526. Beautiful Arrangement

1. Question

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.
  • iis divisible by perm[i].

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

2. Examples

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

3. Constraints

  • 1 <= n <= 15

4. References

来源:力扣(LeetCode) 链接:https://leetcode-cn.com/problems/beautiful-arrangement 著作权归领扣网络所有。商业转载请联系官方授权,非商业转载请注明出处。

Solutions

class Solution {

        ArrayList<Integer>[] list;
    boolean[] visited;
    int res = 0;


    public int countArrangement(int n) {

        list = new ArrayList[n + 1];
        visited = new boolean[n + 1];

        for (int i = 1; i <= n; i++) {
            list[i] = new ArrayList();
            for (int j = 1; j <= n; j++) {
                if (i % j == 0 || j % i == 0) {
                    list[i].add(j);
                }
            }
        }

        backtrace(1, n);
        return res;
    }

    private void backtrace(int index, int n) {
        if (index == n + 1) {
            res++;
            return;
        }
        for (int k : list[index]) {
            if (!visited[k]) {
                visited[k] = true;
                backtrace(index + 1, n);
                visited[k] = false;
            }
        }
    }
}
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