_526.java

package com.fishercoder.solutions;

/**
 * 526. Beautiful Arrangement
 *
 * 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.
 */
public class _526 {
	public static class Solution1 {
		/**
		 * A good post to look at: https://discuss.leetcode.com/topic/79916/java-solution-backtracking
		 * and there's a generic template afterwards for backtracking problems
		 */

		int count = 0;

		public int countArrangement(int N) {
			backtracking(N, new int[N + 1], 1);
			return count;
		}

		private void backtracking(int N, int[] used, int pos) {
			if (pos > N) {
				count++;
				return;
			}

			for (int i = 1; i <= N; i++) {
				if (used[i] == 0 && (i % pos == 0 || pos % i == 0)) {
					used[i] = 1;
					backtracking(N, used, pos + 1);
					used[i] = 0;
				}
			}
		}
	}

}