Bellman Ford Shortest Path algorithm

Bellman Ford Shortest Path algorithm

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The following table records the distance from S to each node:

The first iteration,

S->a = 4, because S->a is now INF. So update min (s->a) is 4

S->b = 6. Because S->b is now INF. So update min (s->b) is 6

S->c=inf (indicates unreachable)

S->d=inf

MIN (S->s)	MIN (S->a)	MIN (S->B)	MIN (S->C)	MIN (S->D)
0	4	6	Inf	Inf

The second iteration from a begins:

A->c=3. Since S->c is currently inf, update min (s->c) is 7

MIN (S->s)	MIN (S->a)	MIN (S->B)	MIN (S->C)	MIN (S->D)
0	4	6	7	Inf

The second iteration begins with B,

B->a=-5, due to s->a=4 s->b=6, so s->b->a=1 < S->a = 4. So update min (s->a) =1

Because the S->a is updated, and a can reach a point set of C, these can be recursive to the point set :

MIN (S->C) is at this time 7. and Min (s->a)->c is 1+3=4. therefore need to update min (s->c) =4

B->d = 1. Because min (s->d) = INF. So min (s->d) needs to be updated to 7

MIN (S->s)	MIN (S->a)	MIN (S->B)	MIN (S->C)	MIN (S->D)
0	1	6	4	7

Start the iteration from point C:

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The C reach point set has only D, because min (s->d) is 7, and min (s->c)->d is 4+2=6, so min (s->d) needs to be updated to 6

To get the final result:

MIN (S->s)	MIN (S->a)	MIN (S->B)	MIN (S->C)	MIN (S->D)
0	1	6	4	6

Bellman Ford Shortest Path algorithm