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46 lines
2.3 KiB
HTML
46 lines
2.3 KiB
HTML
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<p>You are given a <strong>0-indexed</strong> array of <strong>positive</strong> integers <code>nums</code>.</p>
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<p>In one <strong>operation</strong>, you can swap any two <strong>adjacent</strong> elements if they have the <strong>same</strong> number of <span data-keyword="set-bit">set bits</span>. You are allowed to do this operation <strong>any</strong> number of times (<strong>including zero</strong>).</p>
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<p>Return <code>true</code> <em>if you can sort the array, else return </em><code>false</code>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [8,4,2,30,15]
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<strong>Output:</strong> true
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<strong>Explanation:</strong> Let's look at the binary representation of every element. The numbers 2, 4, and 8 have one set bit each with binary representation "10", "100", and "1000" respectively. The numbers 15 and 30 have four set bits each with binary representation "1111" and "11110".
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We can sort the array using 4 operations:
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- Swap nums[0] with nums[1]. This operation is valid because 8 and 4 have one set bit each. The array becomes [4,8,2,30,15].
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- Swap nums[1] with nums[2]. This operation is valid because 8 and 2 have one set bit each. The array becomes [4,2,8,30,15].
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- Swap nums[0] with nums[1]. This operation is valid because 4 and 2 have one set bit each. The array becomes [2,4,8,30,15].
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- Swap nums[3] with nums[4]. This operation is valid because 30 and 15 have four set bits each. The array becomes [2,4,8,15,30].
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The array has become sorted, hence we return true.
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Note that there may be other sequences of operations which also sort the array.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [1,2,3,4,5]
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<strong>Output:</strong> true
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<strong>Explanation:</strong> The array is already sorted, hence we return true.
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [3,16,8,4,2]
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<strong>Output:</strong> false
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<strong>Explanation:</strong> It can be shown that it is not possible to sort the input array using any number of operations.
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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 <= 100</code></li>
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<li><code>1 <= nums[i] <= 2<sup>8</sup></code></li>
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</ul>
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