<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:
    // Convert the vector<int> lock state to a string.
    string to_str(const vector<int>& lock) {
        string res;
        for (int num : lock) {
            res.push_back(num + '0');
        }
        return res;
    }

    int openLock(vector<string>& deadends, string target) {
        if (target == "0000") return 0;

        set<string> deadSet(deadends.begin(), deadends.end());  // Convert to set for faster access
        set<string> visited;  // Track visited combinations
        queue<vector<int>> q;
        vector<int> start(4, 0);
        
        if (deadSet.count("0000")) return -1; // If "0000" is a deadend, return immediately

        q.push(start);
        visited.insert("0000");
        int depth = 0;

        while (!q.empty()) {
            int sz = q.size();
            for (int i = 0; i < sz; i++) {
                vector<int> cur = q.front();
                q.pop();
                string curStr = to_str(cur);

                if (curStr == target) {
                    return depth;
                }

                // Try all 8 possible moves (4 digits * 2 directions each)
                for (int j = 0; j < 4; j++) {
                    int original = cur[j];

                    // Increment digit
                    cur[j] = (original + 1) % 10;
                    string nextStr1 = to_str(cur);
                    if (visited.count(nextStr1) == 0 && deadSet.count(nextStr1) == 0) {
                        q.push(cur);
                        visited.insert(nextStr1);
                    }

                    // Decrement digit
                    cur[j] = (original - 1 + 10) % 10;
                    string nextStr2 = to_str(cur);
                    if (visited.count(nextStr2) == 0 && deadSet.count(nextStr2) == 0) {
                        q.push(cur);
                        visited.insert(nextStr2);
                    }

                    // Restore original digit
                    cur[j] = original;
                }
            }
            depth++;
        }

        return -1;  // If no solution is found
    }
};
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