<p>You are given a <strong>0-indexed</strong> string <code>pattern</code> of length <code>n</code> consisting of the characters <code>&#39;I&#39;</code> meaning <strong>increasing</strong> and <code>&#39;D&#39;</code> meaning <strong>decreasing</strong>.</p>

<p>A <strong>0-indexed</strong> string <code>num</code> of length <code>n + 1</code> is created using the following conditions:</p>

<ul>
	<li><code>num</code> consists of the digits <code>&#39;1&#39;</code> to <code>&#39;9&#39;</code>, where each digit is used <strong>at most</strong> once.</li>
	<li>If <code>pattern[i] == &#39;I&#39;</code>, then <code>num[i] &lt; num[i + 1]</code>.</li>
	<li>If <code>pattern[i] == &#39;D&#39;</code>, then <code>num[i] &gt; num[i + 1]</code>.</li>
</ul>

<p>Return <em>the lexicographically <strong>smallest</strong> possible string </em><code>num</code><em> that meets the conditions.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> pattern = &quot;IIIDIDDD&quot;
<strong>Output:</strong> &quot;123549876&quot;
<strong>Explanation:
</strong>At indices 0, 1, 2, and 4 we must have that num[i] &lt; num[i+1].
At indices 3, 5, 6, and 7 we must have that num[i] &gt; num[i+1].
Some possible values of num are &quot;245639871&quot;, &quot;135749862&quot;, and &quot;123849765&quot;.
It can be proven that &quot;123549876&quot; is the smallest possible num that meets the conditions.
Note that &quot;123414321&quot; is not possible because the digit &#39;1&#39; is used more than once.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> pattern = &quot;DDD&quot;
<strong>Output:</strong> &quot;4321&quot;
<strong>Explanation:</strong>
Some possible values of num are &quot;9876&quot;, &quot;7321&quot;, and &quot;8742&quot;.
It can be proven that &quot;4321&quot; is the smallest possible num that meets the conditions.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= pattern.length &lt;= 8</code></li>
	<li><code>pattern</code> consists of only the letters <code>&#39;I&#39;</code> and <code>&#39;D&#39;</code>.</li>
</ul>

from sortedcontainers import SortedSet
class Solution:
    def smallestNumber(self, pattern: str) -> str:
        self.numbers = SortedSet()
        self.explored = set()

        for i in range(1, 10) :
            self.smallestNumberUtil(pattern, 0, str(i))
        
        return self.numbers[0]
    
    def smallestNumberUtil(self, pattern, i, curr) :
        if i == len(pattern) :
            self.numbers.add(curr)
            return 
        
        last = int(curr[-1])
        self.explored.add(int(curr[-1]))

        if pattern[i] == 'D' :
            if (last-1) != 0 and (last-1) not in self.explored :
                self.smallestNumberUtil(pattern, i+1, curr + str(last-1))
        else :

            while last <= 9 :
                if last not in self.explored :
                    self.smallestNumberUtil(pattern, i+1, curr + str(last))
                
                last += 1
            
        self.explored.remove(int(curr[-1]))
48