Name: Lec 6 | 麻省理工學院6.00計算機科學與程序設計導論，2008年秋季。 (Lec 6 | MIT 6.00 Introduction to Computer Science and Programming, Fall 2008)
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That said, let's continue, and if you remember last time, we

ended up looking at this thing I called square roots bi.

This was using something called a bisection method, which is

related to something called binary search, which we'll see

lots more of later, to find square roots.

And the basic idea was that we had some sort of a line, and we

knew the answer was somewhere between this point

And what that means, is that anything here is smaller

So the integers are totally ordered, the reals are totally

ordered, lots of things are, the rationals are

And that idea was, we make a guess in the middle, we test it

so this is kind of a guess and check, and if the answer was

too big, then we knew that we should be looking over here.

If it was too small, we knew we should be looking over here,

So this is very similar, this is a kind of recursive thinking

we talked about earlier, where we take our problem and we

make it smaller, we solve a smaller problem, et cetera.

So now, we've got it, I've got the code up for you.

I want you to notice the specifications to start.

We're assuming that x is greater than or equal to 0, and

epsilon is strictly greater than 0, and we're going to

return some value y such that y squared is within epsilon of x.

I'd last time talked about the two assert statements.

In some sense, strictly speaking they shouldn't be

necessary, because the fact that my specification starts

with an assumption, says, hey you, who might call square

root, make sure that the things you call me with

On the other hand, as I said, never trust a programmer

to do the right thing, so we're going to check it.

And just in case the assumptions are not true,

we're just going to stop dead in our tracks.

Then we're going to set low to-- low and high, and we're

going to perform exactly the process I talked about.

And along the way, I'm keeping track of how many iterations,

at the end I'll print how many iterations I took, before

So one of the things I want you to observe here, is that

instead of sitting there and typing away a bunch of test

cases, I took the trouble to write a function, called

All right, so what that's doing, is it's taking the

things I would normally type, and putting them in a function,

Why was it worth creating a function to do this?

PROFESSOR JOHN GUTTAG: Then I can I can use it again

By putting it in a function, if I find a bug and I change my

program, I can just run the function again.

The beauty of this is, it keeps me from getting lazy, and not

only testing my program and the thing that found the bug,

We'll talk more about this later, but it often happens

that when you change your program to solve one problem,

you break it, and things that used to work don't work.

And so what you want to do, and again we'll come back to this

later in the term, is something called regression testing.

This has nothing to do with linear regression.

And that's basically trying to make sure our program has not

regressed, as to say, gone backwards in how well it works.

So I've created this function, let's give it a shot

All right, well let's look at our answers.

9, and as I mentioned last time, I didn't find

You know, I was not really disappointed, it found

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Lec 6 | 麻省理工學院6.00計算機科學與程序設計導論，2008年秋季。 (Lec 6 | MIT 6.00 Introduction to Computer Science and Programming, Fall 2008)

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function

method

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