MATLAB Source Code for Calculating Shortest Path Between Any Two Points

Finding the shortest path between any two points in MATLAB is a classic graph theory problem commonly used in network analysis and path planning scenarios. The core implementation relies on selecting appropriate algorithms, with MATLAB providing flexible matrix operations and built-in functions to support such computations.

### Algorithm Selection Floyd Algorithm: Suitable for dense graphs, it computes all-pairs shortest paths using dynamic programming principles. The algorithm has O(n³) time complexity, making it ideal for graphs with moderate node counts. Dijkstra Algorithm: Designed for single-source shortest path problems. To compute distances between all point pairs, you need to execute the algorithm separately from each node as the starting point. With priority queue optimization, time complexity reduces to O(n² log n).

### MATLAB Implementation Key Points Graph Representation: Typically stored as adjacency matrices where `A(i,j)` represents the direct edge weight between nodes i and j. Non-adjacent nodes are initialized with infinite values (e.g., `Inf`). Algorithm Optimization: Utilize MATLAB's vectorized operations instead of loops. For instance, Floyd's algorithm can be implemented using triple-nested matrix operations to update shortest paths efficiently. Built-in Functions: The `graph` and `shortestpath` functions (requiring MATLAB's Graph and Network Toolbox) provide direct implementations, significantly simplifying code development.

### Extended Considerations For path tracing requirements, maintain additional predecessor matrices to track the shortest route. With large-scale sparse graphs, consider combining A* algorithm or Bellman-Ford algorithm for improved efficiency. For dynamic graphs with real-time edge weight changes, implement incremental update algorithms to handle modifications efficiently.

These methods allow users to flexibly choose solutions appropriate for their specific data scale and precision requirements.