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So in fact, over the next thirty or forty minutes we're going to show you a set of examples of sort of canonical algorithms, and the different classes of complexity.
在接下来的三四十分钟里面,我们将要讲一系列的,权威算法，以及不同种类的复杂度问题。
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And I'll remind you, we saw a set of algorithms and part of my goal was to get you to begin to recognize characteristics of algorithms that map into a particular class.
我要提醒你们的是，我们看了很多算法,我的目标之一是让你们开始,意识到算法们的特性,并且能够一一映射到特定的分类中。
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And the reason for the scale is -- that as we saw last week the idea of these algorithms-- I broke the scale already.
之所以要用到它,是因为上周我们讨论的这些算法思想-,我把天平弄坏了。
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One of the things we want to help you do is identify the different classes of algorithms, what their costs are, and how you can map problems into the most efficient class to do the computation.
我们想要教会你们的事情之一就是,学会辨别不同种类的算法，它们的代价是怎么样的，以及怎么样把问题映射到,最有效的算法种类中去做计算。
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OK. Binary search is perhaps the simplest of the divide and conquer algorithms, and what does that mean? It says, in order to solve a problem, cut it down to a smaller problem and try and solve that one.
好了，二分搜索也许是,最简单的分治算法，这意味着什么？,也就是说，为了解决一个问题,把它切割成小的问题,然后再来一个个解决。
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And then we're going to turn to the question of efficiency. How do we measure efficiency of algorithms? Which is going to be a really important thing that we want to deal with, and we'll start it today, it's undoubtedly going to take us a couple more lectures to finish it off.
然后我们会回头继续讨论效率问题,我们如何计算算法的效率？,我们处理这些问题的时候,最重要的事情是什么？,我们今天要去讨论这个问题，毫无疑问我们要用,挺多节课来学习这个。
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This is a very important concept, and we'll see a lot of algorithms essentially implement decision trees.
这是一个很重要的概念，我们可以看到很多,基于决策树的算法。
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and we like log algorithms, because they're really fast. A typical characteristic of a log algorithm is a pro-- or sorry, an algorithm where it reduces the size of the problem by a constant factor.
并且我们也很喜欢对数算法,因为它很快,对数算法的典型特性是高速，哦，抱歉，是他能以常数因子的速度,降低问题的大小，很明显。
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Selection sort too really reduces to a total number of comparisons because I'm again comparing the current smallest to the next thing I see, the next thing, so really a lot of these sorting algorithms boil down to comparisons and the numbers that you actually have to make.
选择排序也可归纳为总数的比较,因为要将当前最小者与下一个进行比较,接着再下一个，可见,很多排序算法都可归结为比较,以及需要比较的次数。
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What is the class of algorithm that's- that probably applies to this, and how do I pull something out of that, if you like, a briefcase of possible algorithms to solve?
以及哪种算法-,可能可以应用到这类问题上,问题本身又能提取出什么东西来，以及可能解决问题的一系列方法的简介？
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And we want to help you learn how to map a problem into a class of algorithms of some efficiency That's our goal.
学会如何将一个问题,映射到一类,提升效率的算法中去,这就是我们的目标。
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But I want you to take away from this how we reason about the complexity of these algorithms. And I'll remind you, we said we're going to mostly talk about time.
但是我想你们理解我们,是怎么推出这些问题的复杂度的,提醒大家，我说过了我们主要讨论时间问题。
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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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It's a very common class of algorithms, and it's very useful one to have.
这是非常常见的一类的算法，并且也非常的实用。
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And part of it is we want you to learn how to have a catalog, if you like, of different classes of algorithms, so that when you get a problem, you try and map it into an appropriate class, and use the leverage, if you like, of that class of algorithms.
另外我希望你们能学会,如何制作一个关于，算法不同课程的目录，这样当你碰到问题的时候，你可以去找到合适的课程，然后在那门课程中，寻找解决方法。
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We saw some quadratic algorithms, typically those are things with multiple nested loops, or iterative or recursive calls, where you're doing, say, a linear amount of time but you're doing it a linear number of times and so it becomes quadratic, and you'll see other polynomial kinds of algorithms.
我们看过一些平方算法，他们一般进行了多次嵌套循环,或者递归迭代调用，对一个线性操作调用线性次,这样就变成平方次了,以后你们能看到,一些多项式算法。
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We don't like exponential algorithms, or at least you shouldn't like them, because they blow up quickly. And we saw some examples of that. And unfortunately, some problems are inherently exponential, you're sort of stuck with that, and then you just have to try be as clever as you can.
我们并不喜欢指数算法，至少你不应该喜欢，因为他们会,爆炸式的增长，我们将看到,这样的例子，不幸的是，一些问题先天是指数型的，你会被它们稍稍的卡住,然后你就得尽可能的发挥你聪明才智了。
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In Week 2 we'll look at things like cryptography and functions and the tools that by which you begin to assemble solutions to problems; in Week 3 we'll introduce what are generally ; known as algorithms and data structures; mechanisms by which you can solve problems more efficiently, effectively.
第2周,我们学习加密技术及其功能,还会学到一些操作工具,通过这些工具的使用来收集解决问题的办法,第3周,我们将介绍;,算法和数据结构,以及可以更有效地解决问题的机制。
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I want you to recognize classes of algorithms and match what you see in the performance of the algorithm to the complexity of that algorithm. All right?
让我再试一次这么说,我期望大家能通过,算法的复杂度,来看到算法的性能？
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What you're much better at doing is saying how do I take the problem I've got and map it into a class of algorithms about which I know and use the efficiencies of those to try and figure out how to make it work.
当你碰到问题的时候,更好的方法是把遇到的问题映射,到已经设计好的算法中去,并用这些算法来提高效率,来保证问题得到解决。
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And we saw a couple of examples of linear algorithms.
这是线性算法的典型例子,我们在过去也看过了大量的线性算法的例子。
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It's a secret number so that if Julius Caesar scrambled his message with the key 13, well, then the recipient had better know what that number is or realistically, -- and this is why it's kind of hard to buy -- into some of these age old algorithms, -- what would an alternative approach be to figuring out Julius Caesar's messages to his generals if he didn't know that secret number was 13?
它是一个机密的数字，以至于,如果凯撒大帝使用密钥13加密了它的消息，然后接收者最好知道那个数字是什么,实际上--这就是为什么很难,破解这些古老的算法-,有什么变换方法使凯撒大帝的将军,可以解密凯撒大帝的消息，如果他不知道,那个机密数字是13呢？
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Let me show you one more class, though about-- sorry, let me show you two more classes of algorithms. Let's look at the next one g- and there's a bug in your handout, it should be g of n and m, I apologize for that, I changed it partway through and didn't catch it.
请大家看，额,在你们的课堂材料中有个错误,应该是g，很抱歉-,我改了一部分这个错误但是没看到这里的，好，这儿的增长率，有人想猜猜么？
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