Correct Answer: Topological sorting of a directed acyclic graph.
Solution:
DFS is commonly used for topological sorting of a directed acyclic graph.
What is a common application of DFS?
Practice Questions
Q1
What is a common application of DFS?
Finding the shortest path in a weighted graph.
Topological sorting of a directed acyclic graph.
Finding the minimum spanning tree.
Finding connected components in a graph.
Questions & Step-by-Step Solutions
What is a common application of DFS?
Step 1: Understand what DFS stands for - it means Depth-First Search, which is a method for exploring graphs.
Step 2: Know what a directed acyclic graph (DAG) is - it's a type of graph that has directed edges and no cycles (no way to return to the same node).
Step 3: Learn about topological sorting - it's a way to arrange the nodes of a DAG in a linear order such that for every directed edge from node A to node B, A comes before B in the order.
Step 4: Recognize that DFS can be used to perform this topological sorting by exploring each node and its connections deeply before moving to the next node.
Depth-First Search (DFS) – A graph traversal algorithm that explores as far as possible along each branch before backtracking.
Topological Sorting – An ordering of the vertices in a directed acyclic graph such that for every directed edge u -> v, vertex u comes before vertex v.
Directed Acyclic Graph (DAG) – A directed graph that has no cycles, meaning it is impossible to start at any vertex and return to it by following the directed edges.
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