Alright, so now here's the crucial point in the development of development forward algorithm. You know, when we talk about cost updates. So after one hop, a router has the following information. It has the cost it takes to get to each of its neighbors. And it has the cost it takes each of its neighbors to get to the destination in at most one hop. So, the question is, can we generalize this and can we use this information to try to figure out how long it'll this router to get to the destination in two hops. 'Kay? because we already computed for one hop and we said okay well some of the nodes I know that I can get to the destination in one hop. We said DNE can get there in one hop. So can we use that information, then, to backtrack and say, okay for the other nodes can we use the fact that DNE can get there in one hop and they're cost to be able to figure out what the cost is going to be for the rest of them? Rather than have it construct an entire view of the network for the router which would be basically impossible. So the real, real key here though is that adding each of these is going to give the node the two-hop cost right. So we have the cost that it takes each node to get to its neighbors, and then we have the cost that it takes each of the neighbors to get to the destination. Right, like in this example right here. And stored as S right, it takes S cost of W to get to A, we're going to say in general. say W is 3 and Y is 5, you don't want to deal with symbols here. so then we know, S is going to know it's path cost to get to A. And it's going to, S make that somehow. It's just knows it's a number. It knows that it's 3. And S knows how, what the cost is to get to B, it knows that it's 5. And then, if A has already figured out how, what the cost is to get to N in, let's say, three hops, just as an example. So, we're doing the three hop case right here for X or for A to N, and we know that in three hops the cost to get from A to N is 16, say. well then, if A can get to N and it costs 16 three hops, then W should be, or then S should be able to get to N And the cost of 3 plus 16 in 4 hops. So really we're just adding this link on to As path already, because we're going to go to A and then A already knows how to get to N and his minimum call. So we'll just use A's minimum cause to get to N in order to go from S and again we're blurring this here because there could be so many routers in between, but it wouldn't matter. That's the whole beauty of this, this is, it doesn't matter what's in between. S doesn't need to know what's past A. He just needs to know the cost to get to A, and he needs to know what A is saying the cost to get to N is, or what, not, A doesn't have to be saying it necessarily, just needs to know what the cost is. So, that's the power of the Bellman-Ford algorithm. So that we can do this dynamically, it's like a dynamic programming problem. So, from source F to N, as we said through A it's going to cost W plus X and through, B it's going to cost then Y plus Z, right? And this could maybe be, maybe with the three hop case again, so three hops. And again, three hops is going to be what we're saying. It's, it's in at most three hops, so the, the cost could be lowest for two hops, in which case we're not going to add another hop in. but it's just giving us more information, so, in three hops B can get to N in cost Z, so then Y plus Z is going to give this cost, Y plus Z, whatever that is. And then this is W plus X. So whichever of the two is smaller, that's the one you're going to choose. So, if Y plus Z is smaller than W plus X, then S is going to say, okay, whenever I have something destined for N, I'm going to choose to forward to B. That's how I'm going to populate routing table. If something is going to N, in my IP address table. 'Kay? if, if somethings going to end, if something comes to me, then I know I'm going to forward to B next. Or, likewise, if it was the opposite and A was the minimum cost and if say if something comes from N you would change the entry in the round table and say A. So you'd build again a whole table based upon different destinations. And then you can say which road you're going to go to next.
