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46 lines
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46 lines
2.0 KiB
HTML
<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>
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<ul>
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<li>Swap the positions of two elements <code>nums[i]</code> and <code>nums[j]</code> if <code>gcd(nums[i], nums[j]) > 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>
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</ul>
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<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>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [7,21,3]
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<strong>Output:</strong> true
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<strong>Explanation:</strong> We can sort [7,21,3] by performing the following operations:
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- Swap 7 and 21 because gcd(7,21) = 7. nums = [<u><strong>21</strong></u>,<u><strong>7</strong></u>,3]
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- Swap 21 and 3 because gcd(21,3) = 3. nums = [<u><strong>3</strong></u>,7,<u><strong>21</strong></u>]
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [5,2,6,2]
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<strong>Output:</strong> false
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<strong>Explanation:</strong> It is impossible to sort the array because 5 cannot be swapped with any other element.
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [10,5,9,3,15]
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<strong>Output:</strong> true
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We can sort [10,5,9,3,15] by performing the following operations:
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- Swap 10 and 15 because gcd(10,15) = 5. nums = [<u><strong>15</strong></u>,5,9,3,<u><strong>10</strong></u>]
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- Swap 15 and 3 because gcd(15,3) = 3. nums = [<u><strong>3</strong></u>,5,9,<u><strong>15</strong></u>,10]
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- Swap 10 and 15 because gcd(10,15) = 5. nums = [3,5,9,<u><strong>10</strong></u>,<u><strong>15</strong></u>]
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= nums.length <= 3 * 10<sup>4</sup></code></li>
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<li><code>2 <= nums[i] <= 10<sup>5</sup></code></li>
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</ul>
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