Can we find longest path using BFS?

Can we find longest path using BFS?

As we can see in the above diagram, if we start our BFS from node-0, the node at the farthest distance from it will be node-5, now if we start our BFS from node-5 the node at the farthest distance will be node-7, finally, the path from node-5 to node-7 will constitute our longest path.

How do you find the length of the longest path in a graph?

Longest Path in a Directed Acyclic Graph

1. 1) Initialize dist[] = {NINF, NINF, ….} and dist[s] = 0 where s is the source vertex. Here NINF means negative infinite.
2. 2) Create a topological order of all vertices.
3. 3) Do following for every vertex u in topological order. ……….. Do following for every adjacent vertex v of u.

Can Dijkstra be used to find the longest path?

The Dijkstra Algorithm is an algorithm that allows you to allocate the shortest path in a graph between a starting node i and an end note j by inlcuding other nodes of the graph. It can also be used to calculate longest paths, if some simple modifications are used.

How do you find the longest path in an undirected graph?

finding longest path in an undirected and unweighted graph

1. Use a weight variable to store weight of the corresponding nodes.
2. Use bfs on any node(e.g. node no.
3. Use a visit variable to mark the visited nodes so that you don’t visit them again.
4. Iterate over every node to find the node with highest number.

How do you find the longest path on a cyclic graph?

To find the longest path in a directed, cyclic graph, G = ( V , E ) G = (V, E) G=(V,E) (as asked in Coding Assignment 4 part e), I implemented an algorithm which generates a number of permutations of DAG reductions, G π G_{\pi} Gπ, of the graph G, and finds the longest path in each of these DAGs.

How do you find the longest path on a weighted graph?

A longest path between two given vertices s and t in a weighted graph G is the same thing as a shortest path in a graph −G derived from G by changing every weight to its negation. Therefore, if shortest paths can be found in −G, then longest paths can also be found in G.

What is a maximal path?

We can say a path is maximal if you cannot add any new vertices to it to make it longer. You can contrast this with a path of maximum length: it is the longest path in a graph (so it is also maximal, but note the difference).

How do you find the longest path of a tree?

There is this standard algorithm for finding longest path in undirected trees using two depth-first searches:

1. Start DFS from a random vertex v and find the farthest vertex from it; say it is v′.
2. Now start a DFS from v′ to find the vertex farthest from it. This path is the longest path in the graph.

How to use bidirectional search to find shortest path?

Just like A* algorithm, bidirectional search can be guided by a heuristic estimate of remaining distance from source to goal and vice versa for finding shortest path possible. Suppose we want to find if there exists a path from vertex 0 to vertex 14. Here we can execute two searches, one from vertex 0 and other from vertex 14.

Is it possible to find the longest path of a graph?

BFS can compute many things, such as shortest path in an unweighted graph or determining if a graph is bipartite, but longest path in general graphs aren’t one of them. In a DAG, you can compute the longest path in polynomial time using topological sorting.

Is there a polynomial time algorithm to find the longest path?

There is no precise polynomial time algorithms to solve this. BFS can compute many things, such as shortest path in an unweighted graph or determining if a graph is bipartite, but longest path in general graphs aren’t one of them. In a DAG, you can compute the longest path in polynomial time using topological sorting.

Is there a linear time solution for the longest path problem?

However, the longest path problem has a linear time solution for directed acyclic graphs. The idea is similar to linear time solution for shortest path in a directed acyclic graph., we use Topological Sorting. We initialize distances to all vertices as minus infinite and distance to source as 0, then we find a topological sorting of the graph.