<p>Given a string <code>s</code> that contains parentheses and letters, remove the minimum number of invalid parentheses to make the input string valid.</p>

<p>Return <em>a list of <strong>unique strings</strong> that are valid with the minimum number of removals</em>. You may return the answer in <strong>any order</strong>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;()())()&quot;
<strong>Output:</strong> [&quot;(())()&quot;,&quot;()()()&quot;]
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;(a)())()&quot;
<strong>Output:</strong> [&quot;(a())()&quot;,&quot;(a)()()&quot;]
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;)(&quot;
<strong>Output:</strong> [&quot;&quot;]
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 25</code></li>
	<li><code>s</code> consists of lowercase English letters and parentheses <code>&#39;(&#39;</code> and <code>&#39;)&#39;</code>.</li>
	<li>There will be at most <code>20</code> parentheses in <code>s</code>.</li>
</ul>


class Solution {
private:
    int isValid(string& s) {
        stack<char> st;

        for (char c : s) {
            if(c == '(') st.push(c);
            else if(c == ')') {
                if(!st.empty() && st.top() == '(') st.pop();
                else st.push(c);
            }
        }
        // cout << st.size() << " ";
        return st.size();
    }

    void backtrack(int ind, string& s, set<string>& ans, int minParen) {
        // base case

        if(minParen == 0) {
            if(isValid(s) == 0) ans.insert(s);
            return;
        }

        for(int i = ind; i < s.size(); i++) {
            char remch = s[i];
            s.erase(s.begin() + i);

            backtrack(i, s, ans, minParen-1);

            s.insert(s.begin() + i, remch);
        }
    }

public:
    vector<string> removeInvalidParentheses(string s) {
        set<string> ans;

        // If the initial string is valid, add it to the answer
        // if (isValid(s)) {
        //     return {s};
        // }

        int minInvalidParen = isValid(s);

        cout << minInvalidParen;

        backtrack(0, s, ans, minInvalidParen);

        if(ans.size() == 0) return {""};

        vector<string> ans_vec;

        for(auto ele : ans) {
            ans_vec.push_back(ele);
        }

        return ans_vec;
    }
};
344919