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2741. Special Permutations

Description

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.

Return the total number of special permutations. As the answer could be large, return it modulo 109 + 7.

 

Example 1:

Input: nums = [2,3,6]
Output: 2
Explanation: [3,6,2] and [2,6,3] are the two special permutations of nums.

Example 2:

Input: nums = [1,4,3]
Output: 2
Explanation: [3,1,4] and [4,1,3] are the two special permutations of nums.

 

Constraints:

  • 2 <= nums.length <= 14
  • 1 <= nums[i] <= 109

Solutions

  • class Solution {
    public int specialPerm(int[] nums) {
        final int mod = (int) 1e9 + 7;
        int n = nums.length;
        int m = 1 << n;
        int[][] f = new int[m][n];
        for (int i = 1; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if ((i >> j & 1) == 1) {
                    int ii = i ^ (1 << j);
                    if (ii == 0) {
                        f[i][j] = 1;
                        continue;
                    }
                    for (int k = 0; k < n; ++k) {
                        if (nums[j] % nums[k] == 0 || nums[k] % nums[j] == 0) {
                            f[i][j] = (f[i][j] + f[ii][k]) % mod;
                        }
                    }
                }
            }
        }
        int ans = 0;
        for (int x : f[m - 1]) {
            ans = (ans + x) % mod;
        }
        return ans;
    }
}

  • class Solution {
public:
    int specialPerm(vector<int>& nums) {
        const int mod = 1e9 + 7;
        int n = nums.size();
        int m = 1 << n;
        int f[m][n];
        memset(f, 0, sizeof(f));
        for (int i = 1; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if ((i >> j & 1) == 1) {
                    int ii = i ^ (1 << j);
                    if (ii == 0) {
                        f[i][j] = 1;
                        continue;
                    }
                    for (int k = 0; k < n; ++k) {
                        if (nums[j] % nums[k] == 0 || nums[k] % nums[j] == 0) {
                            f[i][j] = (f[i][j] + f[ii][k]) % mod;
                        }
                    }
                }
            }
        }
        int ans = 0;
        for (int x : f[m - 1]) {
            ans = (ans + x) % mod;
        }
        return ans;
    }
};

  • 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


  • func specialPerm(nums []int) (ans int) {
	const mod int = 1e9 + 7
	n := len(nums)
	m := 1 << n
	f := make([][]int, m)
	for i := range f {
		f[i] = make([]int, n)
	}
	for i := 1; i < m; i++ {
		for j, x := range nums {
			if i>>j&1 == 1 {
				ii := i ^ (1 << j)
				if ii == 0 {
					f[i][j] = 1
					continue
				}
				for k, y := range nums {
					if x%y == 0 || y%x == 0 {
						f[i][j] = (f[i][j] + f[ii][k]) % mod
					}
				}
			}
		}
	}
	for _, x := range f[m-1] {
		ans = (ans + x) % mod
	}
	return
}

  • function specialPerm(nums: number[]): number {
    const mod = 1e9 + 7;
    const n = nums.length;
    const m = 1 << n;
    const f = Array.from({ length: m }, () => Array(n).fill(0));

    for (let i = 1; i < m; ++i) {
        for (let j = 0; j < n; ++j) {
            if (((i >> j) & 1) === 1) {
                const ii = i ^ (1 << j);
                if (ii === 0) {
                    f[i][j] = 1;
                    continue;
                }
                for (let k = 0; k < n; ++k) {
                    if (nums[j] % nums[k] === 0 || nums[k] % nums[j] === 0) {
                        f[i][j] = (f[i][j] + f[ii][k]) % mod;
                    }
                }
            }
        }
    }

    return f[m - 1].reduce((acc, x) => (acc + x) % mod);
}


  • impl Solution {
    pub fn special_perm(nums: Vec<i32>) -> i32 {
        const MOD: i32 = 1_000_000_007;
        let n = nums.len();
        let m = 1 << n;
        let mut f = vec![vec![0; n]; m];

        for i in 1..m {
            for j in 0..n {
                if (i >> j) & 1 == 1 {
                    let ii = i ^ (1 << j);
                    if ii == 0 {
                        f[i][j] = 1;
                        continue;
                    }
                    for k in 0..n {
                        if nums[j] % nums[k] == 0 || nums[k] % nums[j] == 0 {
                            f[i][j] = (f[i][j] + f[ii][k]) % MOD;
                        }
                    }
                }
            }
        }

        let mut ans = 0;
        for &x in &f[m - 1] {
            ans = (ans + x) % MOD;
        }

        ans
    }
}

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