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"categoryTitle": "Algorithms",
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"title": "Valid Arrangement of Pairs",
"titleSlug": "valid-arrangement-of-pairs",
"content": "<p>You are given a <strong>0-indexed</strong> 2D integer array <code>pairs</code> where <code>pairs[i] = [start<sub>i</sub>, end<sub>i</sub>]</code>. An arrangement of <code>pairs</code> is <strong>valid</strong> if for every index <code>i</code> where <code>1 &lt;= i &lt; pairs.length</code>, we have <code>end<sub>i-1</sub> == start<sub>i</sub></code>.</p>\n\n<p>Return <em><strong>any</strong> valid arrangement of </em><code>pairs</code>.</p>\n\n<p><strong>Note:</strong> The inputs will be generated such that there exists a valid arrangement of <code>pairs</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> pairs = [[5,1],[4,5],[11,9],[9,4]]\n<strong>Output:</strong> [[11,9],[9,4],[4,5],[5,1]]\n<strong>Explanation:\n</strong>This is a valid arrangement since end<sub>i-1</sub> always equals start<sub>i</sub>.\nend<sub>0</sub> = 9 == 9 = start<sub>1</sub> \nend<sub>1</sub> = 4 == 4 = start<sub>2</sub>\nend<sub>2</sub> = 5 == 5 = start<sub>3</sub>\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> pairs = [[1,3],[3,2],[2,1]]\n<strong>Output:</strong> [[1,3],[3,2],[2,1]]\n<strong>Explanation:</strong>\nThis is a valid arrangement since end<sub>i-1</sub> always equals start<sub>i</sub>.\nend<sub>0</sub> = 3 == 3 = start<sub>1</sub>\nend<sub>1</sub> = 2 == 2 = start<sub>2</sub>\nThe arrangements [[2,1],[1,3],[3,2]] and [[3,2],[2,1],[1,3]] are also valid.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> pairs = [[1,2],[1,3],[2,1]]\n<strong>Output:</strong> [[1,2],[2,1],[1,3]]\n<strong>Explanation:</strong>\nThis is a valid arrangement since end<sub>i-1</sub> always equals start<sub>i</sub>.\nend<sub>0</sub> = 2 == 2 = start<sub>1</sub>\nend<sub>1</sub> = 1 == 1 = start<sub>2</sub>\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= pairs.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>pairs[i].length == 2</code></li>\n\t<li><code>0 &lt;= start<sub>i</sub>, end<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n\t<li><code>start<sub>i</sub> != end<sub>i</sub></code></li>\n\t<li>No two pairs are exactly the same.</li>\n\t<li>There <strong>exists</strong> a valid arrangement of <code>pairs</code>.</li>\n</ul>\n",
"translatedTitle": "合法重新排列数对",
"translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始的二维整数数组&nbsp;<code>pairs</code>&nbsp;,其中&nbsp;<code>pairs[i] = [start<sub>i</sub>, end<sub>i</sub>]</code>&nbsp;。如果 <code>pairs</code>&nbsp;的一个重新排列,满足对每一个下标 <code>i</code> &nbsp;<code>1 &lt;= i &lt; pairs.length</code>&nbsp;)都有&nbsp;<code>end<sub>i-1</sub> == start<sub>i</sub></code><sub> </sub>,那么我们就认为这个重新排列是&nbsp;<code>pairs</code> 的一个 <strong>合法重新排列</strong> 。</p>\n\n<p>请你返回 <strong>任意一个</strong>&nbsp;<code>pairs</code> 的合法重新排列。</p>\n\n<p><b>注意:</b>数据保证至少存在一个 <code>pairs</code>&nbsp;的合法重新排列。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre>\n<b>输入:</b>pairs = [[5,1],[4,5],[11,9],[9,4]]\n<b>输出:</b>[[11,9],[9,4],[4,5],[5,1]]\n<strong>解释:\n</strong>输出的是一个合法重新排列,因为每一个 end<sub>i-1</sub> 都等于 start<sub>i</sub>&nbsp;。\nend<sub>0</sub> = 9 == 9 = start<sub>1</sub> \nend<sub>1</sub> = 4 == 4 = start<sub>2</sub>\nend<sub>2</sub> = 5 == 5 = start<sub>3</sub>\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre>\n<b>输入:</b>pairs = [[1,3],[3,2],[2,1]]\n<b>输出:</b>[[1,3],[3,2],[2,1]]\n<strong>解释:</strong>\n输出的是一个合法重新排列因为每一个 end<sub>i-1</sub> 都等于 start<sub>i</sub>&nbsp;。\nend<sub>0</sub> = 3 == 3 = start<sub>1</sub>\nend<sub>1</sub> = 2 == 2 = start<sub>2</sub>\n重新排列后的数组 [[2,1],[1,3],[3,2]] 和 [[3,2],[2,1],[1,3]] 都是合法的。\n</pre>\n\n<p><strong>示例 3</strong></p>\n\n<pre>\n<b>输入:</b>pairs = [[1,2],[1,3],[2,1]]\n<b>输出:</b>[[1,2],[2,1],[1,3]]\n<strong>解释:</strong>\n输出的是一个合法重新排列因为每一个 end<sub>i-1</sub> 都等于 start<sub>i</sub>&nbsp;。\nend<sub>0</sub> = 2 == 2 = start<sub>1</sub>\nend<sub>1</sub> = 1 == 1 = start<sub>2</sub>\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= pairs.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>pairs[i].length == 2</code></li>\n\t<li><code>0 &lt;= start<sub>i</sub>, end<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n\t<li><code>start<sub>i</sub> != end<sub>i</sub></code></li>\n\t<li><code>pairs</code>&nbsp;中不存在一模一样的数对。</li>\n\t<li>至少 <strong>存在</strong> 一个合法的&nbsp;<code>pairs</code>&nbsp;重新排列。</li>\n</ul>\n",
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"Could you convert this into a graph problem?",
"Consider the pairs as edges and each number as a node.",
"We have to find an Eulerian path of this graph. Hierholzers algorithm can be used."
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