LeetCode Beautiful Arrangement

原题链接在这里：https://leetcode.com/problems/beautiful-arrangement/description/

题目：

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.

题解：

典型的backtracking. 用visited记录用过的位置, 挨个position往后permute. 遇到不合规矩的直接返回, 看能不能走到N.

Time Complexity: exponential. 每次走到最后才遇到不和规矩的backtrack回来.

Space: O(N).

AC Java:

 class Solution {
     int res = 0;
     public int countArrangement(int N) {
         if(N <= 0){
             return 0;
         }

         boolean [] visited = new boolean[N+1];
         dfs(visited, 1, N);
         return res;
     }

     private void dfs(boolean [] visited, int pos, int N){
         if(pos > N){
             res++;
             return;
         }

         for(int i = 1; i<=N; i++){
             if(!visited[i] && (i%pos==0 || pos%i==0)){
                 visited[i] = true;
                 dfs(visited, pos+1, N);
                 visited[i] = false;
             }
         }
     }
 }

跟上Beautiful Arrangement II.