Find the shortest route using Bellman’s principle.

Question

Find the shortest route using Bellman’s principle. Image ignouassignments-ignouacademy-com--p-shortest-54923

10 Mar 2024

Answer :

Word Count : 382

Bellman's principle of optimality is a key concept in dynamic programming used to solve shortest path problems. One popular algorithm based on this principle is the Bellman-Ford algorithm. This algorithm can find the shortest path from a source node to all other nodes in a weighted graph, even in the presence of negative weight edges, provided there are no negative weight cycles.

Here's a Python implementation of the Bellman-Ford algorithm:

```python
class Graph:
def __init__(self, vertices):
self.V = vertices
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Activity	Predecessor	Duration in weeks
A	__	6
B	A	24
C	A	6
D	A	12
E	A	9
F	C,D,E	18
G	B,F	12
H	G	24

Activity	Estimated duration (in days)
Activity	Optimistic	Most likely	Pessimistic
A (1, 2)	28	32	36
B (1,3)	22	28	32
C (2, 6)	26	36	46
D (3, 4)	14	16	18
E (3, 5)	32	32	32
F (3, 6)	40	52	74
G (4, 5)	12	16	24
H (5, 6)	16	20	26

Factory	Ware house	$W_1$	$W_2$	$W_2$	Availability
$F_1$		16	20	12	200
$F_2$		14	8	18	160
$F_3$		26	24	16	90
Demand		180	120	150