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So suppose we're converting a car from electric to gas, sorry, from gas to
electric. And we have a set of tasks and task times
or task weights, for those, so times to complete these various tasks.
Now it also makes sense that some of these tasks have to be completed before
others. So for example, we need to remove the
engine before we can stream clean the inside of the car.
And so for this we're going to create what's called a digraph where we use
arrows to represent the ordering requirements of the graph.
So I'm going to make a little more room here, and so let's say we start with task
one. So I'm going to create a vertex or a dot
for a task one and I'm going to say there's task one which I'm going to
represent with task, t for task with the subscript of one and after I'm going to
put the time it takes to complete that task.
So task one takes two days or has a time of two.
And I need to complete task one before I can.
Get to steam cleaning the negine and so I'm going to create an arrow that points
to task two which has a time of 0.5 and this is going to tell me that task one
has to be completed before task two. And now let's see what else we need to
do. We need to buy an eng- an electric motor.
Well, we don't have to do that. Neither of these have to be completed
before that, so we'll put List Task three here separately.
so, your Task four, construct the part that connects the motor to the engine's
transmission. Presuming we know what kind of motor
we're buying and we have the specs, we really don't need To do that.
we don't need to do any of these other things before that.
we needed to construct the battery racks again.
we can probably do that just about any time we want.
And now we want to, lets say, install the motor.
But what do we need to do before we install the motor?
Well, I definitely need to want to have that steamcleaning done, right?
There's no point in installing a motor, in a dirty engine.
I'm also going to need to have bought the engine, so we have a second requirement
coming from T, task three. we're going to need to have done that,
and in order to install the motor, we're also going to have to have constructed
the part that connects the motor in. So we're going to have to have that
requirement as well. So task seven we need to install the
speed controller. Let's see, what do I need to do in order
to install the speed controller? Well, I don't really know, but I'm
going to guess that we're going to have the you know that steam cleaning done.
And chances are we're going to need to have bought the speed controller so, so
we definitely have a requirement, requirement there.
how about task eight installing the battery racks which is going to take half
a day. let's see here.
Again, we have better cleaned the, you know, finished our cleaning, and of
course we're going to need to have constructed those, those racks, and so we
have a requirement there as well. So finally task nine is wire electricity,
and really we're going to have to completed most of this first, so I'm
going to put it over here. So task nine takes one day, and before
want to do that we were going to have to have, kind of have to install the motor,
we were going to have to install the speed controller and we were going to
have to install, have to install the battery racks and then our last task,
task length one Is wiring the electricity and this altogether is a digraph that in
a very simplistic graphical form captures all the information that we had here as
well as all the ordering requirements. So this, this digraph captures a lot of
information that's going to allow us to then figure out how we can schedule this,
to have people complete this task.