<p>You have an undirected, connected graph of <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>. You are given an array <code>graph</code> where <code>graph[i]</code> is a list of all the nodes connected with node <code>i</code> by an edge.</p>

<p>Return <em>the length of the shortest path that visits every node</em>. You may start and stop at any node, you may revisit nodes multiple times, and you may reuse edges.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/05/12/shortest1-graph.jpg" style="width: 222px; height: 183px;" />
<pre>
<strong>Input:</strong> graph = [[1,2,3],[0],[0],[0]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> One possible path is [1,0,2,0,3]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/05/12/shortest2-graph.jpg" style="width: 382px; height: 222px;" />
<pre>
<strong>Input:</strong> graph = [[1],[0,2,4],[1,3,4],[2],[1,2]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> One possible path is [0,1,4,2,3]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == graph.length</code></li>
	<li><code>1 &lt;= n &lt;= 12</code></li>
	<li><code>0 &lt;= graph[i].length &lt;&nbsp;n</code></li>
	<li><code>graph[i]</code> does not contain <code>i</code>.</li>
	<li>If <code>graph[a]</code> contains <code>b</code>, then <code>graph[b]</code> contains <code>a</code>.</li>
	<li>The input graph is always connected.</li>
</ul>

class Solution {
public:
    bool checkAllVisited(int mask, int n) {
        int count = 0;
        while(mask) {
            if((mask & 1 ) == 1) count++;
            mask >>= 1; 
        }
        return count == n;
    }


    int shortestPathLength(vector<vector<int>>& graph) {
        // int a = 3 | (1 << 4);
        // cout << a << endl;
        int n  = graph.size();
        int f = (1 << n) - 1;
        
        deque<vector<int>> q;
        // vector<vector<bool>> visited(n, vector<bool>(f +1, false));
        set<vector<int>> visited;
        for(int i =0; i < n; i++) {
            q.push_back({i, 1 << i});
            int a= 1 << i;
            visited.insert({i, 1 << i});
            // cout << i << " " << a << endl;
        }
        
        int res=0;
        // if(n == 5) cout<< visited[4][19];
        while(q.size()) {
            int len = q.size();
            for(int i =0; i < len; i++) {
                auto top = q.front();
                q.pop_front();
                int mask = top[1], u = top[0];
                // if(mask == 19 && u == 4)cout << mask << " " << u << endl;
                if(checkAllVisited(mask, n)) return res;

                for(auto v : graph[u]) {
                    int temp = mask | (1 << v);
                    // if(temp == 19 && v == 4) cout << temp << " " << v << endl;
                    // if(temp == 19 && v == 4) cout << visited[v][temp] << " ";
                    if(!visited.count({v, temp})) {
                        visited.insert({v,temp});
                        q.push_back({v, temp});
                    }
                }
            }
            res++;
        }
        return res;
        

    }
};
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