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算法题（国外版）/valid-permutations-for-di-sequence.html

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+<p>You are given a string <code>s</code> of length <code>n</code> where <code>s[i]</code> is either:</p>
+
+<ul>
+	<li><code>&#39;D&#39;</code> means decreasing, or</li>
+	<li><code>&#39;I&#39;</code> means increasing.</li>
+</ul>
+
+<p>A permutation <code>perm</code> of <code>n + 1</code> integers of all the integers in the range <code>[0, n]</code> is called a <strong>valid permutation</strong> if for all valid <code>i</code>:</p>
+
+<ul>
+	<li>If <code>s[i] == &#39;D&#39;</code>, then <code>perm[i] &gt; perm[i + 1]</code>, and</li>
+	<li>If <code>s[i] == &#39;I&#39;</code>, then <code>perm[i] &lt; perm[i + 1]</code>.</li>
+</ul>
+
+<p>Return <em>the number of <strong>valid permutations</strong> </em><code>perm</code>. Since the answer may be large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>
+
+<p>&nbsp;</p>
+<p><strong>Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> s = &quot;DID&quot;
+<strong>Output:</strong> 5
+<strong>Explanation:</strong> The 5 valid permutations of (0, 1, 2, 3) are:
+(1, 0, 3, 2)
+(2, 0, 3, 1)
+(2, 1, 3, 0)
+(3, 0, 2, 1)
+(3, 1, 2, 0)
+</pre>
+
+<p><strong>Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> s = &quot;D&quot;
+<strong>Output:</strong> 1
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>n == s.length</code></li>
+	<li><code>1 &lt;= n &lt;= 200</code></li>
+	<li><code>s[i]</code> is either <code>&#39;I&#39;</code> or <code>&#39;D&#39;</code>.</li>
+</ul>