How to solve the shortest path problem in a network?

To solve the shortest path problem in a network, we can use Dijkstra's algorithm.

Dijkstra's algorithm is a popular method for finding the shortest path between two nodes in a network. It works by starting at the source node and iteratively exploring the neighboring nodes, updating the distance to each node as it goes. The algorithm maintains a set of visited nodes and a set of unvisited nodes, and at each iteration it selects the unvisited node with the smallest distance and adds it to the visited set.

To implement Dijkstra's algorithm, we need to initialize the distance to the source node as 0 and the distance to all other nodes as infinity. We also need to keep track of the previous node on the shortest path to each node. Then, we can use a priority queue to select the unvisited node with the smallest distance at each iteration.

Once we have visited the destination node, we can backtrack through the previous nodes to find the shortest path. The total distance of the shortest path is the final distance to the destination node.

Dijkstra's algorithm has a time complexity of O(E log V), where E is the number of edges and V is the number of vertices in the network. This makes it an efficient method for solving the shortest path problem in large networks.