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"question": {
"questionId": "1819",
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"categoryTitle": "Algorithms",
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"title": "Construct the Lexicographically Largest Valid Sequence",
"titleSlug": "construct-the-lexicographically-largest-valid-sequence",
"content": "<p>Given an integer <code>n</code>, find a sequence that satisfies all of the following:</p>\n\n<ul>\n\t<li>The integer <code>1</code> occurs once in the sequence.</li>\n\t<li>Each integer between <code>2</code> and <code>n</code> occurs twice in the sequence.</li>\n\t<li>For every integer <code>i</code> between <code>2</code> and <code>n</code>, the <strong>distance</strong> between the two occurrences of <code>i</code> is exactly <code>i</code>.</li>\n</ul>\n\n<p>The <strong>distance</strong> between two numbers on the sequence, <code>a[i]</code> and <code>a[j]</code>, is the absolute difference of their indices, <code>|j - i|</code>.</p>\n\n<p>Return <em>the <strong>lexicographically largest</strong> sequence</em><em>. It is guaranteed that under the given constraints, there is always a solution. </em></p>\n\n<p>A sequence <code>a</code> is lexicographically larger than a sequence <code>b</code> (of the same length) if in the first position where <code>a</code> and <code>b</code> differ, sequence <code>a</code> has a number greater than the corresponding number in <code>b</code>. For example, <code>[0,1,9,0]</code> is lexicographically larger than <code>[0,1,5,6]</code> because the first position they differ is at the third number, and <code>9</code> is greater than <code>5</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3\n<strong>Output:</strong> [3,1,2,3,2]\n<strong>Explanation:</strong> [2,3,2,1,3] is also a valid sequence, but [3,1,2,3,2] is the lexicographically largest valid sequence.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5\n<strong>Output:</strong> [5,3,1,4,3,5,2,4,2]\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 20</code></li>\n</ul>\n",
"translatedTitle": "构建字典序最大的可行序列",
"translatedContent": "<p>给你一个整数 <code>n</code> ,请你找到满足下面条件的一个序列:</p>\n\n<ul>\n\t<li>整数 <code>1</code> 在序列中只出现一次。</li>\n\t<li><code>2</code> 到 <code>n</code> 之间每个整数都恰好出现两次。</li>\n\t<li>对于每个 <code>2</code> 到 <code>n</code> 之间的整数 <code>i</code> ,两个 <code>i</code> 之间出现的距离恰好为 <code>i</code> 。</li>\n</ul>\n\n<p>序列里面两个数 <code>a[i]</code> 和 <code>a[j]</code> 之间的 <strong>距离</strong> ,我们定义为它们下标绝对值之差 <code>|j - i|</code> 。</p>\n\n<p>请你返回满足上述条件中 <strong>字典序最大</strong> 的序列。题目保证在给定限制条件下,一定存在解。</p>\n\n<p>一个序列 <code>a</code> 被认为比序列 <code>b</code> (两者长度相同)字典序更大的条件是: <code>a</code> 和 <code>b</code> 中第一个不一样的数字处,<code>a</code> 序列的数字比 <code>b</code> 序列的数字大。比方说,<code>[0,1,9,0]</code> 比 <code>[0,1,5,6]</code> 字典序更大,因为第一个不同的位置是第三个数字,且 <code>9</code> 比 <code>5</code> 大。</p>\n\n<p> </p>\n\n<p><strong>示例 1</strong></p>\n\n<pre><b>输入:</b>n = 3\n<b>输出:</b>[3,1,2,3,2]\n<b>解释:</b>[2,3,2,1,3] 也是一个可行的序列,但是 [3,1,2,3,2] 是字典序最大的序列。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre><b>输入:</b>n = 5\n<b>输出:</b>[5,3,1,4,3,5,2,4,2]\n</pre>\n\n<p> </p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 20</code></li>\n</ul>\n",
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