<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>

#include <vector>
#include <string>
#include <unordered_set>
#include <queue>

using namespace std;

class Solution {
public:
    // Function to generate all possible next states
    vector<string> getNextStates(string s) {
        vector<string> nextStates;
        for (int i = 0; i < 4; ++i) {
            string up = s;
            string down = s;
            
            // Turning the wheel up (i.e., increase by 1)
            up[i] = (up[i] == '9') ? '0' : up[i] + 1;
            nextStates.push_back(up);
            
            // Turning the wheel down (i.e., decrease by 1)
            down[i] = (down[i] == '0') ? '9' : down[i] - 1;
            nextStates.push_back(down);
        }
        return nextStates;
    }
    
    int openLock(vector<string>& deadends, string target) {
        // Convert the deadends list to a set for fast lookup
        unordered_set<string> deadSet(deadends.begin(), deadends.end());
        
        // Edge case: if the starting point "0000" is a deadend
        if (deadSet.count("0000")) return -1;
        
        // BFS setup: queue stores pairs of (lock state, number of moves)
        queue<pair<string, int>> q;
        q.push({"0000", 0});
        
        // Visited set to track the states we have already processed
        unordered_set<string> visited;
        visited.insert("0000");
        
        // Start BFS
        while (!q.empty()) {
            auto [current, moves] = q.front();
            q.pop();
            
            // If we've reached the target, return the number of moves
            if (current == target) return moves;
            
            // Generate all possible next states and process them
            for (const string& nextState : getNextStates(current)) {
                if (!visited.count(nextState) && !deadSet.count(nextState)) {
                    q.push({nextState, moves + 1});
                    visited.insert(nextState);
                }
            }
        }
        
        // If we exit the loop without finding the target, return -1
        return -1;
    }
};

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