Find Eventual Safe States | leetcode 802 solution | detect cycle in directed graph

 Find Eventual Safe States

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

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

Return an array containing all the safe nodes of the graph. The answer should be sorted in ascending order.

 

Example 1:

Input: graph = [[1,2],[2,3],[5],[0],[5],[],[]]
Output: [2,4,5,6]
Explanation: 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.

Example 2:

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

 

Constraints:

• n == graph.length
• 1 <= n <= 104
• 0 <= graph[i].length <= n
• 0 <= graph[i][j] <= n - 1
• graph[i] is sorted in a strictly increasing order.
• The graph may contain self-loops.
• The number of edges in the graph will be in the range [1, 4 * 104].

solution:

The solution is based on detecting cycle in a directed graph using dfs. if any particular node make a cycle after going through dfs , it will be not be push into vector<int>result.

class Solution {

public:

    bool dfs(vector<bool>&visited , vector<bool>&visiteddfs , int i , vector<vector<int>>&graph)

    {

        visited[i]= true;

        visiteddfs[i] = true;

        vector<int>x = graph[i];

        for(int i = 0 ; i < x.size(); i++)

        {

            if(!visited[x[i]])

            {

                if(dfs(visited, visiteddfs , x[i] , graph))

                    return true;

            }

            else

            {

                if(visiteddfs[x[i]])

                {

                     return true;

                }

            }

        }

        visiteddfs[i] = false;

        return false;

    }

    vector<int> eventualSafeNodes(vector<vector<int>>& graph) {

        int V = graph.size();

        vector<bool>visited(V , false);

        vector<bool>visiteddfs(V, false);

        vector<int>result;

        for(int i = 0 ; i < V ; i++)

        {

            if(!dfs(visited , visiteddfs , i , graph))

                result.push_back(i);

        }

        return result;

    }

};