Shortest Path Visiting All Nodes
<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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0800-0899/0847.Shortest%20Path%20Visiting%20All%20Nodes/images/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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0800-0899/0847.Shortest%20Path%20Visiting%20All%20Nodes/images/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>
Bit Manipulation; Breadth-First Search; Graph; Dynamic Programming; Bitmask
use std::collections::VecDeque;

impl Solution {
    #[allow(dead_code)]
    pub fn shortest_path_length(graph: Vec<Vec<i32>>) -> i32 {
        let n = graph.len();
        let mut vis = vec![vec![false; 1 << n]; n];
        let mut q = VecDeque::new();

        // Initialize the queue
        for i in 0..n {
            q.push_back(((i, 1 << i), 0));
            vis[i][1 << i] = true;
        }

        // Begin BFS
        while !q.is_empty() {
            let ((i, st), count) = q.pop_front().unwrap();
            if st == (1 << n) - 1 {
                return count;
            }
            // If the path has not been visited
            for j in &graph[i] {
                let nst = st | (1 << *j);
                if !vis[*j as usize][nst] {
                    q.push_back(((*j as usize, nst), count + 1));
                    vis[*j as usize][nst] = true;
                }
            }
        }

        -1
    }
}
