graph - What is difference between BFS and Dijkstra's algorithms when looking for shortest path?

Question

I was reading about Graph algorithms and I came across these two algorithms:

• Dijkstra's algorithm
• Breadth-first search

What is the difference between Dijkstra's algorithm and BFS while looking for the shortest-path between nodes?

I searched a lot about this but didn't get any satisfactory answer!

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The rules for BFS for finding shortest-path in a graph are:

1. We discover all the connected vertices,
2. Add them in the queue and also
3. Store the distance (weight/length) from source u to that vertex v.
4. Update with path from source u to that vertex v with shortest distance and we have it!

This is exactly the same thing we do in Dijkstra's algorithm!

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So why are the time complexities of these algorithms so different?

If anyone can explain it with the help of a pseudo code then I will be very grateful!

I know I am missing something! Please help!

Answer 1

Breadth-first search is just Dijkstra's algorithm with all edge weights equal to 1.

Dijkstra's algorithm is conceptually breadth-first search that respects edge costs.

The process for exploring the graph is structurally the same in both cases.