526. Beautiful Arrangement

Suppose you have n integers labeled 1 through n. A permutation of those n integers perm (1-indexed) is considered a beautiful arrangement if for every i (1 <= i <= n), either of the following is true:

  • perm[i] is divisible by i.
  • i is divisible by perm[i].

Given an integer n, return the number of the beautiful arrangements that you can construct.

 

Example 1:

Input: n = 2
Output: 2
Explanation: 
The first beautiful arrangement is [1,2]:
    - perm[1] = 1 is divisible by i = 1
    - perm[2] = 2 is divisible by i = 2
The second beautiful arrangement is [2,1]:
    - perm[1] = 2 is divisible by i = 1
    - i = 2 is divisible by perm[2] = 1

Example 2:

Input: n = 1
Output: 1

 

Constraints:

  • 1 <= n <= 15

Rust Solution

struct Solution;

impl Solution {
    fn count_arrangement(n: i32) -> i32 {
        let mut res = 0;
        let mut nums = (1..=n).collect();
        let n = n as usize;
        Self::dfs(0, &mut nums, &mut res, n);
        res
    }

    fn dfs(start: usize, nums: &mut Vec<i32>, all: &mut i32, n: usize) {
        if start == n {
            *all += 1;
        } else {
            for i in start..n {
                if nums[i] % (start as i32 + 1) == 0 || (start as i32 + 1) % nums[i] == 0 {
                    nums.swap(start, i);
                    Self::dfs(start + 1, nums, all, n);
                    nums.swap(start, i);
                }
            }
        }
    }
}

#[test]
fn test() {
    let n = 2;
    let res = 2;
    assert_eq!(Solution::count_arrangement(n), res);
}

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