Dujkstra's algorithm Greedy algorithms without Animations

1. Analysis and Design of Algorithms
(2150703)
Presented by :
Jay Patel (130110107036)
Gujarat Technological University
G.H Patel College of Engineering and Technology
Department of Computer Engineering
Greedy Algorithms
Guided by:
Namrta Dave

2. Dijkstra's Algorithm:
dist[s] ←0 (distance to source vertex is zero)
for all v ∈ V–{s}
do dist[v] ←∞ (set all other distances to infinity)
S←∅ (S, the set of visited vertices is initially empty)
Q←V (Q, the queue initially contains all vertices)
while Q ≠∅ (while the queue is not empty)
do u ← mindistance(Q,dist) (select the element of Q with the min. distance)
S←S∪{u} (add u to list of visited vertices)
for all v ∈ neighbors[u]
do if dist[v] > dist[u] + w(u, v) (if new shortest path found)
then d[v] ←d[u] + w(u, v) (set new value of shortest path)
(if desired, add traceback code)
return dist

3. Dijkstra's Algorithm:
Ex:
1
2
3
4
5
6
2
4
21
3
4
2
3
2
Initialize
1
0





Select the node with the
minimum temporary
distance label.

4. 1
43
2
2
3
4
5
6
2
4
21
3
4
2
3
2
2
4
0


1 1
3
4
5
6
2
4
21
3
4
2
3
2
2
4
0
2



1
2
3
4
5
6
2
4
21
3
4
2
3
2
2 6
43
0

The predecessor of node 3 is now
node 2
1
2 4
5
6
2
4
21
3
4
2
3
2
2
3
6
4
0

3

5. 5
87
6
1
2 4
5
6
2
4
21
3
4
2
3
2
0
d(5) is not changed.
3
2
3
6
4
 1
2 4
6
2
4
21
3
4
2
3
2
0
3
2
3
6
4

5
1
2 4
6
2
4
21
3
4
2
3
2
0
3
2
3
6
4
5
d(4) is not changed
6
1
2
6
2
4
21
3
4
2
3
2
0
3
2
3
6
4
5
6
4

6. 9
11
10
1
2
6
2
4
21
3
4
2
3
2
0
3
2
3
6
4
5
6
4
d(6) is not updated
1
2
2
4
21
3
4
2
3
2
0
3
2
3
6
4
5
6
4
6
There is nothing to update
1
2
2
4
21
3
4
2
3
2
0
3
2
3
6
4
5
6
4
6
All nodes are now permanent
The predecessors form a tree
The shortest path from node 1 to node 6 can be found by
tracing back predecessors

7. There are some methods left:
• Huffman’s Algorithm
• Task scheduling
• Travelling salesman Problem etc.
• Dynamic Greedy Problems
Greedy Algorithms:
We can find the optimized solution with Greedy method which may be optimal sometime.

8. THANK YOU