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Let's use what we learned about static methods and the Math class to finish coding up the DistanceTo method.

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Now that we know how to use the static
square root method in the math class,
0:00

let's use it to finish coding up
the DistanceTo method, in the Point class.
0:04

The last thing we needed to do to
complete the Cartesian distance formula,
0:08

is to add these two values together and
take the square root.
0:13

We can actually do that
in a single statement.
0:17

We can say Math.Sqrt of
xDiffSquared + yDiffSquared.
0:21

There we go.
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We've coded up the cartesian
distance formula.
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Now we just need to return the result.
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Let's test our method in main.
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Let's clear out this code and
then get the distance between
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this point at (4, 2) and
the coordinates at (5,
0:49

5) and
print the result using console.rightline.
0:54

Now let's open the console to compile and
run this.
1:02

Looks like we got a compiler error.
1:13

It says the name Math does not
exist in the current context.
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And this is back in the point.cs file,
line 22.
1:18

So let's go back there.
1:22

I see.
1:25

We forgot to add the using System.
1:25

All right.
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Let's run this again.
1:35

Here's another compiler error.
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It says cannot implicitly
convert type double to int.
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And this is in point.cs, line twenty four.
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Again they're Math.Sqrt.
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This error must be saying that
it can't convert the double
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that's returned from
Math.Sqrt to an integer.
1:57

Remember that the documentation for
Math.Sqrt said it returns a double?
2:01

This is one of those rare times when
we don't care about the decimal value
2:06

of the result.
2:10

We're only using whole
numbers in our game.
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An invader can't be halfway
between two grid squares.
2:15

Truncating the decimal value
we get from this formula
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gives us the correct
distance in discrete units.
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Remember that when we cast
a double to an integer
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it removes the decimal
portion of the value.
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This is called truncation.
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And that's what we want to do.
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So we can just type int.
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in parentheses here to
get the desired effect.
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This will cast the result
of Math.Sqrt to an integer.
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Now let's save, compile and run again.
2:43

All right so we see the result is three.
2:48

So the distance between point (4,
2) and coordinate (5,5) is 3.
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If you like, you can verify on
a calculator that this is correct.
2:55

Let's take a final look at
the DistanceTo method before we move on.
3:01

There are five lines in
the DistanceTo method.
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It might surprise you to hear that we
could have written all this in a single
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line of code.
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Let me type it here
underneath the existing code.
3:15

Then we can talk about why we might
prefer one way over the other.
3:18

So the cartesian distance
formula is the square root
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Of the sum of the square for this.
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We use another method in the math
class called POW for power.
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This allows us to raise
a value to a power.
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In this case, two.
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So we have the square root of
the sum of the squared differences.
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So we get X minus x and
Y minus y so this code here,
4:02

does the exact same thing
as this code up here.
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As you can see it puts the entire
math formula on a single line.
4:17

One advantage of putting
the code all in the same line,
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is that it gets rid of
most of the variables.
4:25

The fewer variables there are,
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the less likely you are to type
the wrong one in the wrong place.
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Say, for example,
that I typed xDiff here instead of yDiff.
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>> That's a very common
mistake when programming.
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Because the variables look so similar,
it's not obvious what the problem is.
4:43

Just because you can put all the code on
a single line, doesn't mean you should.
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In fact, this is actually
a good approach to programming.
4:52

You see, by coding it this way,
4:57

we've broken up the solution into smaller
parts that are easier to think about.
4:59

Solutions that are easier to
think about are easier to code.
5:03

Once you think you have
a correct solution implemented,
5:08

you can test it with known values.
5:12

After you verify that the solution is
correct, you can always go back and
5:14

refactor the code into
a less verbose form.
5:18

Then run the same tests again to verify
that the changes didn't break anything.
5:21

This is a very common pattern for
designing, refactoring, optimizing and
5:26

refining software.
5:31

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