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Shortest Paths

This quiz covers the concept of shortest paths in graph theory, including Dijkstra's algorithm, Floyd-Warshall algorithm, and Bellman-Ford algorithm.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

What is the primary goal of shortest path algorithms?

  1. Finding the shortest path between two nodes in a graph
  2. Determining the longest path between two nodes in a graph
  3. Calculating the total weight of all paths in a graph
  4. Identifying cycles in a graph
Question 2 Multiple Choice (Single Answer)

Which algorithm is commonly used for finding the shortest path between a single source node and all other nodes in a graph?

  1. Dijkstra's Algorithm
  2. Floyd-Warshall Algorithm
  3. Bellman-Ford Algorithm
  4. Prim's Algorithm
Question 3 Multiple Choice (Single Answer)

What is the time complexity of Dijkstra's Algorithm for finding the shortest paths in a graph with V vertices and E edges?

  1. O(V^2)
  2. O(E log V)
  3. O(V log V)
  4. O(E^2)
Question 4 Multiple Choice (Single Answer)

Which algorithm is suitable for finding the shortest paths between all pairs of nodes in a graph?

  1. Dijkstra's Algorithm
  2. Floyd-Warshall Algorithm
  3. Bellman-Ford Algorithm
  4. Kruskal's Algorithm
Question 5 Multiple Choice (Single Answer)

What is the time complexity of the Floyd-Warshall Algorithm for finding the shortest paths between all pairs of nodes in a graph with V vertices?

  1. O(V^2)
  2. O(V^3)
  3. O(V log V)
  4. O(E log V)
Question 6 Multiple Choice (Single Answer)

Which algorithm can handle negative edge weights in a graph while finding the shortest paths?

  1. Dijkstra's Algorithm
  2. Floyd-Warshall Algorithm
  3. Bellman-Ford Algorithm
  4. Prim's Algorithm
Question 7 Multiple Choice (Single Answer)

What is the time complexity of the Bellman-Ford Algorithm for finding the shortest paths in a graph with V vertices and E edges?

  1. O(V^2)
  2. O(E log V)
  3. O(V log V)
  4. O(V^3)
Question 8 Multiple Choice (Single Answer)

In Dijkstra's Algorithm, which data structure is typically used to efficiently maintain the set of unvisited nodes?

  1. Queue
  2. Stack
  3. Binary Search Tree
  4. Hash Table
Question 9 Multiple Choice (Single Answer)

In Floyd-Warshall Algorithm, what is the significance of the intermediate nodes in the dynamic programming approach?

  1. They represent the shortest paths between all pairs of nodes
  2. They are used to compute the shortest paths between all pairs of nodes
  3. They are ignored in the computation of shortest paths
  4. They are used to store the distances between all pairs of nodes
Question 10 Multiple Choice (Single Answer)

In Bellman-Ford Algorithm, what is the purpose of the relaxation operation?

  1. To update the distance estimates of nodes
  2. To identify negative cycles in the graph
  3. To terminate the algorithm when the shortest paths are found
  4. To check if there are any unvisited nodes
Question 11 Multiple Choice (Single Answer)

Which of the following is a necessary condition for the existence of a negative cycle in a graph?

  1. The graph must have at least one negative edge
  2. The graph must be directed
  3. The graph must be connected
  4. The graph must have an odd number of vertices
Question 12 Multiple Choice (Single Answer)

In the context of shortest paths, what is the significance of a negative cycle?

  1. It indicates that there is no shortest path between two nodes
  2. It implies that the shortest path between two nodes is not unique
  3. It means that the shortest path between two nodes has a negative weight
  4. It suggests that the graph contains a loop with a negative total weight
Question 13 Multiple Choice (Single Answer)

Which of the following algorithms can detect negative cycles in a graph?

  1. Dijkstra's Algorithm
  2. Floyd-Warshall Algorithm
  3. Bellman-Ford Algorithm
  4. Prim's Algorithm
Question 14 Multiple Choice (Single Answer)

In the context of shortest paths, what is the significance of a directed acyclic graph (DAG)?

  1. DAGs always have unique shortest paths between any two nodes
  2. DAGs never contain negative cycles
  3. DAGs can be efficiently traversed using depth-first search
  4. DAGs have the same shortest path properties as undirected graphs
Question 15 Multiple Choice (Single Answer)

Which of the following is a disadvantage of using Dijkstra's Algorithm for finding shortest paths?

  1. It can handle negative edge weights
  2. It is not suitable for finding shortest paths between all pairs of nodes
  3. It is more efficient than Floyd-Warshall Algorithm
  4. It is not guaranteed to find the shortest path if there are negative cycles
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