Class Solution
java.lang.Object
g1901_2000.s1994_the_number_of_good_subsets.Solution
1994 - The Number of Good Subsets.<p>Hard</p>
<p>You are given an integer array <code>nums</code>. We call a subset of <code>nums</code> <strong>good</strong> if its product can be represented as a product of one or more <strong>distinct prime</strong> numbers.</p>
<ul>
<li>For example, if <code>nums = [1, 2, 3, 4]</code>:
<ul>
<li><code>[2, 3]</code>, <code>[1, 2, 3]</code>, and <code>[1, 3]</code> are <strong>good</strong> subsets with products <code>6 = 2*3</code>, <code>6 = 2*3</code>, and <code>3 = 3</code> respectively.</li>
<li><code>[1, 4]</code> and <code>[4]</code> are not <strong>good</strong> subsets with products <code>4 = 2*2</code> and <code>4 = 2*2</code> respectively.</li>
</ul>
</li>
</ul>
<p>Return <em>the number of different <strong>good</strong> subsets in</em> <code>nums</code> <em><strong>modulo</strong></em> <code>10<sup>9</sup> + 7</code>.</p>
<p>A <strong>subset</strong> of <code>nums</code> is any array that can be obtained by deleting some (possibly none or all) elements from <code>nums</code>. Two subsets are different if and only if the chosen indices to delete are different.</p>
<p><strong>Example 1:</strong></p>
<p><strong>Input:</strong> nums = [1,2,3,4]</p>
<p><strong>Output:</strong> 6</p>
<p><strong>Explanation:</strong> The good subsets are:</p>
<ul>
<li>
<p>[1,2]: product is 2, which is the product of distinct prime 2.</p>
</li>
<li>
<p>[1,2,3]: product is 6, which is the product of distinct primes 2 and 3.</p>
</li>
<li>
<p>[1,3]: product is 3, which is the product of distinct prime 3.</p>
</li>
<li>
<p>[2]: product is 2, which is the product of distinct prime 2.</p>
</li>
<li>
<p>[2,3]: product is 6, which is the product of distinct primes 2 and 3.</p>
</li>
<li>
<p>[3]: product is 3, which is the product of distinct prime 3.</p>
</li>
</ul>
<p><strong>Example 2:</strong></p>
<p><strong>Input:</strong> nums = [4,2,3,15]</p>
<p><strong>Output:</strong> 5</p>
<p><strong>Explanation:</strong> The good subsets are:</p>
<ul>
<li>
<p>[2]: product is 2, which is the product of distinct prime 2.</p>
</li>
<li>
<p>[2,3]: product is 6, which is the product of distinct primes 2 and 3.</p>
</li>
<li>
<p>[2,15]: product is 30, which is the product of distinct primes 2, 3, and 5.</p>
</li>
<li>
<p>[3]: product is 3, which is the product of distinct prime 3.</p>
</li>
<li>
<p>[15]: product is 15, which is the product of distinct primes 3 and 5.</p>
</li>
</ul>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>
<li><code>1 <= nums[i] <= 30</code></li>
</ul>
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Solution
public Solution()
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Method Details
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numberOfGoodSubsets
public int numberOfGoodSubsets(int[] nums)
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