Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Which of the following statements is false?a)...
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Which of the following statements is false?
- a)Optimal binary search tree construction can be performed efficiently using dynamic programming
- b)Breadth-first search cannot be used to find connected components of a graph
- c)Given the prefix and postfix walks over a binary tree, the binary tree cannot be uniquely constructed.
- d)Depth-first search can be used to find connected components of a graph
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Which of the following statements is false?a)Optimal binary search tre...
(a) True.
(b) False.
(c) True.
(d) True.
(b) False.
(c) True.
(d) True.
Most Upvoted Answer
Which of the following statements is false?a)Optimal binary search tre...
Explanation:
Breadth-first search (BFS) is a graph traversal algorithm that visits all the vertices of a graph in breadth-first order, i.e., it visits all the vertices at the same level before moving on to the next level. BFS can be used to find connected components of a graph.
The false statement is that breadth-first search cannot be used to find connected components of a graph. This statement is false because BFS can be used to find connected components of a graph.
BFS to Find Connected Components:
To find the connected components of a graph using BFS, we can follow these steps:
1. Initialize all vertices as unvisited.
2. For each unvisited vertex, perform BFS starting from that vertex.
3. During BFS, mark all visited vertices as belonging to the same connected component.
4. Repeat steps 2-3 until all vertices have been visited.
5. The number of times we perform BFS is equal to the number of connected components in the graph.
Example:
Consider the following undirected graph:
1 -- 2 4
/ | |
3 5 -- 6
The connected components of this graph are {1,2,3} and {4,5,6}.
We can use BFS to find the connected components as follows:
1. Start BFS from vertex 1.
2. Visit vertices 1, 2, and 3 and mark them as belonging to the same connected component.
3. Start BFS from vertex 4.
4. Visit vertices 4, 5, and 6 and mark them as belonging to the same connected component.
Therefore, the connected components of the graph are {1,2,3} and {4,5,6}.
Conclusion:
Breadth-first search can be used to find connected components of a graph, so option B is the false statement.
Breadth-first search (BFS) is a graph traversal algorithm that visits all the vertices of a graph in breadth-first order, i.e., it visits all the vertices at the same level before moving on to the next level. BFS can be used to find connected components of a graph.
The false statement is that breadth-first search cannot be used to find connected components of a graph. This statement is false because BFS can be used to find connected components of a graph.
BFS to Find Connected Components:
To find the connected components of a graph using BFS, we can follow these steps:
1. Initialize all vertices as unvisited.
2. For each unvisited vertex, perform BFS starting from that vertex.
3. During BFS, mark all visited vertices as belonging to the same connected component.
4. Repeat steps 2-3 until all vertices have been visited.
5. The number of times we perform BFS is equal to the number of connected components in the graph.
Example:
Consider the following undirected graph:
1 -- 2 4
/ | |
3 5 -- 6
The connected components of this graph are {1,2,3} and {4,5,6}.
We can use BFS to find the connected components as follows:
1. Start BFS from vertex 1.
2. Visit vertices 1, 2, and 3 and mark them as belonging to the same connected component.
3. Start BFS from vertex 4.
4. Visit vertices 4, 5, and 6 and mark them as belonging to the same connected component.
Therefore, the connected components of the graph are {1,2,3} and {4,5,6}.
Conclusion:
Breadth-first search can be used to find connected components of a graph, so option B is the false statement.
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