<p>You have a lock in front of you with 4 circular wheels. Each wheel has 10 slots: <code>&#39;0&#39;, &#39;1&#39;, &#39;2&#39;, &#39;3&#39;, &#39;4&#39;, &#39;5&#39;, &#39;6&#39;, &#39;7&#39;, &#39;8&#39;, &#39;9&#39;</code>. The wheels can rotate freely and wrap around: for example we can turn <code>&#39;9&#39;</code> to be <code>&#39;0&#39;</code>, or <code>&#39;0&#39;</code> to be <code>&#39;9&#39;</code>. Each move consists of turning one wheel one slot.</p>

<p>The lock initially starts at <code>&#39;0000&#39;</code>, a string representing the state of the 4 wheels.</p>

<p>You are given a list of <code>deadends</code> dead ends, meaning if the lock displays any of these codes, the wheels of the lock will stop turning and you will be unable to open it.</p>

<p>Given a <code>target</code> representing the value of the wheels that will unlock the lock, return the minimum total number of turns required to open the lock, or -1 if it is impossible.</p>

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

<pre>
<strong>Input:</strong> deadends = [&quot;0201&quot;,&quot;0101&quot;,&quot;0102&quot;,&quot;1212&quot;,&quot;2002&quot;], target = &quot;0202&quot;
<strong>Output:</strong> 6
<strong>Explanation:</strong> 
A sequence of valid moves would be &quot;0000&quot; -&gt; &quot;1000&quot; -&gt; &quot;1100&quot; -&gt; &quot;1200&quot; -&gt; &quot;1201&quot; -&gt; &quot;1202&quot; -&gt; &quot;0202&quot;.
Note that a sequence like &quot;0000&quot; -&gt; &quot;0001&quot; -&gt; &quot;0002&quot; -&gt; &quot;0102&quot; -&gt; &quot;0202&quot; would be invalid,
because the wheels of the lock become stuck after the display becomes the dead end &quot;0102&quot;.
</pre>

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

<pre>
<strong>Input:</strong> deadends = [&quot;8888&quot;], target = &quot;0009&quot;
<strong>Output:</strong> 1
<strong>Explanation:</strong> We can turn the last wheel in reverse to move from &quot;0000&quot; -&gt; &quot;0009&quot;.
</pre>

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

<pre>
<strong>Input:</strong> deadends = [&quot;8887&quot;,&quot;8889&quot;,&quot;8878&quot;,&quot;8898&quot;,&quot;8788&quot;,&quot;8988&quot;,&quot;7888&quot;,&quot;9888&quot;], target = &quot;8888&quot;
<strong>Output:</strong> -1
<strong>Explanation:</strong> We cannot reach the target without getting stuck.
</pre>

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

<ul>
	<li><code>1 &lt;= deadends.length &lt;= 500</code></li>
	<li><code>deadends[i].length == 4</code></li>
	<li><code>target.length == 4</code></li>
	<li>target <strong>will not be</strong> in the list <code>deadends</code>.</li>
	<li><code>target</code> and <code>deadends[i]</code> consist of digits only.</li>
</ul>

class Solution {
public:
    unordered_set<string> s;
    string start;
    string target;

    int openLock(vector<string>& deadends, string target) {
        if (target == "0000") return 0;
        for (auto d : deadends) s.insert(d);
        if (s.count("0000")) return -1;
        this->start = "0000";
        this->target = target;
        return bfs();
    }

    int bfs() {
        unordered_map<string, int> m1;
        unordered_map<string, int> m2;
        m1[start] = 0;
        m2[target] = 0;
        queue<string> q1{ {start} };
        queue<string> q2{ {target} };
        while (!q1.empty() && !q2.empty()) {
            int t = q1.size() <= q2.size() ? extend(m1, m2, q1) : extend(m2, m1, q2);
            if (t != -1) return t;
        }
        return -1;
    }

    int extend(unordered_map<string, int>& m1, unordered_map<string, int>& m2, queue<string>& q) {
        for (int n = q.size(); n > 0; --n) {
            string p = q.front();
            int step = m1[p];
            q.pop();
            for (string t : next(p)) {
                if (s.count(t) || m1.count(t)) continue;
                if (m2.count(t)) return step + 1 + m2[t];
                m1[t] = step + 1;
                q.push(t);
            }
        }
        return -1;
    }

    vector<string> next(string& t) {
        vector<string> res;
        for (int i = 0; i < 4; ++i) {
            char c = t[i];
            t[i] = c == '0' ? '9' : (char) (c - 1);
            res.push_back(t);
            t[i] = c == '9' ? '0' : (char) (c + 1);
            res.push_back(t);
            t[i] = c;
        }
        return res;
    }
};
29653