Help Understanding Dijkstra’s Algorithm with Visited and Distance Arrays

Dijkstra's is indeed a greedy algorithm, and it finds the shortest paths based on weights between vertices. The main idea is to track the shortest distances in a 'cost' array, starting with the source node (set to 0) and all others set to infinity. This helps determine the shortest path as you explore nodes.

You actually don't need to stop once you reach your destination in this algorithm because the first minimum you encounter might not necessarily be the shortest path. In many cases, it could be that a later evaluated path turns out to be shorter. The visited list is critical here—it prevents you from visiting the same node multiple times unnecessarily.

As for the distance and visited lists, think of them as essential tools for managing the nodes you're evaluating and keeping the paths optimized. If you’re only concerned about hops and the distances are equal, then you might manage with a different strategy like BFS. But for general use, keeping both lists is crucial.

Video tutorials can help visualize this better, so check those out for different perspectives!

Great question! The distance array is central to Dijkstra’s because it allows you to track the potential shortest paths to all nodes. You're right in thinking you can stop early if you only care about the path to the destination, but that won't always give you the best answer.

Dijkstra works by continually updating your knowledge of the shortest paths. Once you've reached your destination and processed it as the current minimum, it's more likely you'll get the true shortest distance—unless you've explored all possible paths. Also, managing the visited nodes is important to avoid wasting time on paths you already know are longer than their counterparts. It helps keep the algorithm efficient!

Comparing it to BFS can be really helpful, as both tackle shortest paths but in slightly different ways. Check out some comparisons, and you'll start to see the distinctions more clearly!

To add to what's been said, if all edge weights are equal, yes, the shortest path corresponds to the fewest nodes. But when the weights differ, keeping track of the distances is essential. That way, you're adept at finding the true shortest path, even if it might involve more nodes. The visited nodes help here—without them, keeping track gets messy! So in typical scenarios, it's safer to maintain both lists to ensure accuracy.