Leetcode•Mar 22, 2025

526. Beautiful Arrangement

Hazrat Ali

Leetcode

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:

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:

Input: n = 1
Output: 1


Solution

/**
 * @param {number} N
 * @return {number}
 */
const countArrangement = N => {
  const result = [];
  backtracking(N, 0, {}, [], result);
  return result.length;
};

const backtracking = (N, index, used, solution, result) => {
  if (index === N) {
    result.push(solution.slice());
    return;
  }

  for (let i = 1; i <= N; i++) {
    if (!used[i] && ((index + 1) % i === 0 || i % (index + 1) === 0)) {
      used[i] = true;
      solution.push(i);
      backtracking(N, index + 1, used, solution, result);
      used[i] = false;
      solution.pop();
    }
  }
};









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