How hard is LeetCode 2572. Count the Number of Square-Free Subsets?

LeetCode 2572. Count the Number of Square-Free Subsets is rated Medium on LeetCode.

What is the time complexity of LeetCode 2572. Count the Number of Square-Free Subsets?

The Python solution on this page runs in O(n + C \times M).

What is the space complexity of LeetCode 2572. Count the Number of Square-Free Subsets?

The Python solution on this page uses O(M) auxiliary space.

What topics does LeetCode 2572. Count the Number of Square-Free Subsets cover?

LeetCode 2572. Count the Number of Square-Free Subsets is tagged Bit Manipulation, Array, Math, Dynamic Programming and Bitmask on LeetCode.

Count the Number of Square-Free Subsets — LeetCode 2572 Python Solution

MediumBit ManipulationArrayMathDynamic ProgrammingBitmask

Problem: #2572
Pattern: Bit Manipulation
Reading time: 4 min
Source: leetcode.com

The problem

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.

Example

Input: nums = [3,4,4,5]
Output: 3
Explanation: There are 3 square-free subsets in this example:

Python solution

Python

class Solution:
    def squareFreeSubsets(self, nums: List[int]) -> int:
        primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
        cnt = Counter(nums)
        mod = 10**9 + 7
        n = len(primes)
        f = [0] * (1 << n)
        f[0] = pow(2, cnt[1])
        for x in range(2, 31):
            if cnt[x] == 0 or x % 4 == 0 or x % 9 == 0 or x % 25 == 0:
                continue
            mask = 0
            for i, p in enumerate(primes):
                if x % p == 0:
                    mask |= 1 << i
            for state in range((1 << n) - 1, 0, -1):
                if state & mask == mask:
                    f[state] = (f[state] + cnt[x] * f[state ^ mask]) % mod
        return sum(v for v in f) % mod - 1

Complexity

Measure	Complexity
Time	O(n + C \times M)
Space	O(M) auxiliary

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 2572. Count the Number of Square-Free Subsets is filed here because LeetCode tags it Bit Manipulation and Bitmask, which is the vocabulary this hub collects.

The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 2572. Count the Number of Square-Free Subsets?: LeetCode 2572. Count the Number of Square-Free Subsets is rated Medium on LeetCode.
What is the time complexity of LeetCode 2572. Count the Number of Square-Free Subsets?: The Python solution on this page runs in O(n + C \times M).
What is the space complexity of LeetCode 2572. Count the Number of Square-Free Subsets?: The Python solution on this page uses O(M) auxiliary space.
What topics does LeetCode 2572. Count the Number of Square-Free Subsets cover?: LeetCode 2572. Count the Number of Square-Free Subsets is tagged Bit Manipulation, Array, Math, Dynamic Programming and Bitmask on LeetCode.