Question

A. Solve the following instances of the single-source shortest-paths problem with vertex a as the source using Dijkstra's algorithm.

4
b ----------> c
/ \ / \
3 / 2 \ /5 \6
/ \ / \
a --------> d <---------- e
7 4
b. Write pseudocode for a simpler version of Dijkstra's algorithm that finds only the distances (i.e. the lengths of shortest paths but not shortest paths themselves) from a given vertex to all other vertices of a graph represented by its weight matrix

Answer 1

Dijkstra's algorithm is used to solve the single-source shortest-paths problem. It finds the shortest paths from a source vertex to all other vertices in a graph.

Step-by-step explanation:

The pseudocode provided shows a simpler version of Dijkstra's algorithm that only finds the distances from a given vertex to all other vertices.

Dijkstra's algorithm is a popular algorithm used to solve the single-source shortest-paths problem. To solve this problem, we start from a source vertex and find the shortest paths to all other vertices in the graph. Using Dijkstra's algorithm, we process each vertex in the graph and update the distances to the neighboring vertices based on the edge weights. Eventually, we obtain the shortest distance from the source vertex to all other vertices.

Here is the pseudocode for a simpler version of Dijkstra's algorithm that finds only the distances:

function Dijkstra(graph, source):
distances = initialize with infinity for all vertices
distances[source] = 0
queue = priority queue initialized with source
while queue is not empty:
current = vertex with minimum distance in queue
for neighbor in graph.adjacent(current):
distance = distances[current] + graph.weight(current, neighbor)
if distance < distances[neighbor]:
distances[neighbor] = distance
queue.update(neighbor, distance)
return distances