Dijkstra's algorithm with a graph

    A
   / \
  B   C
 / \ / \
D  E  F

The weight of each edge is shown next to the edge. The goal is to find the shortest path from A to all other vertices.

Here are the steps on how to apply Dijkstra's algorithm on this graph:

1. Initialize the distance of all vertices to infinity except A, which is initialized to 0.

Vertex | Distance from A
------- | --------
A | 0
B | INF
C | INF
D | INF
E | INF
F | INF

2. Create a set of visited vertices and initialize it to be empty.

Visited vertices = {}

3. Add A to the visited vertices set.

Visited vertices = {A}

4. For each unvisited neighbor of A, calculate the tentative distance to that neighbor as the distance to A plus the weight of the edge between A and that neighbor.

Vertex | Distance from A
------- | --------
B | 2 (0 + 2)
C | 3 (0 + 3)

5. If the tentative distance is less than the current distance to that neighbor, update the current distance to that neighbor.

Vertex | Distance from A
------- | --------
B | 2
C | 3

6. Repeat steps 4 and 5 for all unvisited neighbors of A.

Vertex | Distance from A
------- | --------
B | 2
C | 3
D | 4 (2 + 2)

7. Remove A from the unvisited vertices set.

Visited vertices = {B, C}

8. Repeat steps 3 to 7 until all vertices have been visited.

Vertex | Distance from A
------- | --------
B | 2
C | 3
D | 4
E | 5 (4 + 1)
F | 6 (4 + 2)

The shortest path from A to each vertex is as follows:

• A to B: A-B
• A to C: A-C
• A to D: A-B-D
• A to E: A-B-D-E
• A to F: A-B-D-F