Package g2501_2600.s2572_count_the_number_of_square_free_subsets

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    2572 - Count the Number of Square-Free Subsets.

    Medium

    You are given a positive integer 0-indexed array nums.

    A subset of the array nums is square-free if the product of its elements is a square-free integer.

    A square-free integer is an integer that is divisible by no square number other than 1.

    Return the number of square-free non-empty subsets of the array nums. Since the answer may be too large, return it modulo <code>10<sup>9</sup> + 7</code>.

    A non-empty subset of nums is an array that can be obtained by deleting some (possibly none but not all) elements from nums. Two subsets are different if and only if the chosen indices to delete are different.

    Example 1:

    Input: nums = 3,4,4,5

    Output: 3

    Explanation: There are 3 square-free subsets in this example:

    • The subset consisting of the 0<sup>th</sup> element 3. The product of its elements is 3, which is a square-free integer.

    • The subset consisting of the 3<sup>rd</sup> element 5. The product of its elements is 5, which is a square-free integer.

    • The subset consisting of 0<sup>th</sup> and 3<sup>rd</sup> elements 3,5. The product of its elements is 15, which is a square-free integer.

    It can be proven that there are no more than 3 square-free subsets in the given array.

    Example 2:

    Input: nums = 1

    Output: 1

    Explanation: There is 1 square-free subset in this example:

    • The subset consisting of the 0<sup>th</sup> element 1. The product of its elements is 1, which is a square-free integer.

    It can be proven that there is no more than 1 square-free subset in the given array.

    Constraints:

    • 1 &lt;= nums.length &lt;= 1000

    • 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 squareFreeSubsets(IntArray nums)

      • Methods inherited from class java.lang.Object

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