<p>Given an array of strings <code>nums</code> containing <code>n</code> <strong>unique</strong> binary strings each of length <code>n</code>, return <em>a binary string of length </em><code>n</code><em> that <strong>does not appear</strong> in </em><code>nums</code><em>. If there are multiple answers, you may return <strong>any</strong> of them</em>.</p>

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

<pre>
<strong>Input:</strong> nums = [&quot;01&quot;,&quot;10&quot;]
<strong>Output:</strong> &quot;11&quot;
<strong>Explanation:</strong> &quot;11&quot; does not appear in nums. &quot;00&quot; would also be correct.
</pre>

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

<pre>
<strong>Input:</strong> nums = [&quot;00&quot;,&quot;01&quot;]
<strong>Output:</strong> &quot;11&quot;
<strong>Explanation:</strong> &quot;11&quot; does not appear in nums. &quot;10&quot; would also be correct.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [&quot;111&quot;,&quot;011&quot;,&quot;001&quot;]
<strong>Output:</strong> &quot;101&quot;
<strong>Explanation:</strong> &quot;101&quot; does not appear in nums. &quot;000&quot;, &quot;010&quot;, &quot;100&quot;, and &quot;110&quot; would also be correct.
</pre>

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

<ul>
	<li><code>n == nums.length</code></li>
	<li><code>1 &lt;= n &lt;= 16</code></li>
	<li><code>nums[i].length == n</code></li>
	<li><code>nums[i] </code>is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
	<li>All the strings of <code>nums</code> are <strong>unique</strong>.</li>
</ul>

'''
length of each element in nums = the length of nums array itself
n = len(nums) -> each element is a string of length n consisting of 0 and 1s
approach 1:
- generate all combinations of 0 and 1 of length n and return the first one not in nums
- O(2^n)

'0','1'
'00','10','01','11'
'''

class Solution:
    def findDifferentBinaryString(self, nums: List[str]) -> str:
        nums = set(nums)
        n = len(nums)
        possible = ['']
        for _ in range(n):
            new = []
            for b in possible:
                new.append(b+'0')
                new.append(b+'1')
            possible = new
        
        for b in possible:
            if b not in nums:
                return b
25000