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Everybody knows Akenside didn't mean polymers, but now we're all into cyberborgs and we take all of this very seriously.
所有人都知道阿肯塞德说的不是假肢的意思，但是我们现在都在网上查找,而且我们都很认真。
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We were looking up new trails to hike and run,
我们一直在查找徒步旅行和跑步的新路径，
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So binary search, the phonebook example, binary search on the pieces of paper on the white board, why is that?
是二分查找，例如电话簿的例子,对其中的某一页进行二分查找，为什么呢？
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If you look on the Periodic Table this is 598 atomic hydrogen. And, sure enough, there is 13.598, which is this number here in electron volts.
如果你查找元素周期表上的氢原子,毫无疑问，它的电离能就是13。,这个数值也是电子伏的值。
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This is on purpose, because one of the things I hope you have learned to do this semester, is look up things you don't know, and figure out what they do. What they mean.
我举这个程序是有目的的，因为我希望你们这续期能学到,如何去查找你不知道的东西并，且弄懂它,们是干什么的，是什么意思。
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I asked my graduate student research assistant to research the whole literature and find out where did the word forward rate come from.
我让我的助研去查找,所有相关文献,试图找到,谁最先提出了远期利率的概念
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Go through the literature, see what--but mostly, for the most part, it shows minor--major.
查找文献,看一看,但大多数,大多数,是小调,哦,不,是大调
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You can look up in the catalog.
你可以从目录中查找出
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Certainly this is like mid 1990s, we did have the web and the internet but things were slow and it just wasn't really conducive to actually finding things quickly unless you really gave some thought to the problem.
它有些像20世纪90年代，当然我们有网络和互联网,但是做事情很慢,在快速查找东西的时候不是很有效,除非我们对这个问题真正深入思考了。
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OK. At the end of the lecture last time, I also showed you an example of binary search.
好的，在上次课程的最后，我也给你们看了一个二分查找的例子。
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Let's pull together what this algorithm actually does. If I generalize binary search, here's what I'm going to stake that this thing does.
总结下二分查找法,下面列举几点它的操作，首先，找中点。
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So let's not put him only on the spot; there's a whole bunch of us in this room and we can actually apply this same idea not to these phone books but actually to other real world problems, there's a whole bunch of people in this room.
所以我们不要只让他一个人体验,教室里还有一大帮人,其实这种方法不仅可以用来查找电话簿,还可以应用到现实生活当中,教室里有这么多人。
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Where's the penalty? What did I trade off here?
所以我可以在常数时间内做查找，太棒了？
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So the search is really easy.
因此查找过程也就十分的简单。
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OK. With that in mind, let's go back to where we were. And where were we?
我们回过头来看看，我们讲到哪里了？,我们正在开始讲二分查找？
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And it also allows us to look for certain key words and themes.
它也允许我们查找,特定的关键字和主题。
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You will have to look that one up. What about this one?
你们得去元素表中查找它，那么这个呢？
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I tried to find it on Google really quick and nothing came up, but I think there is this idea of how you organize a tapestry in that fashion.
我试图在谷歌上查找但是没有结果,但是我想有这么个想法,就是怎么用那种方式编织挂毯
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All right? I don't care what's in there, but just assume that's my list. And just to remind you, on your handout, and there it is on the screen, I'm going to bring it back up, there's the little binary search algorithm.
好，我不管列表里是什么，就假定那是一个列表,要提醒你们的是,在你们的讲义上和屏幕上，有一个简单的二分查找算法。
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And then, if I want to find out if something's there, I do the same thing. But notice now, hash is converting the input into an integer.
然后，我想查找出某些元素是否在列表中,我做同样的事，但是现在注意，哈希是将输入转化成一个整数，所以，其思想是什么？
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OK. So, what do I want you to take away from this? This idea of binary search is going to be a really powerful tool. And it has this property again, of chopping things into pieces.
从这里学到些什么？二分查找的思想,是一个非常有用的工具,我重复一遍，把问题拆成几部分来解决,那事实上，这里的增长率是多少？
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Again. Basic premise of binary search, or at least we set it up was, imagine I have a sorted list of elements. We get, in a second, to how we're going to get them sorted, and I want to know, is a particular element in that list..
好，二分查找的基本前提，或者是我们建立二分查找的基础,我们已经有了一个排好序的元素列表，我们就需要知道如何来快速的排序,如何从列表中找到特定的元素。
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There's been a lot of work done on these over the years, but in fact, it's pretty hard to invent a good hash function. So my advice to you is, if you want to use something was a hash, go to a library. Look up a good hash function.
已经做过了很多的尝试和努力,但是事实是，很难发明出一个好的哈希函数,所以我给你们的建议是,如果你们想使用哈希功能,到函数库中查找一个好的哈希函数。
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Now, one of the questions we could still ask is, right, we've got binary search, which has got this nice log behavior.
目前，还有一个问题我们仍然要问的是，对，我们已经学了二分查找，有着非常好的log级别的行为。
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If I look for, say, minus 1, you might go, gee, wait a minute, if I was just doing linear search, I would've known right away that minus one wasn't in this list, because it's sorted and it's smaller than the first elements.
如果我要查找-1，你可能要怒了，呵呵，等一等，如果我用的是线性查找，我不会知道-1不在这个列表中,但是列表是排好序的,1又比第一个元素小。
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Right? If that was the case in that code, then my complexity is no longer log, because I need linear access for each time I've got to go to the list, and it's going to Lisp be much worse than that.
这里的复杂度不再是对数的了，因为每次在列表中，查找需要线性访问,可能还要糟糕,其实，有些编程语言，如。
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And if you just look at the numbers, you can see how it cuts in from one side and then the other side as it keeps narrowing that range until it gets down to the place where there are at most two things left, and then it just has to check those two to say whether it's there or not.
你能看到他是如何不断的，从一个大的范围被拦腰劈开,知道最终只剩下两个数字,然后就只需要,比一比就知道结果了,将它同线性查找比较下。
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And tracing back where it came from can be really hard.
然后去查找问题来源,可能会很困难。
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OK. That's the basic idea of binary search.
好了，这就是二分查找的基本思想。
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Think about this compared to a linear search.
线性查找总是从开头开始遍历。
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