<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:
    
    // Using of visited map so that if you move foward from current state then make sure you mark visited the current state so that in future you should not move back to that state.
    
    int openLock(vector<string>& deadends, string target) {

        set<string> st(deadends.begin() , deadends.end());
        map<string,int> visited;

        unordered_map<char,char> next = {{'0','1'} , {'1','2'} , {'2','3'} , {'3','4'} , {'4','5'} , {'5','6'} , {'6','7'} , {'7','8'} , {'8','9'} , {'9','0'}};
        unordered_map<char,char> prev = {{'0','9'} , {'1','0'} , {'2','1'} , {'3','2'} , {'4','3'} , {'5','4'} , {'6','5'} , {'7','6'} , {'8','7'} , {'9','8'}};

        queue<pair<string , int>> q;
        string start = "0000";

        if(st.count(start) <= 0 && visited[start] == 0) 
        {
            q.push({start, 0});
            visited[start] = 1;
        }

        int ans = 1e9;

        while(q.size() > 0)
        {
            auto front = q.front();
            q.pop();

            string str = front.first;
            int num = front.second;
            
            if(str == target)
            {
                ans = min(ans , num);
            }

            for(int i = 0 ; i < str.length() ; i++)
            {
                char original = str[i];

                // forward.
                str[i] = next[original];

                if(st.count(str) <= 0 && visited[str] == 0)
                {
                    q.push({str , num+1});
                    visited[str] = 1;
                }

                // Backward
                str[i] = prev[original];
                if(st.count(str) <= 0 && visited[str] == 0)
                {
                    q.push({str , num+1});
                    visited[str] = 1;
                }

                str[i] = original;
            }
        }

        if(ans == 1e9)
        {
            return -1;
        }

        return ans;
    }
};
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