<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:
    def shortestPathLength(self, graph: List[List[int]]) -> int:
        num_nodes = len(graph)
        all_visited_mask = (1 << num_nodes) - 1
        q = deque()

        # Initialize visited array
        visited = [[False for _ in range(num_nodes)] for _ in range(all_visited_mask + 1)]

        # Start from each node and add it to the queue as a starting point
        for node in range(num_nodes):
            initial_mask = (1 << node)
            q.append((node, initial_mask, 1))
            visited[initial_mask][node] = True

        while q:
            current = q.popleft()
            current_node, current_mask, current_length = current

            # Check if all nodes have been visited
            if current_mask == all_visited_mask:
                return current_length - 1

            # Explore the neighbors of the current node
            for neighbor in graph[current_node]:
                new_mask = current_mask | (1 << neighbor)

                # Check if this state has been visited before
                if visited[new_mask][neighbor]:
                    continue

                # Add the neighbor to the queue with updated state
                q.append((neighbor, new_mask, current_length + 1))
                visited[new_mask][neighbor] = True

        return -1  # No valid path found
17800