<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>

"""
___
Goal:
___

return length of longest cycle in tree

___
Examples:
___

Input: edges = [3,3,4,2,3]
Output: 3

Input: edges = [2,-1,3,1]
Output: -1

___
Assumptions:
___

1. If we use topological sort, we would know if no cycles exist

2. index: denotes node, value denotes directed edge to child


___
PsuedoCode: T: O(n + v), S: O(n)
___

1. Use topological search to prune all nodes with indegree of 0

2. if none left, return -1, otherwise use DFS on all nodes and capture max length


"""


class Solution:
    def longestCycle(self, edges: List[int]) -> int:
        
        visited = set()

        indegree = [0 for _ in edges]
        
        for node in edges:
            if node != -1:
                indegree[node] += 1


        queue = deque([n for n, d in enumerate(indegree) if not d])

        while queue:

            node = queue.popleft()

            visited.add(node)

            if (child := edges[node]) != -1:
                indegree[child] -= 1
                if not indegree[child]:
                    queue.append(child)
        
        if len(visited) == len(edges):
            return -1

        longest_cycle = 0

        def dfs(node: int) -> int:
            if node in visited:
                return 0
            visited.add(node)
            return 1 + dfs(edges[node])


        for i in range(len(edges)):
            longest_cycle = max(longest_cycle, dfs(i))


        return longest_cycle
97795