Table of Contents
What is the limitation of shortest path algorithm?
➢ The major disadvantage of the algorithm is the fact that it does a blind search there by consuming a lot of time waste of necessary resources. ➢ It cannot handle negative edges. This leads to acyclic graphs and most often cannot obtain the right shortest path.
Does the shortest path change when weights of all edges are multiplied by 10?
Does the shortest path change when weights of all edges are multiplied by 10? If we multiply all edge weights by 10, the shortest path doesn’t change. The reason is simple, weights of all paths from s to t get multiplied by same amount.
How can the edge weighted case find the shortest path?
Compute the shortest path from s to every other vertex; compute the shortest path from every vertex to t. For each edge e = (v, w), compute the sum of the length of the shortest path from s to v and the length of the shortest path from w to t. The smallest such sum provides the shortest such path.
Would the shortest paths change due to the change in weights?
Solution: False. the shortest path would change if 1 was added to every edge weight.
How do you find the shortest path on a weighted graph?
Given a directed graph where every edge has weight as either 1 or 2, find the shortest path from a given source vertex ‘s’ to a given destination vertex ‘t’. Expected time complexity is O(V+E). A Simple Solution is to use Dijkstra’s shortest path algorithm, we can get a shortest path in O(E + VLogV) time.
What is shortest path problem in data structure?
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
How do you find the shortest path on a directed graph?
Given a directed graph where every edge has weight as either 1 or 2, find the shortest path from a given source vertex ‘s’ to a given destination vertex ‘t’. Expected time complexity is O (V+E). A Simple Solution is to use Dijkstra’s shortest path algorithm, we can get a shortest path in O (E + VLogV) time.
What is the shortest path length of the input vertex?
Output: Shortest path length is:2 Path is:: 0 3 7 Input: source vertex is = 2 and destination vertex is = 6. Output: Shortest path length is:5 Path is:: 2 1 0 3 4 6 Recommended: Please try your approach on {IDE} first, before moving on to the solution. One solution is to solve in O (VE) time using Bellman–Ford.
How do you solve an unweighted graph with Dijkstra’s algorithm?
One solution is to solve in O (VE) time using Bellman–Ford. If there are no negative weight cycles, then we can solve in O (E + VLogV) time using Dijkstra’s algorithm . Since the graph is unweighted, we can solve this problem in O (V + E) time.
How to find the vertex of a graph with smallest value?
We first extract the vertex in Q = [A,B,C] which has smallest value, i.e. A, after which Q = [B, C]. Note A has a directed edge to B and C, also both of them are in Q, therefore we update both of those values, Now we extract C as (2<5), now Q = [B].