Write code for complete application that includes all the code for computing the shortest paths using Dijkstra’s algorithm, along with a program to test the implementation:
Write code for complete application that includes all the code for computing the shortest paths using Dijkstra’s
Introduction:
Dijkstra's algorithm is a shortest path algorithm for finding the shortest path between a source node and all other nodes in a weighted graph. The algorithm works by maintaining a set of unvisited nodes and a set of distances from the source node to all nodes. The algorithm starts with the source node and sets its distance to 0. Then, in each iteration, it selects the node with the shortest distance that has not been visited and updates the distances of its neighbors if they can be improved. The algorithm continues until all nodes have been processed.
Here's a step-by-step description of the algorithm:
Initialize the distance of the source node to 0 and the distance of all other nodes to infinity.
Initialize the set of unvisited nodes with all nodes in the graph.
While there are unvisited nodes:
a. Select the node with the shortest distance from the source node that has not been visited.
b. Mark the selected node as visited.
c. For each neighbor of the selected node:
i. Calculate the distance to the neighbor through the selected node.
ii. If the calculated distance is less than the current distance of the neighbor, update the distance of the neighbor.
The distance of each node from the source node is now the shortest distance.
The algorithm can be implemented using a priority queue to efficiently select the node with the shortest distance in each iteration. The priority queue stores nodes along with their distances and the nodes are processed in order of increasing distance.
Step by step
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