How do you find the shortest path in BFS?

And so, the only possible way for BFS (or DFS) to find the shortest path in a weighted graph is to search the entire graph and keep recording the minimum distance from source to the destination vertex.

Does Dijkstra give all shortest paths?

The algorithm exists in many variants. Dijkstra’s original algorithm found the shortest path between two given nodes, but a more common variant fixes a single node as the “source” node and finds shortest paths from the source to all other nodes in the graph, producing a shortest-path tree.

Can a graph have more than one shortest path?

All edges have discrete costs. And there are 2 paths from a to d that both cost 5.

Which of the following finds the shortest path in any unweighted graph?

In an unweighted graph, breadth first search(for a node x) guarantees that when we find the node we have also found the shortest path to it.

How do you solve the shortest path algorithm?

We step through Dijkstra’s algorithm on the graph used in the algorithm above:

1. Initialize distances according to the algorithm.
2. Pick first node and calculate distances to adjacent nodes.
3. Pick next node with minimal distance; repeat adjacent node distance calculations.
4. Final result of shortest-path tree.

Why BFS fails to find the shortest path in a weighted graph?

The shortest path between two vertices is defined to be the path whose sum of edge weights is the least. BFS will not work on weighted graphs since the path with the fewest edges may not be the shortest if the edges it contains are expensive.

How do you do Dijkstra’s shortest path?

Dijkstra’s Algorithm

1. Mark the ending vertex with a distance of zero. Designate this vertex as current.
2. Find all vertices leading to the current vertex. Calculate their distances to the end.
3. Mark the current vertex as visited.
4. Mark the vertex with the smallest distance as current, and repeat from step 2.

How do you find the shortest path in graph theory?

1. 5 Ways to Find the Shortest Path in a Graph. Dijkstra’s algorithm is not your only choice.
2. Depth-First Search (DFS) This is probably the simplest algorithm to get the shortest path.
3. Breadth-First Search (BFS)
4. Bidirectional Search.
5. Dijkstra’s Algorithm.
6. Bellman-Ford Algorithm.