<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) {
        set<pair<int,string>> myset;
        vector<int> dist(10000,INT_MAX);
        int p;
        set<string> danger(deadends.begin(),deadends.end());
        if (danger.find("0000") != danger.end())
            return -1;
        dist[0]=0;
        myset.insert({0,"0000"});
        while (!myset.empty())
        {
            pair<int,string> q=*(myset.begin());
            int d=q.first;
            string s=q.second;
            myset.erase(q);
            string store=s;
            for (int j=0;j<4;j++)
            {
                if (store[j]>'0' && store[j]<'9')
                {
                    store[j]=store[j]+1;
                    if (danger.find(store) == danger.end())
                    {
                        p=stoi(store);
                        if (d+1 < dist[p])
                        {
                            if (dist[p] != INT_MAX)
                                myset.erase({dist[p],store});
                            dist[p]=d+1;
                            myset.insert({dist[p],store});
                        }
                    }
                    store=s;
                    store[j]=store[j]-1;
                    if (danger.find(store) == danger.end())
                    {
                        p=stoi(store);
                        if (d+1 < dist[p])
                        {
                            if (dist[p] != INT_MAX)
                                myset.erase({dist[p],store});
                            dist[p]=d+1;
                            myset.insert({dist[p],store});
                        }
                    } 
                    store=s;                   
                }
                else if(store[j]=='0')
                {
                    store[j]=store[j]+1;
                    if (danger.find(store) == danger.end())
                    {
                        p=stoi(store);
                        if (d+1 < dist[p])
                        {
                            if (dist[p] != INT_MAX)
                                myset.erase({dist[p],store});
                            dist[p]=d+1;
                            myset.insert({dist[p],store});
                        }
                    }
                    store=s;
                    store[j]='9';
                    if (danger.find(store) == danger.end())
                    {
                        p=stoi(store);
                        if (d+1 < dist[p])
                        {
                            if (dist[p] != INT_MAX)
                                myset.erase({dist[p],store});
                            dist[p]=d+1;
                            myset.insert({dist[p],store});
                        }
                    } 
                    store=s;                     
                }
                else
                {
                    store[j]='0';
                    if (danger.find(store) == danger.end())
                    {
                        p=stoi(store);
                        if (d+1 < dist[p])
                        {
                            if (dist[p] != INT_MAX)
                                myset.erase({dist[p],store});
                            dist[p]=d+1;
                            myset.insert({dist[p],store});
                        }
                    }
                    store=s;
                    store[j]=store[j]-1;
                    if (danger.find(store) == danger.end())
                    {
                        p=stoi(store);
                        if (d+1 < dist[p])
                        {
                            if (dist[p] != INT_MAX)
                                myset.erase({dist[p],store});
                            dist[p]=d+1;
                            myset.insert({dist[p],store});
                        }
                    } 
                    store=s; 
                }
            }
        }
        int t=stoi(target);
        if (dist[t]==INT_MAX)
            return -1;
        return dist[t];        
    }
};
71371