Remove Invalid Parentheses
<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>
Breadth-First Search; String; Backtracking
class Solution {
    private String s;
    private int n;
    private Set<String> ans = new HashSet<>();

    public List<String> removeInvalidParentheses(String s) {
        this.s = s;
        this.n = s.length();
        int l = 0, r = 0;
        for (char c : s.toCharArray()) {
            if (c == '(') {
                ++l;
            } else if (c == ')') {
                if (l > 0) {
                    --l;
                } else {
                    ++r;
                }
            }
        }
        dfs(0, l, r, 0, 0, "");
        return new ArrayList<>(ans);
    }

    private void dfs(int i, int l, int r, int lcnt, int rcnt, String t) {
        if (i == n) {
            if (l == 0 && r == 0) {
                ans.add(t);
            }
            return;
        }
        if (n - i < l + r || lcnt < rcnt) {
            return;
        }
        char c = s.charAt(i);
        if (c == '(' && l > 0) {
            dfs(i + 1, l - 1, r, lcnt, rcnt, t);
        }
        if (c == ')' && r > 0) {
            dfs(i + 1, l, r - 1, lcnt, rcnt, t);
        }
        int x = c == '(' ? 1 : 0;
        int y = c == ')' ? 1 : 0;
        dfs(i + 1, l, r, lcnt + x, rcnt + y, t + c);
    }
}