leetcode526 Beautiful Arrangement Java

Description:

Suppose you have N integers from 1 to N. We define a beautiful arrangement as an array that is constructed by these N numbers successfully if one of the following is true for the ith position (1 ≤ i ≤ N) in this array:

The number at the ith position is divisible by i.
i is divisible by the number at the ith position.
Now given N, how many beautiful arrangements can you construct?

Example 1:
Input: 2
Output: 2
Explanation:

The first beautiful arrangement is [1, 2]:

Number at the 1st position (i=1) is 1, and 1 is divisible by i (i=1).

Number at the 2nd position (i=2) is 2, and 2 is divisible by i (i=2).

The second beautiful arrangement is [2, 1]:

Number at the 1st position (i=1) is 2, and 2 is divisible by i (i=1).

Number at the 2nd position (i=2) is 1, and i (i=2) is divisible by 1.
Note:
N is a positive integer and will not exceed 15.

解法：

思路是“从后向前”依次验证每一个数是否可以占这一位置。

    int count = 0;
    public int countArrangement(int N) {
        helper(N, N, new int[N+1]);
        return count;
    }
    private void helper(int N, int pos, int[] visited) {
        if(pos < 2){
            count++;
            return;
        }
        for(int i=1; i<=N; i++) {
            if(visited[i] ==0 && (pos % i ==0 || i % pos == 0)) {
                visited[i] = 1;
                helper(N, pos - 1, visited);
                visited[i] = 0;
            }
        }
    }