<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 {
public:
  vector<string> removeInvalidParentheses(string s) {
    // f[i][j] = list of results for s[i..j]
    
    int n = s.length();
    
    vector<vector<int>> f(n, vector<int>(n, 0));
    vector<vector<unordered_set<string>>> g(n, vector<unordered_set<string>>(n));
    
    
    for (int j = 0; j < n; ++j) {
      for (int i = j; i >= 0; --i) {
        if (i == j) {
          if (isalpha(s[i])) {
            f[i][j] = 1;
            g[i][j].insert(string(1, s[i]));
          }
          else {
            f[i][j] = 0;
            g[i][j].insert("");
          }
        }
        else {
          if (s[i] == '(' && s[j] == ')') {
            if (i+1 <= j-1) {
              f[i][j] = f[i+1][j-1] + 2;
              for (const string& x : g[i+1][j-1]) {
                g[i][j].insert("(" + x + ")");
              }
            }
            else {
              f[i][j] = 2;
              g[i][j].insert("()");
            }
          }
          
          for (int k = i; k < j; ++k) {
            if (f[i][j] <= f[i][k] + f[k+1][j]) {
              if (f[i][j] < f[i][k] + f[k+1][j]) {
                g[i][j].clear();
              }
              
              f[i][j] = f[i][k] + f[k+1][j];
              
              for (const string& x : g[i][k]) {
                for (const string& y : g[k+1][j]) {
                  g[i][j].insert(x + y);
                }
              }
            }
          }
        }
        
        // cout << i << " " << j << ": ";
        // for (const string& str : g[i][j]) cout << str << ", "; cout << endl;
      }
    }
    
    vector<string> res(g[0][n-1].begin(), g[0][n-1].end());
    return res;
  }
};
18395