<p>There is a directed graph of <code>n</code> nodes with each node labeled from <code>0</code> to <code>n - 1</code>. The graph is represented by a <strong>0-indexed</strong> 2D integer array <code>graph</code> where <code>graph[i]</code> is an integer array of nodes adjacent to node <code>i</code>, meaning there is an edge from node <code>i</code> to each node in <code>graph[i]</code>.</p>

<p>A node is a <strong>terminal node</strong> if there are no outgoing edges. A node is a <strong>safe node</strong> if every possible path starting from that node leads to a <strong>terminal node</strong> (or another safe node).</p>

<p>Return <em>an array containing all the <strong>safe nodes</strong> of the graph</em>. The answer should be sorted in <strong>ascending</strong> order.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="Illustration of graph" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/03/17/picture1.png" style="height: 171px; width: 600px;" />
<pre>
<strong>Input:</strong> graph = [[1,2],[2,3],[5],[0],[5],[],[]]
<strong>Output:</strong> [2,4,5,6]
<strong>Explanation:</strong> The given graph is shown above.
Nodes 5 and 6 are terminal nodes as there are no outgoing edges from either of them.
Every path starting at nodes 2, 4, 5, and 6 all lead to either node 5 or 6.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> graph = [[1,2,3,4],[1,2],[3,4],[0,4],[]]
<strong>Output:</strong> [4]
<strong>Explanation:</strong>
Only node 4 is a terminal node, and every path starting at node 4 leads to node 4.
</pre>

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

<ul>
	<li><code>n == graph.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= graph[i].length &lt;= n</code></li>
	<li><code>0 &lt;= graph[i][j] &lt;= n - 1</code></li>
	<li><code>graph[i]</code> is sorted in a strictly increasing order.</li>
	<li>The graph may contain self-loops.</li>
	<li>The number of edges in the graph will be in the range <code>[1, 4 * 10<sup>4</sup>]</code>.</li>
</ul>

class Solution {
public:
    bool function(vector<vector<int>> &adj, int index, unordered_map<int, bool>& visited, vector<int>& ans,
    vector<bool> &safe){
        //we check all the neighbours of the current node
        //if there are no neighbours or all the neighbours are safe state, we say this is safe
        for(int x: adj[index]){
            //we check for each node
            if(visited[x] == false){
                visited[x] = true;
                bool a = function(adj, x, visited, ans, safe);
                if(!a) return safe[index] = false;
            }
            else{
                //if this node has been visited, then we check whether it is a safe node or not
                if(safe[x] != true) return safe[index] = false;
            }
        }
        ans.push_back(index);
        return safe[index] = true;    //because if it is inserted in the ans, must be a safe state
    }
    vector<int> eventualSafeNodes(vector<vector<int>>& graph) {
        vector<bool> safe(graph.size(), false);
        vector<int> ans;
        unordered_map<int, bool> visited;
        for(int i=0; i<=graph.size()-1; i++){
            if(visited.find(i) == visited.end()){
                //check for this disconnected component as well
                visited[i] = true;
                function(graph, i, visited, ans, safe);
            }
        }
        sort(ans.begin(), ans.end());
        return ans;
    }
};
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