To understand shortest path algorithms like Dijkstra's and Bellman-Ford, we can use graphs. Graphs help us see the problem clearly.

1. Graph Representation:

• Vertices: These are points or locations, like cities.
• Edges: These are the connections between the points. They often have weights, which could mean distances or costs.

2. Dijkstra's Algorithm:

• This method uses a special queue to find the shortest path from one starting point to all other points.
• The time it takes to run this algorithm is shown as $O((V + E) \log V)$.
  • Here, $V$ means the number of points, and $E$ is the number of connections.
• You can see how the shortest path estimates change over time with a visual representation.

3. Bellman-Ford Algorithm:

• This method looks at the connections several times to find the best path. It can also work with connections that have negative weights.
• The time to run this algorithm is $O(V \cdot E)$.
• Visual tools show how this algorithm improves the path step-by-step, and it checks for any negative cycles.

Using tools like graph simulators, you can watch these algorithms in action. This makes it easier to understand how both methods work for finding the best path.