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53 lines
2.4 KiB
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53 lines
2.4 KiB
HTML
<p>You are given a positive integer <code>p</code>. Consider an array <code>nums</code> (<strong>1-indexed</strong>) that consists of the integers in the <strong>inclusive</strong> range <code>[1, 2<sup>p</sup> - 1]</code> in their binary representations. You are allowed to do the following operation <strong>any</strong> number of times:</p>
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<ul>
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<li>Choose two elements <code>x</code> and <code>y</code> from <code>nums</code>.</li>
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<li>Choose a bit in <code>x</code> and swap it with its corresponding bit in <code>y</code>. Corresponding bit refers to the bit that is in the <strong>same position</strong> in the other integer.</li>
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</ul>
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<p>For example, if <code>x = 11<u>0</u>1</code> and <code>y = 00<u>1</u>1</code>, after swapping the <code>2<sup>nd</sup></code> bit from the right, we have <code>x = 11<u>1</u>1</code> and <code>y = 00<u>0</u>1</code>.</p>
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<p>Find the <strong>minimum non-zero</strong> product of <code>nums</code> after performing the above operation <strong>any</strong> number of times. Return <em>this product</em><em> <strong>modulo</strong> </em><code>10<sup>9</sup> + 7</code>.</p>
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<p><strong>Note:</strong> The answer should be the minimum product <strong>before</strong> the modulo operation is done.</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> p = 1
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> nums = [1].
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There is only one element, so the product equals that element.
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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> p = 2
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<strong>Output:</strong> 6
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<strong>Explanation:</strong> nums = [01, 10, 11].
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Any swap would either make the product 0 or stay the same.
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Thus, the array product of 1 * 2 * 3 = 6 is already minimized.
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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> p = 3
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<strong>Output:</strong> 1512
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<strong>Explanation:</strong> nums = [001, 010, 011, 100, 101, 110, 111]
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- In the first operation we can swap the leftmost bit of the second and fifth elements.
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- The resulting array is [001, <u>1</u>10, 011, 100, <u>0</u>01, 110, 111].
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- In the second operation we can swap the middle bit of the third and fourth elements.
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- The resulting array is [001, 110, 0<u>0</u>1, 1<u>1</u>0, 001, 110, 111].
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The array product is 1 * 6 * 1 * 6 * 1 * 6 * 7 = 1512, which is the minimum possible product.
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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 <= p <= 60</code></li>
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</ul>
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