Application of Dijkstra's Algorithm in Shortest Path Problems Analysis

This report provides a comprehensive analysis of Dijkstra's algorithm for solving the shortest path problem, a fundamental concept in computer networks and map-related systems. The paper begins with an introduction to the shortest path problem, explaining its representation using graphs, including vertices, edges, and weights. It then outlines the motivation behind studying this problem, which includes understanding graph representations, the general concepts of Dijkstra's Algorithm and its evaluation. The core of the report involves a detailed explanation and implementation of Dijkstra's Algorithm, including the use of adjacency matrices and Boolean arrays to track visited nodes. The report addresses a specific problem statement involving calculating the shortest path and alternative paths considering distance and fare between two cities, with the ability to remove intermediate nodes. The solution involves calculating and displaying the shortest distance, fare, and alternative routes. The report concludes by evaluating the algorithm's time complexity and suggests the potential use of other artificial intelligence techniques to improve shortest path algorithms.