Question Definition
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.
Java Solution
public int countArrangement(int N) {
boolean[] visited = new boolean[N + 1];
return helper(1, visited);
}
private int helper(int index, boolean[] visited){
if(index == visited.length){
return 1;
}
int result = 0;
for(int i = 1; i < visited.length; i++) {
if(!visited[i] && (index % i == 0 || i % index == 0)){
visited[i] = true;
result += helper(index + 1, visited);
visited[i] = false;
}
}
return result;
}
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