Topological Sort Problem Statement

You have a directed acyclic graph (DAG). The task is to determine any topological sorting of this graph.

Explanation:

A Directed Acyclic Graph (DAG) is a graph that has directed edges and no cycles. Topological sorting is a linear ordering of the vertices such that for every directed edge from vertex u to vertex v, u comes before v in the ordering.

Input:

The first line of input contains an integer ‘T’ representing the number of test cases. For each test case:
- The first line contains two integers, ‘N’ and ‘M’, where ‘N’ is the number of nodes and ‘M’ is the number of edges.
- The following ‘M’ lines each contain two integers, ‘U’ and ‘V’, indicating a directed edge from node ‘U’ to node ‘V’.

Output:

For each test case, output a single line containing N space-separated integers denoting a valid topological sort of the graph. Each test case's output should be on a new line.

Example:

Given the following DAG graph:
Image representation (not shown here)
Possible output topological sort: 1 2 3

Constraints:

  • 1 <= T <= 100
  • 1 <= N <= 5000
  • 0 <= M <= min(5000, (N*(N-1))/2)
  • 1 <= U, V <= N and U != V
  • Time Limit: 1 second

Note:

You are not required to print the expected output; Just implement the function to return the answer.

AnswerBot
1mo

Implement a function to determine any topological sorting of a directed acyclic graph (DAG).

  • Create a graph using the given input of nodes and edges

  • Perform a topological sort on the graph to find a val...read more

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