<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 {
    int tsp(int i,int mask,vector<vector<int>>&cost,vector<vector<int>>&dp){
        if(!mask) return 0;
        if(dp[i][mask]!=-1) return dp[i][mask];
        int ans=1E9;
        for(int j=0;j<cost.size();j++){
            if(mask&(1<<j)){
                ans=min(ans,tsp(j,mask^(1<<j),cost,dp)+cost[i][j]);
            }
        }
        return dp[i][mask]=ans;
    }
public:
    int shortestPathLength(vector<vector<int>>& graph) {
        const int n=graph.size();
        vector<vector<int>>cost(n,vector<int>(n,int(1E9)));
        for(int u=0;u<n;u++){
            for(int v:graph[u]){
                cost[u][v]=1;
                cost[v][u]=1;
            }
            cost[u][u]=0;
        }
        for(int u=0;u<n;u++){
            for(int v=0;v<n;v++){
                for(int w=0;w<n;w++){
                    cost[u][v]=min(cost[u][v],cost[u][w]+cost[w][v]);
                }
            }
        }
        int ans=1E9;
        for(int u=0;u<n;u++){
            vector<vector<int>>dp(n,vector<int>(1<<n,-1));
            ans=min(ans,tsp(u,((1<<n)-1)^(1<<u),cost,dp));
        }
        return ans;
    }
};
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