MediumNo. 2572
Count the Number of Square-Free Subsets — LeetCode 2572 Python Solution
- Pattern
- Bit Manipulation
- Topics
- Bit Manipulation, Array, Math, Dynamic Programming, Bitmask
- 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
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 - 1Complexity
- Time
- O(n + C × M)
- Space · auxiliary
- O(M)
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.
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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 × 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.