<p>You are given a <strong>directed</strong> graph of <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code>, where each node has <strong>at most one</strong> outgoing edge.</p>

<p>The graph is represented with a given <strong>0-indexed</strong> array <code>edges</code> of size <code>n</code>, indicating that there is a directed edge from node <code>i</code> to node <code>edges[i]</code>. If there is no outgoing edge from node <code>i</code>, then <code>edges[i] == -1</code>.</p>

<p>Return <em>the length of the <strong>longest</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 <strong>same</strong> node.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/06/08/graph4drawio-5.png" style="width: 335px; height: 191px;" />
<pre>
<strong>Input:</strong> edges = [3,3,4,2,3]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The longest cycle in the graph is the cycle: 2 -&gt; 4 -&gt; 3 -&gt; 2.
The length of this cycle is 3, so 3 is returned.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/06/07/graph4drawio-1.png" style="width: 171px; height: 161px;" />
<pre>
<strong>Input:</strong> edges = [2,-1,3,1]
<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>n == edges.length</code></li>
	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>-1 &lt;= edges[i] &lt; n</code></li>
	<li><code>edges[i] != i</code></li>
</ul>

class Solution:
    from collections import deque
    def longestCycle(self, edges: List[int]) -> int:
        n = len(edges)
        graph = {i:[] for i in range(n)}
       
        indegree = [0]*n
        for i in range(len(edges)):
            if edges[i]!=-1:
                graph[i].append(edges[i])
                indegree[edges[i]]+=1

        q = deque([])
        for node in range(len(indegree)):
            if indegree[node]==0:
                q.append(node)

        nodes_in_cycle = {i for i in range(n)}
        
        while q:
            node = q.popleft()
            nodes_in_cycle.remove(node)
            for other in graph[node]:
                indegree[other]-=1
                if indegree[other]==0:
                    q.append(other)

        # now for nodes in nodes_in_cycle, let's find the biggest cycle
        grand_visited = set()
        def dfs(node):
            stack = []
            visited = {}
            current = node
            index = 0
            
            while current not in grand_visited and current != -1 and current not in visited:
                visited[current] = index
                stack.append(current)
                index += 1
                grand_visited.add(current)
                current = edges[current]
            
            # Check if we have found a cycle
            if current in visited:
                return index - visited[current]
            return 0
        
        largest_cycle = -1
        for node in nodes_in_cycle:
            if node not in grand_visited:
                size = dfs(node)
                largest_cycle = max(largest_cycle, size)
        return largest_cycle

            



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