Question

In the context of graph algorithms, what is the significance of Dijkstra’s algorithm?

• A. It finds the shortest path in a weighted graph with non-negative weights
• B. It detects cycles in a directed graph
• C. It computes the minimum spanning tree
• D. It performs topological sorting

Hint:

Dijkstra’s algorithm is used to find the shortest path in graphs with non-negative weights, making it very useful for routing and navigation problems.

Answer 1

The Correct Option is A

Dijkstra's algorithm is a prevalent method for determining the shortest path in a graph, especially when edge weights are non-negative. It iteratively selects the node with the smallest provisional distance and examines its adjacent nodes, updating their distances as it progresses.
- Cycle detection in directed graphs (B) is addressed by algorithms like Depth First Search (DFS), not Dijkstra's.
- Minimum spanning tree computation (C) is the domain of algorithms such as Kruskal's or Prim's, not Dijkstra's.
- Topological sorting (D) applies to directed acyclic graphs (DAGs) and is commonly performed with algorithms like Kahn's, not Dijkstra's.
Consequently, option (A) is the accurate choice, as Dijkstra's algorithm is designed to find the shortest path in weighted graphs with non-negative weights.