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When we talk about space, what we usually refer to is, how much computer memory does it take to complete a computation of a particular size?
我们经常指的是，当我们计算，一个特定大小的问题的时候,要占用计算机的多少内存？
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The notion of recipes, the notion of computation, why you want to do this, what you're going to learn.
秘诀和计算的一些概念啊，以及我们为什么要学这些知识，和要学习的具体内容。
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Then, there's a lot of computation going on to figure out what's the right answer.
将进行大量计算,以找到正确答案。
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The mind reflects the workings of the brain just like computation reflects the working of a computer.
心理反映了大脑的活动,就像运算结果反映了计算机的运行一样
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Literally, return the control from this function, and take the value of the next expression, and return that as the value of the whole computation.
正如字面意义上说的，从这个函数返回，然后取得下一个表达式的值,并把这个值作为整个计算的结果返回。
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For all students, what we want to do is we want to give you an understanding of the role computation can and cannot play in tackling technical problems.
对所有学生来讲，我们想做的就是,给你们关于计算在能否解决技术问题中,所扮演角色的,认识。
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The real issue is to figure out how to build constructs out of this that tackle particular problems, but the fundamental basics of computation are just captured in that set of mechanisms.
坏消息是当然这不是真的,真正的问题是怎么来,构建解决特定的问题的这些结构，但是运算的最基本的东西,仅仅体现在机制集里。
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It's going to let us bury away the specifics of something, and treat that computation like a black box. And by black box, I mean, literally behaves like a mysterious little black box.
通过抽象我们可以将一些细节,掩埋起来并将这一段计算当成黑盒,说到黑盒我的意思就是,字面上的像一个神秘的小黑盒。
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The body of that function looks exactly like the computation up above, except I'm simply using those in place of the specific message I had before.
方法体内部看起来,很像上面的计算过程,除了我用这些来替代了,原来的那些特殊信息。
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We'll see later on, there are classes of computation that are inherently much more complex. We hate them, because they're costly, but they're sometimes inherently that way.
我们会稍后详细的讲讲这个,有许多内在更加复杂的种类的算法,我们痛恨它们，因为它们很耗时。
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I can use that to return values, which I can then use elsewhere, which I did-- and if I just come back and highlight this-- inside of that computation.
我可以用它来返回值，然后我可以在别的地方使用这些返回值，正是我做的--如果我回过头来,在高亮一下这个--在这部分计算内部。
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All right? If you run it, you have a sense of the upper bound, about how much time it's going to take to do this computation, so you're not going to get surprised by something showing up.
第一，这样做意味着没有意外了对不对？,你去运行程序,你已经大致知道运行时间的上限了，因此发生任何事情,你都不会吃惊了。
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I can check it, so if this was part of some other computation, I want to know, did it find a perfect square or not?
我可以检验它,因此如果这是其它计算的一部分我想知道，它能否找到一个完全平方根呢？
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So even within this framework of, given a description of a computation as a set of steps, in the idea that I could build a circuit to do it, let me suggest for you what would be a wonderful circuit to build.
所以即使需要在将计算描述，当成一系列步骤中的一步,这个框架之内,我也完全可以建立一个线路,来完成那个想法，让我为你们假设能建造起,一个多么棒的线路吧。
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And so what I see is that as I run this, I'm doing a lot of redundant computation.
因此我在这里,看到的是随着我的运行，我将会进行很多冗余的计算。
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The other obvious one to do would be worst case. Again, over all possible inputs to this function, what's the most number of steps it takes to do the computation?
很明显另一种就是针对最坏的情况了,也就是在所有可能的输入,里面选出用的,步骤最多的那个输入？
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It's the same computation. But this is a nice way of writing it, often called defensive programming.
这跟原来的计算过程没什么不同,但这是写代码的更优秀的一种方式。
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The idea of a function is, that I'm going to capture a common pattern of computation.
函数的目的,就是寻找计算的共同模式。
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If I look at those two pieces of computation, I can see a pattern there.
我们可以看到这两块的计算过程，是有个模式的。
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As I said, what we want to do is, we want to count the number of basic steps it takes to compute a computation as a function of input size.
我刚才提到了，我们要建立，一个根据输入大小的方法来计算,一个计算过程需要的时间,建立这个方法需要几步呢？
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OK. Today, for the rest of the lecture, we're going to take a break from the topic of algorithms, and computation, and things of the sort. And do something pretty pragmatic.
好，今天剩下的时间里，我们不再讲算法，计算和排序这些话题了,我们会做一些非常实用的事,我们主要的讲讲测试。
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And that leads to a lot of redundant computation.
这就导致了累赘计算。
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Let me write a function, in fact the literal thing I would do is to say, identify the things that change, give each of them a variable name because I want to refer to them, and then write a function that captures the rest of that computation just with those variable names inside.
让我来写个方法,实际上我的意思是，辨别出变化的东西,然后给它们逐个命名以区分,然后写一个用来计算,这些变量的,包括计算过程的方法。
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It should be the notion of, "What does it mean to do computation?"
这应该是这么一个概念：,“进行计算是什么意思呢？“
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Second thing we've got to worry about is, what's a basic step? All right, if I bury a whole lot of computation inside of something, I can say, wow, this program, you know, runs in one step. Unfortunately, that one step calls the Oracle at Delphi and gets an answer back. Maybe not quite what you want.
我们需要担心的第二件事情就是，什么该作为一个基本的步骤呢？,如果我把一大堆的计算过程放到里面，我可以说，噢，这个程序你知道的，一步就完成了，不幸的是,这一步可能要靠预言家才能得到答案,这可能跟你想要的结果不太相同吧。
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And here's the basis of the computation.
这就是计算的基础。
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Computing square root. I'm going to capture it in a piece of code, I'm going to be able to refer to it by a name, and I'm going to suppress the details, meaning inside of that computation, you don't need to know what it does. You just need to know, if I give it the right kind of input, it'll give me back an input that satisfies the contract that I set up.
比如计算平方根,我会用一段代码来说明,我将给它命名,并且忽略细节,意思就是在这一段计算过程中,你不用知道它做了什么，你只需知道，如果我进行了正确的输入,它将会给我符合条件的输出。
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What we're saying is, in order to do computation, we want to describe recipes, we want to describe this sequence of steps built on some primitives, and we want to describe the flow of control that goes through those sequence of steps as we carry on So the last thing we need before we can start talking about real programming is, we need to describe those recipes.
我们在说，为了做计算，我们想描述一个方法，想描述建立在,相同基本类型上的步骤序列，而且我们想描述经过我们设计的,步骤的序列的，控制流程,因此我们开始谈论真正的编程之前,的最后一件事是，我们需要描述一下那些方法。
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Because in doing that, Python would then have a value that it could pass on into some other part of a computation, and if it wasn't what I wanted, I might be a long ways downstream in the computation before I actually hit some result that makes no sense.
因为如果这样做的话，Python会将,输入的值传递到下面的,一些运算中去，如果这个值的类型不是我想要的，我可能会在得到,一个毫无意义的结果之前,经历一个很长时间的,计算过程。
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This was one of the very first recorded bugs in the history of computation.
在关于计算的历史上,有一个最早记录的bug，如果你们。
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