<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:
    string change(string a, bool inc, int pos)
    {
        string ret = a;
        if(inc) ret[pos] += 1;
        else ret[pos] -= 1;

        if(ret[pos] > '9') ret[pos] = '0';
        if(ret[pos] < '0') ret[pos] = '9';   
    
        return ret;
    }
    int openLock(vector<string>& deadends, string target) {
        queue<string> qu;
        map<string, int> mp;
        string check, temp;
        bool dead = 0;

        sort(deadends.begin(),deadends.end());
        function<bool(string,int,int)> bns = [&](string des, int start, int end)
        {
            int mid = (end + start)/2;
            if(des.compare(deadends[mid]) == 0) return true;
            if(end < start) return false;
            // if(end - start == 1) return (des.compare(deadends[mid+1]) == 0);
            if(des.compare(deadends[mid]) > 0) return bns(des,mid+1,end);
            if(des.compare(deadends[mid]) < 0) return bns(des,start,mid-1);
            return false;
        };

        if(target.compare("0000") == 0) return 0;
        qu.push("0000");
        mp["0000"] = 0;

        while(!qu.empty())
        {
            check = qu.front();
            qu.pop();
            
            // for(auto i:deadends)
            // {
            //     if(check.compare(i) == 0)
            //     {
            //         dead = 1;
            //         break;
            //     }
            // }
            dead = bns(check, 0, deadends.size() - 1);

            if(dead == 1)
            {
                dead = 0;
                continue;
            }

            for(int i = 0; i < 4; i++)
            {
                temp = change(check,1,i);
                if(mp[temp] == 0 || mp[temp] > mp[check] + 1)
                {
                    mp[temp] = mp[check] + 1;
                    qu.push(temp);
                }

                temp = change(check,0,i);
                if(mp[temp] == 0 || mp[temp] > mp[check] + 1)
                {
                    mp[temp] = mp[check] + 1;
                    qu.push(temp);
                }
            }
        }

        if(mp[target] == 0) return -1;
        else return mp[target];
    }
};
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