526. Beautiful Arrangement

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526. Beautiful Arrangement

Description

Suppose you have n integers labeled 1 through n. A permutation of those n integers perm (1-indexed ) is considered a beautiful arrangement if for every i (1 <= i <= n), either of the following is true:

  • perm[i] is divisible by i.
  • i is divisible by perm[i].

Given an integer n, return the number of the beautiful arrangements that you can construct.

Example 1:

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2
Input: n = 2
Output: 2

Explanation:

The first beautiful arrangement is [1,2]:

  • perm[1] = 1 is divisible by i = 1
  • perm[2] = 2 is divisible by i = 2

The second beautiful arrangement is [2,1]:

  • perm[1] = 2 is divisible by i = 1
  • i = 2 is divisible by perm[2] = 1

Example 2:

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Input: n = 1
Output: 1

Constraints:

  • 1 <= n <= 15

Hints/Notes

  • dynamic programming

Solution

Language: C++

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class Solution {
public:
    map<int, int> dp;
    int n_;

    int countArrangement(int n) {
        n_ = n;
        return dfs(0);
    }

    int dfs(int i) {
        if (i == (1 << n_) - 1) {
            return 1;
        }
        if (dp.contains(i)) {
            return dp[i];
        }
        int index = __builtin_popcount(i), ans = 0;
        for (int j = 0; j < n_; j++) {
            if (i & (1 << j)) {
                continue;
            }
            if ((j + 1) % (index + 1) == 0 || (index + 1) % (j + 1) == 0) {
                ans += dfs(i | (1 << j));
            }
        }
        dp[i] = ans;
        return ans;
    }
};