To find the topological sort order of a directed acyclic graph (DAG), you can use the depth-first search (DFS) algorithm. Here is the step-by-step process:

  1. Create a list to store the topological sort order.

  2. Apply the DFS algorithm on the graph, starting from any node that has no incoming edges.

  3. During the DFS traversal, mark each visited node as "visited" to avoid revisiting it.

  4. After visiting all the neighbors of a node, add it to the front of the topological sort order list.

  5. Repeat step 4 for all unvisited nodes in the graph until all nodes are visited.

  By following this approach, the resulting list will represent the topological sort order of the graph.

  It is important to note that the graph must be a directed acyclic graph for a valid topological sort order to exist. If the graph contains a cycle, it is impossible to find a topological sort order. Therefore, it is crucial to confirm that the graph is acyclic before applying the topological sort algorithm.

  The time complexity of finding the topological sort order using this method is O(V + E), where V is the number of vertices and E is the number of edges in the graph. This approach ensures an efficient and accurate way to determine the topological sort order of a DAG.