leetcode-problemset/leetcode-cn/originData/gcd-sort-of-an-array.json

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            "title": "GCD Sort of an Array",
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            "content": "<p>You are given an integer array <code>nums</code>, and you can perform the following operation <strong>any</strong> number of times on <code>nums</code>:</p>\n\n<ul>\n\t<li>Swap the positions of two elements <code>nums[i]</code> and <code>nums[j]</code> if <code>gcd(nums[i], nums[j]) &gt; 1</code> where <code>gcd(nums[i], nums[j])</code> is the <strong>greatest common divisor</strong> of <code>nums[i]</code> and <code>nums[j]</code>.</li>\n</ul>\n\n<p>Return <code>true</code> <em>if it is possible to sort </em><code>nums</code><em> in <strong>non-decreasing</strong> order using the above swap method, or </em><code>false</code><em> otherwise.</em></p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [7,21,3]\n<strong>Output:</strong> true\n<strong>Explanation:</strong> We can sort [7,21,3] by performing the following operations:\n- Swap 7 and 21 because gcd(7,21) = 7. nums = [<u><strong>21</strong></u>,<u><strong>7</strong></u>,3]\n- Swap 21 and 3 because gcd(21,3) = 3. nums = [<u><strong>3</strong></u>,7,<u><strong>21</strong></u>]\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,2,6,2]\n<strong>Output:</strong> false\n<strong>Explanation:</strong> It is impossible to sort the array because 5 cannot be swapped with any other element.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [10,5,9,3,15]\n<strong>Output:</strong> true\nWe can sort [10,5,9,3,15] by performing the following operations:\n- Swap 10 and 15 because gcd(10,15) = 5. nums = [<u><strong>15</strong></u>,5,9,3,<u><strong>10</strong></u>]\n- Swap 15 and 3 because gcd(15,3) = 3. nums = [<u><strong>3</strong></u>,5,9,<u><strong>15</strong></u>,10]\n- Swap 10 and 15 because gcd(10,15) = 5. nums = [3,5,9,<u><strong>10</strong></u>,<u><strong>15</strong></u>]\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;= 3 * 10<sup>4</sup></code></li>\n\t<li><code>2 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "数组的最大公因数排序",
            "translatedContent": "<p>给你一个整数数组 <code>nums</code> ，你可以在 <code>nums</code> 上执行下述操作 <strong>任意次</strong> ：</p>\n\n<ul>\n\t<li>如果 <code>gcd(nums[i], nums[j]) &gt; 1</code> ，交换 <code>nums[i]</code> 和 <code>nums[j]</code> 的位置。其中 <code>gcd(nums[i], nums[j])</code> 是&nbsp;<code>nums[i]</code> 和 <code>nums[j]</code> 的最大公因数。</li>\n</ul>\n\n<p>如果能使用上述交换方式将 <code>nums</code> 按 <strong>非递减顺序</strong> 排列，返回 <code>true</code> ；否则，返回 <code>false</code> 。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>nums = [7,21,3]\n<strong>输出：</strong>true\n<strong>解释：</strong>可以执行下述操作完成对 [7,21,3] 的排序：\n- 交换 7 和 21 因为 gcd(7,21) = 7 。nums = [<em><strong>21</strong></em>,<em><strong>7</strong></em>,3]\n- 交换 21 和 3 因为 gcd(21,3) = 3 。nums = [<em><strong>3</strong></em>,7,<em><strong>21</strong></em>]\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>nums = [5,2,6,2]\n<strong>输出：</strong>false\n<strong>解释：</strong>无法完成排序，因为 5 不能与其他元素交换。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre><strong>输入：</strong>nums = [10,5,9,3,15]\n<strong>输出：</strong>true\n<strong>解释：</strong>\n可以执行下述操作完成对 [10,5,9,3,15] 的排序：\n- 交换 10 和 15 因为 gcd(10,15) = 5 。nums = [<em><strong>15</strong></em>,5,9,3,<em><strong>10</strong></em>]\n- 交换 15 和 3 因为 gcd(15,3) = 3 。nums = [<em><strong>3</strong></em>,5,9,<em><strong>15</strong></em>,10]\n- 交换 10 和 15 因为 gcd(10,15) = 5 。nums = [3,5,9,<em><strong>10</strong></em>,<em><strong>15</strong></em>]\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;= 3 * 10<sup>4</sup></code></li>\n\t<li><code>2 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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