Greedy

Presented By:
Minhaz Uddin
ID: 151001612

Greedy algorithm Definition:
A greedy algorithm always makes the choice that seems
to be the best at that moment. So it makes a locally
optimal choice in the hope that this choice will lead to a
globally optimal solution.
GreedyAlgorithm : Dijkstra's Algorithm
Step:
1.Set all vertices distances equal to infinity without for
the source vertex, set the source distance equal zero.
2.Push the source vertex in a min-priority queue in the
form as the comparison in the min-priority queue will
be according to vertices distances.

3.Pop the vertex with the minimum distance from the
priority queue .
4.Update the distances of the connected vertices to the
popped vertex in case of
"current vertex distance + edge weight < next vertex
distance", then push the vertex with the new distance to
the priority queue.
5.If the popped vertex is visited before, just continue
without using it.
6.Apply the same algorithm again until the priority
queue is empty.

Dijkstra's Example:
2
B C
5 1 3
A D
8

Dijkstra's Example:
2
∞ B C ∞
5 1 3
0 A D ∞
8

Dijkstra's Example:
Start from A because A distance equal zero.
2
5 B C ∞
5 3
0 A D 8
8
Now A to B (0+5)< ∞ So B distance =5
Now A to D (0+8)< ∞ So D distance = 8
Output : A

Dijkstra's Example:
New start point B because B distance (5) < D distance
(8)
5 B 2 C 7
5 1 3
0 A D 8
8
Now B to A is not needed because A already visited
Now B to C (5+2)< ∞ So C distance = 7
Output : A B

Dijkstra's Example:
New start point C
5 B 2 C 7
5 3
0 A D 10
8
Now C to B is not needed because B already
visited
Now C to D (7+3)< ∞ So D distance = 10
Output : A B C

Dijkstra's Example:
New start point D
5 B 2 C 7
5 3
0 A D 10
8
No unvisited edges are present.
So the work is done.
Output : A B C D

Greedy

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