(Topological ordering with DFS) The algorithm for topological ordering that we discussed in the class has...

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(Topological ordering with DFS) The algorithm for topological ordering that we discussed in the class has a run time of O(V²). In this exercise, we explore a more efficient algorithm. The idea is based on the DFS algorithm. (a) (10 points) Consider the graph below. Consider the DFS implementation with stack. Run DF with 1 being the starting node. What is the order of the nodes appearing in the stack from the top to the bottom? How can this stack be used to find the topological ordering 3 4 = (b) (10 points) Design an algorithm for finding the topological ordering of a graph G run time O(V|+|E). Write a pseudo code for the algorithm. (V, E) with (Topological ordering with DFS) The algorithm for topological ordering that we discussed in the class has a run time of O(V²). In this exercise, we explore a more efficient algorithm. The idea is based on the DFS algorithm. (a) (10 points) Consider the graph below. Consider the DFS implementation with stack. Run DF with 1 being the starting node. What is the order of the nodes appearing in the stack from the top to the bottom? How can this stack be used to find the topological ordering 3 4 = (b) (10 points) Design an algorithm for finding the topological ordering of a graph G run time O(V|+|E). Write a pseudo code for the algorithm. (V, E) with

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To find the topological ordering of a directed acyclic graph DAG using DepthFirst Search DFS we can follow these steps Start DFS from any node in the ... View the full answer