<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 {
    using LockSetting = std::tuple<uint8_t, uint8_t, uint8_t, uint8_t>;
    LockSetting toLockSetting(string s) {
        return {
            static_cast<uint8_t>(s[0] - '0'),
            static_cast<uint8_t>(s[1] - '0'),
            static_cast<uint8_t>(s[2] - '0'),
            static_cast<uint8_t>(s[3] - '0')
        };
    }

    static inline uint8_t mod10(uint8_t x) {
        return x - (x >= 10) * 10;
    }

    static std::array<LockSetting, 8> neighbors(LockSetting ls) {
        return {
            LockSetting{mod10(get<0>(ls) + 1), get<1>(ls), get<2>(ls), get<3>(ls)},
            LockSetting{mod10(get<0>(ls) + 9), get<1>(ls), get<2>(ls), get<3>(ls)},
            LockSetting{get<0>(ls), mod10(get<1>(ls) + 1), get<2>(ls), get<3>(ls)},
            LockSetting{get<0>(ls), mod10(get<1>(ls) + 9), get<2>(ls), get<3>(ls)},
            LockSetting{get<0>(ls), get<1>(ls), mod10(get<2>(ls) + 1), get<3>(ls)},
            LockSetting{get<0>(ls), get<1>(ls), mod10(get<2>(ls) + 9), get<3>(ls)},
            LockSetting{get<0>(ls), get<1>(ls), get<2>(ls), mod10(get<3>(ls) + 1)},
            LockSetting{get<0>(ls), get<1>(ls), get<2>(ls), mod10(get<3>(ls) + 9)},
        };
    }

public:
    int openLock(vector<string>& deadendsStr, string targetStr) {
        using Visited = std::set<LockSetting>;
        auto visited = Visited{};
        for (auto& str : deadendsStr) {
            visited.insert(toLockSetting(str));
        }

        constexpr auto source = LockSetting{0, 0, 0, 0};
        auto target = toLockSetting(targetStr);

        using Queue = std::queue<std::pair<LockSetting, uint8_t>>;
        auto queue = Queue{};
        queue.emplace(source, 0);

        while (!queue.empty()) {
            auto [setting, dist] = queue.front();
            queue.pop();
            if (setting == target) return dist;
            if (visited.contains(setting)) continue;
            visited.insert(setting);

            for (LockSetting next : neighbors(setting)) {
                queue.emplace(next, dist + 1);
            }
        }
        
        return -1;
    }
};
32990