To solve for the shortest path from $A$ to $L$ using Dijkstra's Algorithm, I'll outline the steps:

Step-by-Step Process

1. Initialization:

   • Set the distance to $A$ (the source) as $0$ and all others to infinity ($\infty$).
   • Mark all nodes as unvisited.

2. Iterative Updates:

   • Visit the node with the smallest distance value (starting with $A$).
   • Update the distances to its neighbors if a shorter path is found.
   • Mark the current node as visited (do not revisit).
   • Repeat until $L$ is reached or all nodes are visited.

I'll calculate this step by step import networkx as nx

Define the graph as adjacency matrix with weights

graph_data = { 'A': {'B': 3, 'C': 2, 'E': 9}, 'B': {'D': 2, 'E': 4}, 'C': {'F': 6}, 'D': {'G': 3, 'E': 2}, 'E': {'G': 1, 'H': 2, 'F': 9}, 'F': {'H': 1, 'I': 2}, 'G': {'J': 5}, 'H': {'J': 5, 'K': 6}, 'I': {'K': 2}, 'J': {'L': 5}, 'K': {'L': 3} }

Create a graph using NetworkX

graph = nx.DiGraph() for node, edges in graph_data.items(): for neighbor, weight in edges.items(): graph.add_edge(node, neighbor, weight=weight)

Use Dijkstra's algorithm to find the shortest path from A to L

shortest_path = nx.shortest_path(graph, source='A', target='L', weight='weight') shortest_distance = nx.shortest_path_length(graph, source='A', target='L', weight='weight')

shortest_path, shortestUsing Dijkstra's Algorithm, the shortest path from $A$ to $L$ is:

$A \to C \to F \to I \to K \to L$

The total distance of this path is $15$.

Let me know if you would like a detailed breakdown of each step or have further questions.

Here are five related questions:

1. Would you like to see how the algorithm processed each node step-by-step?
2. Should I visualize the graph with the shortest path highlighted?
3. Do you want me to calculate shortest paths from $A$ to all other nodes?
4. Should we analyze how Dijkstra's Algorithm compares with other pathfinding algorithms, like A*?
5. Would you like to understand scenarios where Dijkstra's Algorithm may not be optimal (e.g., negative edge weights)?

Tip: When solving shortest path problems, ensure all