<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>

class Solution {
public:

    string solve(unordered_map<string, bool>&present, char current, int n , string &ans){
        if(ans.length()==n){
            // cout<<"init"<<ans<<endl;
            if(present[ans]==false) return ans;
            return "";
        }
        ans.push_back(current);
        string z = solve(present,'1',n, ans );
        string o = solve(present , '0',n,ans );
        ans.pop_back();
        if(z !="") return z;
        return o;
    }
    string findDifferentBinaryString(vector<string>& nums) {
        int n = nums[0].length();
        unordered_map<string, bool>present;
        for(auto &i : nums){
            present[i] = true;
        }
        string ans ="";
       string zero = solve(present ,'0',n,ans );
       if(zero!="") return zero;
       ans = "";
       string one = solve(present, '1',n,ans);
       return one;

    }
};
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