MATLAB Implementation of Dijkstra's Algorithm for Shortest Path Computation

This MATLAB program implements Dijkstra's algorithm to calculate the shortest path distances between all nodes in a graph. We demonstrate the algorithm using an undirected graph with nine vertices to solve the shortest path problem between any two points. Each step of the program includes comprehensive explanations to facilitate understanding of the algorithm's implementation details. At the beginning of the program, we initialize key variables including the distance matrix and path tracking arrays. The implementation uses a while loop to iterate through all nodes until the entire graph has been processed. Within each iteration, the algorithm selects the node with the minimum distance from the source node using a priority queue mechanism, then performs relaxation operations on its neighboring nodes. These relaxation steps update the distance values and path information when a shorter path is discovered through the current node. This process repeats until all nodes have been visited, resulting in complete shortest-path distance information from the source node to all other nodes. The code structure includes several key components: distance matrix initialization using INF values for unconnected nodes, a visited node tracking array, and a path reconstruction mechanism that stores predecessor information. The implementation highlights Dijkstra's greedy selection strategy where the algorithm always expands the closest unvisited node first, ensuring optimality for graphs with non-negative edge weights. This program serves as an educational tool to understand Dijkstra's algorithm implementation and can be adapted for practical applications. For any technical questions regarding the code structure or algorithm implementation, please feel free to contact us for further clarification.