<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 {
public: // kosaraju algorithm find the maximum length of all
        // of the strongly connected component
    int longestCycle(vector<int>& edges) {
            int V = edges.size();
            vector<vector<int>> adj(V);
            
            // Build the adjacency list
            for (int i = 0; i < V; ++i) {
                if (edges[i] != -1) {
                    adj[i].push_back(edges[i]);
                }
            }

            // Find strongly connected components using Kosaraju's algorithm
            return kosaraju(V, adj);
    }

    void dfs(int node, vector<int> &vis, vector<vector<int>>& adj,
             stack<int> &st) {
        vis[node] = 1;
        for (auto it : adj[node]) {
            if (!vis[it]) {
                dfs(it, vis, adj, st);
            }
        }

        st.push(node);
    }

    void dfs3(int node, vector<int> &vis, vector<int> adjT[],int &count) {
        vis[node] = 1;
        count++;
        for (auto it : adjT[node]) {
            if (!vis[it]) {
                dfs3(it, vis, adjT,count);
            }
        }
    }

    //Function to find number of strongly connected components in the graph.
    int kosaraju(int V, vector<vector<int>>& adj)
    {
        vector<int> vis(V, 0);
        stack<int> st;
        for (int i = 0; i < V; i++) {
            if (!vis[i]) {
                dfs(i, vis, adj, st);
            }
        }

        vector<int> adjT[V];
        for (int i = 0; i < V; i++) {
            vis[i] = 0;
            for (auto it : adj[i]) {
                // i -> it
                // it -> i
                adjT[it].push_back(i);
            }
        }
        int longest = 0;
        while (!st.empty()) {
            int node = st.top();
            st.pop();
            if (!vis[node]) {
                int count = 0;
                dfs3(node, vis, adjT,count);
                if (count > 1) longest = max(longest , count);
            }
        }
        if(longest == 0)return -1;
        else return longest;
    }
};
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