If a graph has a cycle, which traversal method can detect it?
Practice Questions
Q1
If a graph has a cycle, which traversal method can detect it?
Only BFS
Only DFS
Both BFS and DFS
Neither BFS nor DFS
Questions & Step-by-Step Solutions
If a graph has a cycle, which traversal method can detect it?
Step 1: Understand what a cycle in a graph is. A cycle occurs when you can start at a node and return to it by following edges without repeating any edges.
Step 2: Learn about graph traversal methods. The two common methods are Depth-First Search (DFS) and Breadth-First Search (BFS).
Step 3: Focus on Depth-First Search (DFS) for cycle detection. DFS explores as far as possible along each branch before backtracking.
Step 4: Keep track of visited nodes during the DFS. This helps to know which nodes have already been explored.
Step 5: Check for back edges. A back edge is an edge that points from a node to one of its ancestors in the DFS tree. If you find a back edge, it indicates a cycle.
Step 6: Conclude that DFS is the method that can detect cycles in a graph.
Graph Traversal – Understanding different methods of traversing graphs, such as Depth-First Search (DFS) and Breadth-First Search (BFS).
Cycle Detection – The ability to identify cycles within a graph using traversal methods.
Back Edges – Recognizing back edges in DFS as indicators of cycles in directed and undirected graphs.
