Question

5. How would you adapt Dijkstra’s algorithm to solve the single-destination shortest paths problem? In other words, find the shortest path from each node to a single destination node. Consider this question for both (a) undirected and (b) directed graphs.

Answer 1

Answer:

The single-destination shortest path problem, in which we have to find shortest paths from all vertices in the directed graph to a single destination vertex v.This can be reduced to the single-source shortest path problem by reversing the edges in the directed graph.

Dijkstra's algorithm is an algorithm for finding the shortest paths between nodes in a graph. It can also be used for finding the shortest paths from a single node to a single destination node by stopping the algorithm once the shortest path to the destination node has been determined.

For example, if the nodes of the graph represent cities and edge path costs represent driving distances between pairs of cities connected by a direct road, Dijkstra's algorithm can be used to find the shortest route between one city and all other cities.

a)shortest path from each node to a single destination node in a weighted undirected graph

の 2

smallest cost of each node to destination node is the shortest route to the destination.

cost from 1-2-4-5 is 10

3-4-5 is 6 2-4-5 is 7

1-4-5 is 6 1-3-4-5 is 7 4-5 is 4

so 4-5 is the shorest path .

b)for weighted directed graph:

2 2

cost from 1-2-4-5 is 10

from 3-1-2-4-5 is 11

4-5 is 4

2-4-5 is 7 and 1-4-5 is 6

so here also 4-5 is shorest path .