What does Dijkstra's algorithm find in a weighted graph?

Study for the HSC Mathematics Standard 2 Exam. Utilize flashcards and multiple choice questions, each with hints and explanations. Prepare confidently for your exam success!

Dijkstra's algorithm is specifically designed to find the shortest path from a starting node to all other nodes in a weighted graph, where the weights of the edges represent distances, costs, or any other metric that can be minimized. The algorithm systematically explores the graph, updating the shortest known distance to each node, based on the weights of the edges leading to those nodes.

As the algorithm progresses, it maintains a priority queue to always expand the least-cost node, ensuring that once a node's shortest path is determined, it will not change. This means that Dijkstra's algorithm effectively guarantees the shortest paths are found efficiently without the need to examine all possible paths, which would be computationally expensive.

The other options do not accurately describe the function of Dijkstra's algorithm. For instance, it does not focus on finding the longest path or a maximum weight path, as those would require different approaches and could involve cycles or paths that do not minimize distance. Additionally, measuring the average weight of edges is unrelated to the objective of finding specific paths within a graph. Thus, the focus on finding the shortest paths aligns directly with what Dijkstra's algorithm is intended to achieve.

Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy