<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:
    def longestCycle(self, edges: List[int]) -> int:
        visited = [0] * len(edges)
        inStack = [0] * len(edges)  # Keep track of nodes in the current DFS stack
        count_container = [0]       # A mutable counter to track the current depth of DFS
        max_container = [0]         # Store the length of the longest cycle found

        def dfs(edges, s, visited, inStack, count_container, max_container):
            visited[s] = 1
            inStack[s] = count_container[0] + 1  # Mark node as part of current DFS stack
            count_container[0] += 1

            if edges[s] != -1:
                if visited[edges[s]] == 0:
                    # Recur for the next node if it hasn't been visited yet
                    dfs(edges, edges[s], visited, inStack, count_container, max_container)
                elif inStack[edges[s]] > 0:
                    # Found a back edge, calculate the cycle length
                    cycle_length = count_container[0] - inStack[edges[s]] + 1
                    if cycle_length > max_container[0]:
                        max_container[0] = cycle_length

            # Mark the node as not in the stack anymore
            inStack[s] = 0
            count_container[0] -= 1
        
        # Run DFS for each node
        for i in range(len(edges)):
            if visited[i] == 0:
                dfs(edges, i, visited, inStack, count_container, max_container)

        return max_container[0] if max_container[0] > 0 else -1  # Return -1 if no cycle is found

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