## 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..

## Why does BFS find the shortest path?

The BFS will first visit nodes with distance 0 then all nodes with distance 1 and so on. This property is the reason why we can use a BFS to find the shortest path even in cyclic graphs.

## How do you determine the number of shortest paths?

Use BFS to determine the length of the shortest v-w-path. Then use DFS to find the number of the v-w-shortest paths such that two nodes are connected and the length of path equals to the output of BFS.

## Can BFS be used to find cycles?

BFS wont work for a directed graph in finding cycles. Consider A->B and A->C->B as paths from A to B in a graph. BFS will say that after going along one of the path that B is visited. When continuing to travel the next path it will say that marked node B has been again found,hence, a cycle is there.

## Is Dijkstra BFS or DFS?

You can implement Dijkstra’s algorithm as BFS with a priority queue (though it’s not the only implementation). Dijkstra’s algorithm relies on the property that the shortest path from s to t is also the shortest path to any of the vertices along the path. This is exactly what BFS does. … Exactly like BFS.

## Does BFS always give shortest path?

Breadth-first search will always find the shortest path in an unweighted graph.