add leetcode problem-cn part5

算法题（国内版）/problem (English)/优美的排列(English) [beautiful-arrangement].html

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+<p>Suppose you have <code>n</code> integers labeled <code>1</code> through <code>n</code>. A permutation of those <code>n</code> integers <code>perm</code> (<strong>1-indexed</strong>) is considered a <strong>beautiful arrangement</strong> if for every <code>i</code> (<code>1 &lt;= i &lt;= n</code>), <strong>either</strong> of the following is true:</p>
+
+<ul>
+	<li><code>perm[i]</code> is divisible by <code>i</code>.</li>
+	<li><code>i</code> is divisible by <code>perm[i]</code>.</li>
+</ul>
+
+<p>Given an integer <code>n</code>, return <em>the <strong>number</strong> of the <strong>beautiful arrangements</strong> that you can construct</em>.</p>
+
+<p>&nbsp;</p>
+<p><strong>Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 2
+<strong>Output:</strong> 2
+<b>Explanation:</b> 
+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
+</pre>
+
+<p><strong>Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 1
+<strong>Output:</strong> 1
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= n &lt;= 15</code></li>
+</ul>