The document demonstrates the Floyd-Warshall algorithm for finding the shortest paths between all pairs of vertices in a weighted graph. It shows the algorithm being applied to a sample graph with 4 vertices through a series of steps where the distances are updated. In each step, it considers all vertices as possible intermediates and updates the distances between vertex pairs accordingly until it reaches the shortest paths between all pairs of vertices in the graph.

1. Floyd-Warshall algorithm
Easiest Way
*(reference: http://www.youtube.com/watch?v=XI1ufteQ2FQ)

3. 1
2
3
4
1
0
8
inf
1
2
inf
0
1
inf
3
4
inf
0
inf
4
inf
2
9
0

4. 1
2
3
4
1
0
8
inf
1
2
inf
0
1
inf
3
4
inf
0
inf
4
inf
2
9
0

5. 1
2
3
4
1
0
8
inf
1
2
inf
0
1
inf
3
4
inf
0
inf
4
inf
2
9
0

6. 1
2
3
4
1
0
8
inf
1
2
inf
0
1
inf
3
4
(8+4)
0
(1+4)
4
inf
2
9
0

7. 1
2
3
4
1
0
8
inf
1
2
inf
0
1
inf
3
4
12
0
5
4
inf
2
9
0

8. 1
2
3
4
1
0
8
inf
1
2
inf
0
1
inf
3
4
12
0
5
4
inf
2
9
0

9. 1
2
3
4
1
0
8
inf
1
2
inf
0
1
inf
3
4
12
0
5
4
inf
2
9
0

10. 1
2
3
4
1
0
8
inf
1
2
inf
0
1
inf
3
4
12
0
5
4
inf
2
9
0

11. 1
2
3
4
1
0
8
Inf, 9
1
2
inf
0
1
inf
3
4
12
0
5
4
inf
2
9, 3
0

12. 1
2
3
4
1
0
8
9
1
2
inf
0
1
inf
3
4
12
0
5
4
inf
2
3
0

13. 1
2
3
4
1
0
8
9
1
2
inf
0
1
inf
3
4
12
0
5
4
inf
2
3
0

14. 1
2
3
4
1
0
8
9
1
2
5
0
1
6
3
4
12
0
5
4
7
2
3
0

15. 1
2
3
4
1
0
8
9
1
2
5
0
1
6
3
4
12
0
5
4
7
2
3
0

16. 1
2
3
4
1
0
3
4
1
2
5
0
1
6
3
4
7
0
5
4
7
2
3
0

17. The End