Dijkstra Algorithm, Beath First Algorithm, Bellman-Ford Algorithm, Depth First Algorithm.

1. Presentation
On
Graph
PRESENTED BY
TEAM ALPHA

2. Team Members
Kazi Emad
ID no. 191902025
01
Forhad Ahmed
ID no. 191902002
02
• Dijkstra’s Algorithm
• BFS Method
• DFS Method
• Bellman Ford Algorithm

3. Dijkstra’s Algorithm
Given a graph and a source vertex in the graph, find shortest paths
from source to all vertices in the given graph.

4. Dijkstra’s Algorithm

5. BFS Method
BFS follows the Queue structure.

6. BFS Method
Let’s solve this problem
through engaging audience

7. Bellman-Ford algorithm

8. Bellman-Ford algorithm
Initialize all the
distances

9. Bellman-Ford algorithm
iterate over all
edges/vertices
and apply update
rule

10. Bellman-Ford algorithm

11. Bellman-Ford algorithm
check for negative
cycles

12. Negative cycles
A
B
C E
D1
1
-10
5
10
3
What is the shortest path
from a to e?

13. Bellman-Ford algorithm

14. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
How many edges is
the shortest path
from s to:
A:

15. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
How many edges is
the shortest path
from s to:
A: 3

16. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
How many edges is
the shortest path
from s to:
A: 3
B:

17. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
How many edges is
the shortest path
from s to:
A: 3
B: 5

18. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
How many edges is
the shortest path
from s to:
A: 3
B: 5
D:

19. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
How many edges is
the shortest path
from s to:
A: 3
B: 5
D: 7

20. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
0 





Iteration: 0

21. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
0 10




8
Iteration: 1

22. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
0 10


12
9
8
Iteration: 2

23. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
0 5
10

8
9
8
Iteration: 3
A has the correct
distance and path

24. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
0 5
6
11
7
9
8
Iteration: 4

25. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
0 5
5
7
147
9
8
Iteration: 5
B has the correct
distance and path

26. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
0 5
5
6
107
9
8
Iteration: 6

27. Bellman-Ford algorithm
G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
0 5
5
6
97
9
8
Iteration: 7
D (and all other
nodes) have the
correct distance
and path

28. Any Question?

29. Thank You