<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) {
        queue<pair<string,int>> pending_combinations;
        char prev[10] = {'9','0','1','2','3','4','5','6','7','8'};
        char next[10] = {'1','2','3','4','5','6','7','8','9','0'};
        unordered_map<string, int> seen;

        pending_combinations.push(make_pair("0000",0));

        for (int i = 0; i < deadends.size(); i++) {
            seen[deadends[i]] = 1;
        }

        while(!pending_combinations.empty()) {
            pair<string,int> current = pending_combinations.front();
            pending_combinations.pop();

            //cout << "current string: " << current.first << " & depth: " << current.second << '\n';

            if (current.first == target) {
                return current.second;
            } else if (seen.find(current.first) != seen.end()) {
                continue;
            } else {
                // for each number in the string
                seen[current.first] = 1;
                for (int i = 0; i < 4; i++) {
                    int curr_num = current.first[i] - '0';

                    // Create the next and previous states by incrementing or decrementing the current digit
                    string nxt = current.first.substr(0, i) + next[curr_num] + current.first.substr(i + 1);
                    string prv = current.first.substr(0, i) + prev[curr_num] + current.first.substr(i + 1);

                    // Add the new combinations to the queue with an incremented step count
                    pending_combinations.push(make_pair(nxt, current.second + 1));
                    pending_combinations.push(make_pair(prv, current.second + 1));
                }
            }
        }
        return -1;
    }
};
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