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But don't worry about it, it's not, I'm just using it because it's a simpler example than the one I really want to get to, which is knapsack.
但是别担心，我讲这些是因为它比我,真正想讲的问题简单一些，我想讲的是背包问题。
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But practice this, because it's something that's such an easy way to ask such a variety of questions.
但是你仍然需要好好练习，因为这个简单的用法能够提出各种各样的问题。
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And I want to talk briefly about each of these three parts of language before looking at some other issues.
在探讨一些其他问题之前,我想简单的讲一下语言的这三个成分
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It's a simple problem, but I just want to do it so you get used to working with vectors.
这是个简单的问题,但我还是想做一下好让你们习惯矢量运算
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The problem is as simple as the fact that millions of people who are unable to move or to communicate.
问题很简单,数以百万的人们无法行动，或者与人交流。
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These are stupid questions, because once you understand what they're asking, the answer is just built in. It follows trivially.
这是些很愚蠢的问题,因为一旦你明白了他们的问题,答案就在其中,一切简单明了
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And so I would ask you to think about a couple of simple questions as you move through this book, and as you think about what I have to say about it.
所以，我想让大家在继续读这本书时,想出一些简单的问题，并且想想我会对此说些什么。
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We call that a base case. It's basically the simplest possible solution to the problem.
我们说这是一个基础案例,这是这个问题最简单的解决方案。
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So let's start by asking a simple question.
就让我们以问个简单的问题开始。
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That was Cartesian space. When I plot r as a distance out from the nucleus that is sort of our simple-minded planetary model. Now let's look at energy.
笛卡尔坐标系，当我用r表示,离原子核的距离时，那只是我们头脑中简单的,类似行星的模型，现在我们看一下能量问题。
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I mean that, that's an endemic problem. But, you know, I mean the rules are actually pretty simple.
那是一个地域性的问题。但是，这其实是非常简单的规则。
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So, I know this is a simple example and I can see everyone pretty much got it right, and probably those that didn't actually made some sort of clicker error is my guess.
分别是质子和电子,我知道这是个很简单的问题，你们大部分人都做对了,我猜那些没做对的大概是因为点错了。
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And this is in an isolated, in an adiabatic container.
这应该是个很简单的问题，桨轮处在一个与外界隔离额绝热环境中。
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So honestly, one of the best strategies in this course and in programming in general is-- generally speaking design, but it's these little tricks of the trade that will honestly make things much more fun, much more easier, and really allow you to focus on the juicy parts of the problem and not little tiny bugs that you may have started tripping over already.
说实在的，这堂课在编程方面最棒的策略之一,简而言之，就是--设计，但这只是一些让事情更简单,更容易的小技巧，让你专注于问题的核心关键,而不是一些可能让你绊倒的,这样或那样的小错误。
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But finally, Reiner says, well, thank you for visiting us, it's all very wonderful, but you know our audience would really like to know; it seems like a simple question but it's awfully hard to understand, but how can a great, big, enormous, heavy thing like this airplane get off the ground?
但最后 雷纳说到,谢谢你的来访,太棒了,但你知道吗,我们的观众非常想知道,这问题貌似简单,但却很难让人明白,问题是,像这么一个巨大且沉重的飞机,是如何飞起来的呢
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And so, it's not an easy, clear-cut question.
所以，这不是一个简单的非黑即白的问题。
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How many" is very simple. You will have no problem with this question.
How many”的用法也非常简单。相信你不会遇到太大的问题的。
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There are different ways of playing the game, and some of us find great pride in finding the most simple way to understand something.
条条大路通罗马,当找到简单的方法来理解问题时,我们会很有成就感
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So things that are good candidates for divide And conquer are problems where it's easy to figure out how to divide down, and the combination is of little complexity.
因为适合用分治算法解决的问题,最好是能够简单的将问题进行分解,并且合并的过程不是非常的复杂,只要比线性方案要小。
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I'm going to start with the simplest example and slowly add on bells and whistles and make it more and more complicated.
我会从最简单的例子开始,逐渐增加难度,让问题越来越复杂
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And I think this is best illustrated by giving you a simple little piece of code.
我认为给你看一段简单的代码,可以很好的说明这个问题。
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There are other problems that are much more naturally thought of in a recursive fashion.
有一些问题不递归,也可以很简单的解决。
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That's certainly one way to do it, but for computers that's not necessarily the easiest way. So another way of solving it is to do something we already saw last time, which is basically, why not simply enumerate all possible examples and check them?
将一个等式代入另一个等式，这当然是一种办法,但是对电脑来说这绝对不是一件简单的事,所以解决这个问题的办法，正如我们上一次看过的,非常基本？
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And it's called divide and conquer for the obvious reason. I'm going to divide it up into sub-problems with the hope that those sub-problems get easier. It's going to be easier to conquer if you like, and then I'm going to merge them back. Now, in the binary search case, in some sense, this is a little bit trivial.
因此被称为分治的原因就这么简单,将一个问题分解成一些子问题,并希望这些子问题解决起来比较方便,正如你希望的，求解的过程也会变得简单,下面就是把结果合并起来,现在，在二分搜索的例子里,从某些方面来说，这有点微不足道。
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That's an important observation, and as we get to the part of the course we talk about computational complexity, you'll see that what we really care about is not how efficient the program is on easy problems but how efficient it is on hard problems.
我们已经学习了这门课程的一部分了，我们要开始认识到,计算的复杂度这个概念，你会学习到我们在乎的并不是,算法在简单问题上的工作效率,而是解决复杂问题的效率。
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When we're just interacting with idol, with the interactive editor or sorry, interactive environment if you like, that's what you expect. What's happening is that we're typing in something, an expression it doesn't know how to deal. It's raising the exception, but is this simply bubbling up at the top level saying you've got a problem.
就发生了其中之一是吧，当你在交互数据处理或者是在交互编辑器，抱歉，任何你喜欢的交互式环境中，你可能会遇到这些，如果你在输入什么内容,譬如一个它不知道怎么处理的表达式,它就会报一个异常,但这是否是简单的,把你遇到的问题冒到最顶层呢？
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Those nine hours are going to be primarily working on problem sets, and all the problems sets are going to involve programming in Python, which is the language we're going to be using this term Now, one of the things you're going to see is the first problem sets are pretty easy.
这九个小时会是问题,提出的基本锻炼，所有的问题提出,都将涵盖，我们这学期,将使用的Python语言的程序,现在，你们将要看见的,第一个问题的提出非常简单。
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What's the point of this? Again, now that I can think about things recursively, I can similarly break things down into simpler versions of the same problem. It could be one version.
这些的意思是什么呢？再一次我想说,我既然能够以递归的方式思考了,那么我就可以简单地把问题,转化为更简单的同类问题。
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So, numbers count, but it's not an easy one-to-one question, various issues will determine who comes out ahead.
所以,人多力量大,但这不是简单一对一的问题,很多因素决定了谁将更胜一筹
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So Selection Sort, while it might be easier perhaps to think through than Bubble Sort, or maybe it's pretty much equivalent, it's just a different approach to the same problem.
因此，仔细想想，选择排序也许比,冒泡排序更简单，或者这两者都差不多，只是对同一问题的不同方法而已。
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