<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 sol(string &cur, string &t, set<string> &d, map<string,int> &vis, map<string,int> &dp){
    //     if(d.count(cur)) return 1e9;
    //     if(cur==t) return 0;
    //     if(vis[cur]==2) return dp[cur];
    //     vis[cur]=1;
    //     int &ans = dp[cur];
    //     ans = 1e9;
    //     for(int i=0;i<4;i++){
    //         int ch = cur[i] - '0';
    //         int nxt = (ch+1)%10;
    //         cur[i]='0'+nxt;
    //         if(vis[cur]!=1) ans = min(ans, 1 + sol(cur,t,d,vis,dp));
    //         int prev = (ch - 1 + 10)%10;
    //         cur[i]='0'+prev;
    //         if(vis[cur]!=1) ans = min(ans, 1 + sol(cur,t,d,vis,dp));
    //         cur[i] = '0' + ch;
    //     }
    //     vis[cur]=2;
    //     return ans;
    // }
    int openLock(vector<string>& a, string t) {
        map<string,int>  vis;
        set<string> st;
        for(auto x:a) st.insert(x);
        string init = "0000";
        if(st.count(init)) return -1;
        vis[init] = 0;
        queue<string> q;
        q.push(init);
        while(q.size()){
            auto u = q.front();
            q.pop();
            for(int i=0;i<4;i++){
                string cur = u;
                int ch = cur[i] - '0';
                int nxt = (ch+1)%10;
                cur[i]='0'+nxt;
                if(!vis.count(cur) && !st.count(cur)) {
                    vis[cur]=vis[u]+1;
                    q.push(cur);
                }
                int prev = (ch - 1 + 10)%10;
                cur[i]='0'+prev;
                if(!vis.count(cur) && !st.count(cur)) {
                    vis[cur]=vis[u]+1;
                    q.push(cur);
                }
            }
        }
        if(!vis.count(t)) return -1;
        return vis[t];
    }
};
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