Special Permutations — LeetCode 2741 Python Solution

The problem

You are given a 0-indexed integer array nums containing n distinct positive integers. A permutation of nums is called special if: For all indexes 0 <= i < n - 1, either nums[i] % nums[i+1] == 0 or nums[i+1] % nums[i] == 0.

Example

Input

nums = [2,3,6]

Output

2

Explanation

[3,6,2] and [2,6,3] are the two special permutations of nums.

Python solution

class Solution:
    def specialPerm(self, nums: List[int]) -> int:
        mod = 10**9 + 7
        n = len(nums)
        m = 1 << n
        f = [[0] * n for _ in range(m)]
        for i in range(1, m):
            for j, x in enumerate(nums):
                if i >> j & 1:
                    ii = i ^ (1 << j)
                    if ii == 0:
                        f[i][j] = 1
                        continue
                    for k, y in enumerate(nums):
                        if x % y == 0 or y % x == 0:
                            f[i][j] = (f[i][j] + f[ii][k]) % mod
        return sum(f[-1]) % mod

Complexity

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 2741. Special Permutations 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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