Minimum Number of Vertices to Reach All Nodes Problem Statement

In a directed acyclic graph with 'N' nodes, given a matrix 'edges' of size M x 2 representing 'M' edges where each edge is directed from node edges[i][0] to node edges[i][1], find the smallest set of vertices from which all the nodes in the graph are reachable.

Input:

The first line contains a single integer ‘T’, denoting the number of test cases.
The first line of each test case contains two integers ‘N’ and ‘M’, where ‘N’ represents the number of vertices and ‘M’ denotes the number of edges.
The next ‘M’ lines of each test case contain two integers ‘X’ and ‘Y’, where ‘X’ is the start vertex and ‘Y’ is the end vertex of a directed edge.

Output:

For each test case, output the smallest set of vertices from which all the nodes in the graph are reachable, in sorted order.
Print each test case result on a new line.

Example:

Sample Input:
2
6 5
0 1
0 2
2 5
3 4
4 2
5 4
0 1
2 1
1 4
2 4
Sample Output:
0 3
0 2 3
Explanation of Sample Output:
In the first test case, the vertices 0 and 3 can collectively reach all other nodes in the graph.
In the second test case, the vertices 0, 2, and 3 can collectively reach all nodes.

Constraints:

  • 1 ≤ T ≤ 5
  • 2 ≤ N ≤ 105
  • 1 ≤ M ≤ 105
  • 0 ≤ X, Y ≤ N - 1
  • Time Limit: 1 second
Note:
Nodes are numbered from 0 to N - 1.
The provided graph is connected.
Vertices in the result should be printed in sorted order.
AnswerBot
4mo

The problem involves finding the smallest set of vertices from which all nodes in a directed acyclic graph are reachable.

  • Create a directed graph using the given edges.

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