Package g1901_2000.s1994_the_number_of_good_subsets

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    1994 - The Number of Good Subsets.

    Hard

    You are given an integer array nums. We call a subset of nums good if its product can be represented as a product of one or more distinct prime numbers.

    • For example, if nums = [1, 2, 3, 4]:

    Return the number of different good subsets in nums modulo <code>10<sup>9</sup> + 7</code>.

    A subset of nums is any array that can be obtained by deleting some (possibly none or all) elements from nums. Two subsets are different if and only if the chosen indices to delete are different.

    Example 1:

    Input: nums = 1,2,3,4

    Output: 6

    Explanation: The good subsets are:

    • 1,2: product is 2, which is the product of distinct prime 2.

    • 1,2,3: product is 6, which is the product of distinct primes 2 and 3.

    • 1,3: product is 3, which is the product of distinct prime 3.

    • 2: product is 2, which is the product of distinct prime 2.

    • 2,3: product is 6, which is the product of distinct primes 2 and 3.

    • 3: product is 3, which is the product of distinct prime 3.

    Example 2:

    Input: nums = 4,2,3,15

    Output: 5

    Explanation: The good subsets are:

    • 2: product is 2, which is the product of distinct prime 2.

    • 2,3: product is 6, which is the product of distinct primes 2 and 3.

    • 2,15: product is 30, which is the product of distinct primes 2, 3, and 5.

    • 3: product is 3, which is the product of distinct prime 3.

    • 15: product is 15, which is the product of distinct primes 3 and 5.

    Constraints:

    • <code>1 <= nums.length <= 10<sup>5</sup></code>

    • 1 &lt;= nums[i] &lt;= 30

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Integer numberOfGoodSubsets(IntArray nums)

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait