here there are 5 algorithm which is help you to learn about algorithm

1. Welcome
GROUP 5

2. • Safayet Hossain 151-15-4938
student of CSE dept
Daffodil Internationa University

3. A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
List the edges in
order of size:
ED 2
AB 3
AE 4
CD 4
BC 5
EF 5
CF 6
AF 7
BF 8
CF 8
Kruskal’s Algorithm

4. Select the shortest
edge in the network
ED 2
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Kruskal’s Algorithm

5. Select the next
shortest
edge which does not
create a cycle
ED 2
AB 3A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Kruskal’s Algorithm

6. Select the next
shortest
edge which does not
create a cycle
ED 2
AB 3
CD 4 (or AE 4)
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Kruskal’s Algorithm

7. Select the next
shortest edge which
does not create a cycle
ED 2
AB 3
CD 4
AE 4
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Kruskal’s Algorithm

8. Select the next shortest
edge which does not
create a cycle
ED 2
AB 3
CD 4
AE 4
BC 5 – forms a cycle
EF 5
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Kruskal’s Algorithm

9. All vertices have been
connected.
The solution is
ED 2
AB 3
CD 4
AE 4
EF 5
Total weight of tree:
18
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Kruskal’s Algorithm

10. A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Select any vertex
A
Select the shortest
edge connected to
that vertex
AB 3
Prim’s Algorithm

11. A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Select the shortest
edge connected to
any vertex already
connected.
AE 4
Prim’s Algorithm

12. Select the shortest
edge connected to
any vertex already
connected.
ED 2
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Prim’s Algorithm

13. Select the shortest
edge connected to
any vertex already
connected.
DC 4
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Prim’s Algorithm

14. Select the shortest
edge connected to
any vertex already
connected.
EF 5A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Prim’s Algorithm

15. A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
All vertices have been
connected.
The solution is
AB 3
AE 4
ED 2
DC 4
EF 5
Total weight of tree:
18
Prim’s Algorithm

16. Hamilton path
In the mathematical field of graph theory, a Hamiltonian path (or traceable
path) is a path in an undirected or directed graph that visits each vertex
exactly once.
Traceable graph

17. Hamilton path & cycle
A Hamiltonian cycle is a cycle that visits each vertex exactly once
(except for the vertex that is both the start and end, which is visited
twice).

18. Dijkstra's algorithm
Dijkstra's algorithm - is a solution to the single-source
shortest path problem in graph theory.
Works on both directed and undirected graphs. However,
all edges must have nonnegative weights.
Approach: Greedy
Input: Weighted graph G={E,V} and source vertex v∈V,
such that all edge weights are nonnegative
Output: Lengths of shortest paths (or the shortest paths
themselves) from a given source vertex v∈V to all other
vertices
18

19. Dijkstra Animated Example-1
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20. Dijkstra Animated Example-1
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21. Dijkstra Animated Example-1
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22. Dijkstra Animated Example-1
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23. Dijkstra Animated Example-1
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24. Dijkstra Animated Example-1
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25. Dijkstra Animated Example-1
25

26. Dijkstra Animated Example-2
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27. Dijkstra Animated Example-2
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28. Dijkstra Animated Example-2
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29. Dijkstra Animated Example-2
29

30. Dijkstra Animated Example-2
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31. Dijkstra Animated Example-2
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32. Dijkstra Animated Example-2
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33. Dijkstra Animated Example-2
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34. Dijkstra Animated Example-2
Shortest Path from A to H,
A to C, C to D, D to E, E to G, G to F, F to H
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