leetcode 526. Beautiful Arrangement

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:

1. The number at the ith position is divisible by i.
2. 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:

1. N is a positive integer and will not exceed 15.

基本题：回溯法。

解法一：开辟一个新的数组，标记是否访问过。

class Solution {
    int cnt = 0;
public:
    int countArrangement(int N) {
        vector<bool> visited(N + 1, false);
        calculate(N, visited, 1);
        return cnt;
    }
    void calculate(int N, vector<bool> &visited, int pos) {
        if (pos > N) {
            cnt++;
            return;
        }
        for (int i = 1; i <= N; ++i) {
            if (!visited[i] && ((pos % i == 0) || (i % pos == 0))) {
                visited[i] = true;
                calculate(N, visited, pos + 1);
                visited[i] = false;
            } 
        }
    }
};

解法二：