<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:
    int openLock(vector<string>& deadends, string target) {
        string start = "0000";
        queue<string> bfsQueue;
        unordered_map<string, int> dist;
        bfsQueue.push(start);
        dist[start] = 0;

        if(target == start)
            return 0;

        unordered_set<string> deadendsSet(deadends.begin(), deadends.end());

        if(deadendsSet.find(start) != deadendsSet.end())
            return -1;

        while(!bfsQueue.empty()) {
            string curr = bfsQueue.front();
            bfsQueue.pop();

            for(int idx = 0; idx < 4; idx++) {
                int val = curr[idx] - '0';
                int next1 = (val + 1) % 10;
                char next1Ch = '0' + next1;
                string nextStr = curr;
                nextStr[idx] = next1Ch;

                if((dist.find(nextStr) == dist.end()) && (deadendsSet.find(nextStr) == deadendsSet.end())) {
                    dist[nextStr] = dist[curr] + 1;
                    bfsQueue.push(nextStr);
                }

                next1 = (val + 9) % 10;
                next1Ch = '0' + next1;
                string nextStr2 = curr;
                nextStr2[idx] = next1Ch;

                if((dist.find(nextStr2) == dist.end()) && (deadendsSet.find(nextStr2) == deadendsSet.end())) {
                    dist[nextStr2] = dist[curr] + 1;
                    bfsQueue.push(nextStr2);
                }
            }
        }  

        if(dist.find(target) == dist.end())
            return -1;

        return dist[target];    
    }
};
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