Solution: The Number of Good Subsets

Understand how to use dynamic programming with bitmasking to count subsets whose product has distinct prime factors. Explore the concept of square-free numbers, frequency mapping, and efficient state transitions to handle large input arrays. This lesson teaches you to implement a solution that balances time and space complexity while solving complex subset problems.

We'll cover the following...

Statement
Solution
- Time complexity
- Space complexity

Statement

For a given integer array, nums, you can say that a subset of nums is called “good” if the product of its elements can be expressed as a product of one or more distinct prime numbers, i.e., no prime factor appears more than once.

For example, if nums $= [1, 2, 5, 6]$ , then:

$[2, 5]$ , $[1, 2, 5]$ , and $[6]$ are good subsets with products $2 \times 5 = 10$ , $1 \times 2 \times 5 = 10$ , and $2 \times 3 = 6$ , respectively.
$[2, 6]$ ...