <code>(4 + 8)</code>.\n(2 + 4 + 6) has the maximum number of integers, which is 3. Thus, we return [2,4,6].\nNote that [2,6,4], [6,2,4], etc. are also accepted.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> finalSum = 7\n<strong>Output:</strong> []\n<strong>Explanation:</strong> There are no valid splits for the given finalSum.\nThus, we return an empty array.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> finalSum = 28\n<strong>Output:</strong> [6,8,2,12]\n<strong>Explanation:</strong> The following are valid splits: <code>(2 + 26)</code>, <code>(6 + 8 + 2 + 12)</code>, and <code>(4 + 24)</code>. \n<code>(6 + 8 + 2 + 12)</code> has the maximum number of integers, which is 4. Thus, we return [6,8,2,12].\nNote that [10,2,4,12], [6,2,4,16], etc. are also accepted.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= finalSum &lt;= 10<sup>10</sup></code></li>\n</ul>\n",
            "translatedTitle": "拆分成最多数目的正偶数之和",
            "translatedContent": "<p>给你一个整数&nbsp;<code>finalSum</code>&nbsp;。请你将它拆分成若干个&nbsp;<strong>互不相同</strong> 的正偶数之和，且拆分出来的正偶数数目&nbsp;<strong>最多</strong>&nbsp;。</p>\n\n<ul>\n\t<li>比方说，给你&nbsp;<code>finalSum = 12</code>&nbsp;，那么这些拆分是&nbsp;<strong>符合要求</strong> 的（互不相同的正偶数且和为&nbsp;<code>finalSum</code>）：<code>(2 + 10)</code>&nbsp;，<code>(2 + 4 + 6)</code>&nbsp;和&nbsp;<code>(4 + 8)</code>&nbsp;。它们中，<code>(2 + 4 + 6)</code>&nbsp;包含最多数目的整数。注意&nbsp;<code>finalSum</code>&nbsp;不能拆分成&nbsp;<code>(2 + 2 + 4 + 4)</code>&nbsp;，因为拆分出来的整数必须互不相同。</li>\n</ul>\n\n<p>请你返回一个整数数组，表示将整数拆分成 <strong>最多</strong> 数目的正偶数数组。如果没有办法将&nbsp;<code>finalSum</code>&nbsp;进行拆分，请你返回一个&nbsp;<strong>空</strong>&nbsp;数组。你可以按 <b>任意</b>&nbsp;顺序返回这些整数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>finalSum = 12\n<b>输出：</b>[2,4,6]\n<b>解释：</b>以下是一些符合要求的拆分：<code>(2 + 10)<span style=\"\">，</span></code><code>(2 + 4 + 6) </code>和 <code>(4 + 8) 。</code>\n(2 + 4 + 6) 为最多数目的整数，数目为 3 ，所以我们返回 [2,4,6] 。\n[2,6,4] ，[6,2,4] 等等也都是可行的解。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>finalSum = 7\n<b>输出：</b>[]\n<b>解释：</b>没有办法将 finalSum 进行拆分。\n所以返回空数组。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>finalSum = 28\n<b>输出：</b>[6,8,2,12]\n<b>解释：</b>以下是一些符合要求的拆分：<code>(2 + 26)<span style=\"\">，</span></code><code>(6 + 8 + 2 + 12)</code> 和 <code>(4 + 24) 。</code>\n<code>(6 + 8 + 2 + 12)</code> 有最多数目的整数，数目为 4 ，所以我们返回 [6,8,2,12] 。\n[10,2,4,12] ，[6,2,4,16] 等等也都是可行的解。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= finalSum &lt;= 10<sup>10</sup></code></li>\n</ul>\n",
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                "First, check if finalSum is divisible by 2. If it isn’t, then we cannot split it into even integers.",
                "Let k be the number of elements in our split. As we want the maximum number of elements, we should try to use the first k - 1 even elements to grow our sum as slowly as possible.",
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