Well, most of us get confused when it comes to finding the shortest path in a graph. We might think it can be easily solved using the BFS and DFS. Why we think so, because we used DFS and BFS for the same in tree data structure.
- BFS is Level-by-Level Search:
- Think of BFS like ripples in a pond. It starts at the source node and then checks all the nodes directly connected to it (neighbors). Next, it looks at the neighbors of the those neighbors, and so on. This means that when you reach a node, you know you have taken the shortest route (in terms of steps or edges) to get there.
- DFS:
- DFS is like exploring a maze by going as deep as possible along one path before trying another. It might go down a long, winding path and reach a node far away, even if there was a much shorter route available.
Reason:
In a graph, there can be many ways to get form one node to another. BFS makes sure to check all the closer options first, so when it finds a path to a node, that path is guaranteed to be the shortest.
Why It Works for Graphs and Not Just Trees ?
- Trees: In a tree, there's only one way to get from one node to another. So whether you use DFS or BFS, you always get the only path available.
- Graphs: In graphs, because there are many possible paths, you need a method that finds the quickest one. BFS is designed to do just that by expanding outwards evenly from the start.