<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>

const int INF = 1e9 + 5;

bool valid(string &str){
    stack<int> s;
    int n = str.size();
    for(int i = 0; i < n; i++){
        if(str[i] == '('){
            s.push('(');
        }
        else if(str[i] == ')'){
            if(s.empty()){
                return false;
            }
            else{
                s.pop();
            }
        }
    }
    if(s.empty()) return true;
    return false;
}

class Solution {
public:
    vector<string> removeInvalidParentheses(string str) {
        int n = str.size();
        map<int, vector<string>> m;
        string str2 = "";
        for(int i = 0; i < n; i++){
            if(str[i] != '(' && str[i] != ')'){ continue; }
            str2.push_back(str[i]);
        }
        int n2 = str2.size();
        int maxm = -INF;
        map<int, int> mp;
        int j = 0;
        for(int i = 0; i < n; i++){
            if(str[i] != '(' && str[i] != ')'){ continue; }
            mp[i] = j;
            j++;
        }
        for(int mask = (1 << n2) - 1; mask >= 0; mask--){
            int cnt = __builtin_popcount(mask);
            if(cnt < maxm){ continue; }
            string t = "";
            int close = 0, open = 0;
            if(cnt % 2){ continue; }
            for(int i = 0; i < n; i++){
                if(str[i] != '(' && str[i] != ')'){ t += str[i]; }
                else if(mask & (1 << mp[i])){ 
                    t += str[i]; 
                    if(str[i] == ')'){ close++; } 
                    else{ open++; }
                }
            }
            if(close != open){ continue; }
            if(valid(t)){
                m[cnt].push_back(t);
                maxm = max(maxm, cnt);
            }
        }
        auto it = m.end();
        it--;
        set<string> st;
        for(auto s : (*it).second){
            st.insert(s);
        }
        vector<string> res;
        for(auto s : st){
            res.push_back(s);
        }
        return res;
    }
};
324928