标签:Beautiful beautiful 0526 ith int Number Arrangement divisible position
Beautiful Arrangement (M)
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:
- The number at the
ith
position is divisible byi
. i
is divisible by the number at theith
position.
Given an integer n
, return the number of the beautiful arrangements that you can construct.
Example 1:
Input: n = 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.
Example 2:
Input: n = 1
Output: 1
Constraints:
1 <= n <= 15
题意
对1-n这n个数进行排列,使得对于序列中第i个数字x满足i是x的倍数或者x是i的倍数。
思路
回溯法,对1-n每个位置挑选一个满足的数字放上去,判断最终得到的序列是否有效。
代码实现
Java
class Solution {
public int countArrangement(int n) {
return dfs(1, n, new boolean[n + 1]);
}
private int dfs(int index, int n, boolean[] used) {
if (index == n + 1) {
return 1;
}
int count = 0;
for (int i = 1; i <= n; i++) {
if (!used[i] && (index % i == 0 || i % index == 0)) {
used[i] = true;
count += dfs(index + 1, n, used);
used[i] = false;
}
}
return count;
}
}
标签:Beautiful,beautiful,0526,ith,int,Number,Arrangement,divisible,position
来源: https://www.cnblogs.com/mapoos/p/14226982.html
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