Dijkstra Algo, BFS, Bellman–Ford Algo, DFS

Presentation
On
Graph
PRESENTED BY
TEAM ALPHA

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

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.

BFS Method
BFS follows the Queue structure.

BFS Method
Let’s solve this problem
through engaging audience

Bellman-Ford algorithm
Initialize all the
distances

iterate over all
edges/vertices
and apply update
rule

check for negative
cycles

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

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:

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

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:

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

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:

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

G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
0 





Iteration: 0

G
S
F
E
A
D
B
C
10
8
1
-1
-1
3
1
1
2
-2
-4
0 10




8
Iteration: 1

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

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

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

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

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

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

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