<p>There is a <strong>bi-directional </strong>graph with <code>n</code> vertices, where each vertex is labeled from <code>0</code> to <code>n - 1</code>. The edges in the graph are represented by a given 2D integer array <code>edges</code>, where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> denotes an edge between vertex <code>u<sub>i</sub></code> and vertex <code>v<sub>i</sub></code>. Every vertex pair is connected by at most one edge, and no vertex has an edge to itself.</p>

<p>Return <em>the length of the <strong>shortest </strong>cycle in the graph</em>. If no cycle exists, return <code>-1</code>.</p>

<p>A cycle is a path that starts and ends at the same node, and each edge in the path is used only once.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2023/01/04/cropped.png" style="width: 387px; height: 331px;" />
<pre>
<strong>Input:</strong> n = 7, edges = [[0,1],[1,2],[2,0],[3,4],[4,5],[5,6],[6,3]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The cycle with the smallest length is : 0 -&gt; 1 -&gt; 2 -&gt; 0 
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2023/01/04/croppedagin.png" style="width: 307px; height: 307px;" />
<pre>
<strong>Input:</strong> n = 4, edges = [[0,1],[0,2]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> There are no cycles in this graph.
</pre>

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

<ul>
	<li><code>2 &lt;= n &lt;= 1000</code></li>
	<li><code>1 &lt;= edges.length &lt;= 1000</code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>0 &lt;= u<sub>i</sub>, v<sub>i</sub> &lt; n</code></li>
	<li><code>u<sub>i</sub> != v<sub>i</sub></code></li>
	<li>There are no repeated edges.</li>
</ul>

import math
from collections import deque

class Solution(object):
    graph = []
    visited = {}

    def findShortestCycle(self, n, edges):
        """
        :type n: int
        :type edges: List[List[int]]
        :rtype: int
        """
        self.graph = [[] for _ in range(n)]
        for edge in edges:
            self.graph[edge[0]].append(edge[1])
            self.graph[edge[1]].append(edge[0])
        print(self.graph)
        shortest = float('inf')
        
        for i in range(n):
            # print(f'Starting bff from node {i}')
            x = self.findCycle(i)
            shortest = min(shortest, x)
            # print(f'Result from {i} was {x} =========================')

        return -1 if shortest == float('inf') else shortest


    def findCycle(self, start):
        self.visited = {}
        q = deque([(start,-1,0)])
        while len(q) != 0:
            cur, prev, depth = q.popleft()
            # print(f'Node {cur}')
            if cur in self.visited:
                continue
            self.visited[cur] = depth

            for neighbor in self.graph[cur]:
                if neighbor == prev:
                    continue
                # print(f'\tchecking neighbor {neighbor}')
                if neighbor not in self.visited:
                    # print(f'\tAdding {neighbor} to queue')
                    q.append((neighbor, cur, depth + 1))
                else:
                    return self.visited[neighbor] + depth + 1
            
            # print(f'\tNew queue: {q}')
        return float('inf')
                
                

        
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