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In an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most efficiently, in terms of time complexity by
- a)Dijkstra’s algorithm starting from S.
- b)Warshall’s algorithm
- c)Performing a DFS starting from S.
- d)Performing a BFS starting from S.
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In an unweighted, undirected connected graph, the shortest path from a...
* Time Comlexity of the Dijkstra’s algorithm is O(|V|^2 + E)
* Time Comlexity of the Warshall’s algorithm is O(|V|^3) *
DFS cannot be used for finding shortest paths
* BFS can be used for unweighted graphs. Time Complexity for BFS is O(|E| + |V|)
* Time Comlexity of the Warshall’s algorithm is O(|V|^3) *
DFS cannot be used for finding shortest paths
* BFS can be used for unweighted graphs. Time Complexity for BFS is O(|E| + |V|)
Most Upvoted Answer
In an unweighted, undirected connected graph, the shortest path from a...
Shortest Path in a Graph
Graph traversal algorithms are used to visit nodes of a graph. The shortest path problem is to find the shortest path or distance from a source node to all other nodes in the graph. There are two types of graphs: weighted and unweighted. In a weighted graph, the distance between any two nodes is a weight or cost. In an unweighted graph, the distance between any two nodes is the number of edges that connect them.
BFS Algorithm
Breadth-First Search (BFS) algorithm is used to traverse a graph. It starts from a source node and visits all the nodes that are reachable from it in breadth-first order. BFS algorithm is used to find the shortest path or distance from a source node to all other nodes in an unweighted graph.
Steps of BFS Algorithm
1. Create a queue and mark the source node as visited.
2. Enqueue the source node into the queue.
3. While the queue is not empty, dequeue a node from the queue and print it.
4. Enqueue all the adjacent nodes of the dequeued node that are not visited and mark them as visited.
5. Repeat steps 3 to 4 until the queue is empty.
Advantages of BFS Algorithm
1. It is the simplest algorithm for finding the shortest path in an unweighted graph.
2. It guarantees finding the shortest path in an unweighted graph.
3. It has a time complexity of O(V+E), where V is the number of vertices and E is the number of edges in the graph.
Conclusion
In an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most efficiently by performing a BFS starting from S. The reason is that BFS algorithm guarantees finding the shortest path in an unweighted graph and has a time complexity of O(V+E), which is the most efficient for this problem.
Graph traversal algorithms are used to visit nodes of a graph. The shortest path problem is to find the shortest path or distance from a source node to all other nodes in the graph. There are two types of graphs: weighted and unweighted. In a weighted graph, the distance between any two nodes is a weight or cost. In an unweighted graph, the distance between any two nodes is the number of edges that connect them.
BFS Algorithm
Breadth-First Search (BFS) algorithm is used to traverse a graph. It starts from a source node and visits all the nodes that are reachable from it in breadth-first order. BFS algorithm is used to find the shortest path or distance from a source node to all other nodes in an unweighted graph.
Steps of BFS Algorithm
1. Create a queue and mark the source node as visited.
2. Enqueue the source node into the queue.
3. While the queue is not empty, dequeue a node from the queue and print it.
4. Enqueue all the adjacent nodes of the dequeued node that are not visited and mark them as visited.
5. Repeat steps 3 to 4 until the queue is empty.
Advantages of BFS Algorithm
1. It is the simplest algorithm for finding the shortest path in an unweighted graph.
2. It guarantees finding the shortest path in an unweighted graph.
3. It has a time complexity of O(V+E), where V is the number of vertices and E is the number of edges in the graph.
Conclusion
In an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most efficiently by performing a BFS starting from S. The reason is that BFS algorithm guarantees finding the shortest path in an unweighted graph and has a time complexity of O(V+E), which is the most efficient for this problem.
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In an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most efficiently, in terms of time complexity bya)Dijkstra’s algorithm starting from S.b)Warshall’s algorithmc)Performing a DFS starting from S.d)Performing a BFS starting from S.Correct answer is option 'D'. Can you explain this answer?
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