# 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.

**(1) Backtracking**

class Solution {

public int countArrangement(int N) {

boolean[] used = new boolean[N + 1];

int[] count = new int[1];

getArrangement(1, N, used, count);

return count[0];

}

public void getArrangement(int curNum, int N, boolean[] used, int[] count) {

if (curNum == N + 1) {

++count[0];

return;

}

for (int i = 1; i <= N; i++) {

if (!used[i] && (curNum % i == 0 || i % curNum == 0)) {

used[i] = true;

getArrangement(curNum + 1, N, used, count);

used[i] = false;

}

}

}

}

**Backtracking:**时间复杂度O(N!), 空间复杂度O(N)

Last modified 3yr ago