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Which of the following statements is true regarding Depth First Search (DFS)?
- a)DFS always finds the shortest path between two vertices.
- b)DFS can detect cycles in a graph.
- c)DFS guarantees the minimum spanning tree of a graph.
- d)DFS can only be applied to connected graphs.
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Which of the following statements is true regarding Depth First Search...
DFS Can Detect Cycles in a Graph
DFS (Depth First Search) is a graph traversal algorithm that explores vertices as far as possible along each branch before backtracking. It is commonly used to traverse or search a graph data structure. Let's take a look at why option 'B' is the correct answer.
DFS Algorithm
DFS starts at a given vertex and explores as far as possible along each branch before backtracking. It uses a stack to keep track of the vertices to be visited. The algorithm follows these steps:
1. Start with an empty stack and an empty visited set.
2. Push the starting vertex onto the stack.
3. While the stack is not empty:
- Pop a vertex from the stack.
- If the vertex has not been visited:
- Mark it as visited.
- Process the vertex.
- Push its unvisited neighbors onto the stack.
Detecting Cycles
DFS can be used to detect cycles in a graph. It does this by keeping track of the vertices it has visited and checking for back edges. A back edge is an edge that connects a vertex to one of its ancestors in the DFS traversal tree.
When DFS encounters an edge (u, v), where u is the current vertex and v is one of its neighbors, it checks if v has already been visited. If v has been visited and is not the parent of u, then there is a back edge and hence a cycle in the graph.
Example
Let's consider an example to illustrate this. Suppose we have a graph with the following edges: (A, B), (B, C), (C, D), (D, A). Starting from vertex A, the DFS traversal would be A -> B -> C -> D -> A.
When DFS reaches vertex D, it encounters the edge (D, A). Since vertex A has already been visited and is not the parent of D, there is a back edge and hence a cycle in the graph.
Therefore, option 'B' is true. DFS can detect cycles in a graph by checking for back edges during its traversal.
DFS (Depth First Search) is a graph traversal algorithm that explores vertices as far as possible along each branch before backtracking. It is commonly used to traverse or search a graph data structure. Let's take a look at why option 'B' is the correct answer.
DFS Algorithm
DFS starts at a given vertex and explores as far as possible along each branch before backtracking. It uses a stack to keep track of the vertices to be visited. The algorithm follows these steps:
1. Start with an empty stack and an empty visited set.
2. Push the starting vertex onto the stack.
3. While the stack is not empty:
- Pop a vertex from the stack.
- If the vertex has not been visited:
- Mark it as visited.
- Process the vertex.
- Push its unvisited neighbors onto the stack.
Detecting Cycles
DFS can be used to detect cycles in a graph. It does this by keeping track of the vertices it has visited and checking for back edges. A back edge is an edge that connects a vertex to one of its ancestors in the DFS traversal tree.
When DFS encounters an edge (u, v), where u is the current vertex and v is one of its neighbors, it checks if v has already been visited. If v has been visited and is not the parent of u, then there is a back edge and hence a cycle in the graph.
Example
Let's consider an example to illustrate this. Suppose we have a graph with the following edges: (A, B), (B, C), (C, D), (D, A). Starting from vertex A, the DFS traversal would be A -> B -> C -> D -> A.
When DFS reaches vertex D, it encounters the edge (D, A). Since vertex A has already been visited and is not the parent of D, there is a back edge and hence a cycle in the graph.
Therefore, option 'B' is true. DFS can detect cycles in a graph by checking for back edges during its traversal.
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Which of the following statements is true regarding Depth First Search...
DFS can be used to detect cycles in a graph.
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Which of the following statements is true regarding Depth First Search (DFS)?a)DFS always finds the shortest path between two vertices.b)DFS can detect cycles in a graph.c)DFS guarantees the minimum spanning tree of a graph.d)DFS can only be applied to connected graphs.Correct answer is option 'B'. Can you explain this answer?
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Which of the following statements is true regarding Depth First Search (DFS)?a)DFS always finds the shortest path between two vertices.b)DFS can detect cycles in a graph.c)DFS guarantees the minimum spanning tree of a graph.d)DFS can only be applied to connected graphs.Correct answer is option 'B'. Can you explain this answer? for Software Development 2024 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about Which of the following statements is true regarding Depth First Search (DFS)?a)DFS always finds the shortest path between two vertices.b)DFS can detect cycles in a graph.c)DFS guarantees the minimum spanning tree of a graph.d)DFS can only be applied to connected graphs.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Software Development 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is true regarding Depth First Search (DFS)?a)DFS always finds the shortest path between two vertices.b)DFS can detect cycles in a graph.c)DFS guarantees the minimum spanning tree of a graph.d)DFS can only be applied to connected graphs.Correct answer is option 'B'. Can you explain this answer?.
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