Package g1901_2000.s1994_the_number_of_good_subsets

Class Solution

java.lang.Object
g1901_2000.s1994_the_number_of_good_subsets.Solution
public class Solution extends java.lang.Object
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]:
    • [2, 3], [1, 2, 3], and [1, 3] are good subsets with products 6 = 2*3, 6 = 2*3, and 3 = 3 respectively.
    • [1, 4] and [4] are not good subsets with products 4 = 2*2 and 4 = 2*2 respectively.

Return the number of different good subsets in nums modulo 109 + 7.

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:

  • 1 <= nums.length <= 105
  • 1 <= nums[i] <= 30

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    numberOfGoodSubsets(int[] nums)
     

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • numberOfGoodSubsets

      public int numberOfGoodSubsets(int[] nums)