<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 {
private:
    void findAdj(vector<int>& adj, int i) {
        adj.clear();

        int neigh(0);
        int d = i % 10;
        neigh = (i - d) + (d + 1) % 10;
        adj.push_back(neigh);
        neigh = (i - d) + (d + 9) % 10;
        adj.push_back(neigh);
        
        d = (i % 100) / 10 * 10;
        neigh = (i - d) + (d + 10) % 100;
        adj.push_back(neigh);
        neigh = (i - d) + (d + 90) % 100;
        adj.push_back(neigh);

        d = (i % 1000) / 100 * 100;
        neigh = (i - d) + (d + 100) % 1000;
        adj.push_back(neigh);
        neigh = (i - d) + (d + 900) % 1000;
        adj.push_back(neigh);

        d = i / 1000;
        neigh = (i + 1000) % 10000;
        adj.push_back(neigh);
        neigh = (i + 9000) % 10000;
        adj.push_back(neigh);

    }
    int BFSHelper(vector<bool>& avoid, int src, int dst) {
        int count(0);
        if (avoid[src]) {
            return -1;
        }
        if (src == dst) {
            return count;
        }
        queue<int> Q;
        avoid[src] = true;
        count ++;
        Q.push(src);
        Q.push(-1);
        vector<int> adj;
        while (!Q.empty()) {
            int i = Q.front();
            Q.pop();
            if (i == -1) {
                if (Q.empty()) {
                    break;
                }
                count ++;
                Q.push(-1);
                continue;
            }
            findAdj(adj, i);
            for (int neigh : adj) {
                if (neigh == dst) {
                    return count;
                }
                if (!avoid[neigh]) {
                    avoid[neigh] = true;
                    Q.push(neigh);
                }
            }
        }
        return -1;
    }
public:
    int openLock(vector<string>& deadends, string target) {
        vector<bool> avoid(10000, false);
        for (auto & s : deadends) {
            avoid[stoi(s)] = true;
        }
        return BFSHelper(avoid, 0, stoi(target));
    }
};
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