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I think that's really something that happens to a lot of students in all different ways, really coming to grips with.
我想，这也正是现在,很多同学遇到的问题，也都在尽力解决这种事。
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I think that would help solve a lot of the medical difficulties that people have these days.
我认为这种办法可以帮助解决现在困扰人们的许多医学难题。
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Now Joseph's brothers are jealous of Jacob's partiality to Joseph, And they conspire to be rid of him.
现在约瑟夫的兄弟们都妒忌雅各布对他的偏爱，他们密谋要解决掉他。
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Now, this is a pretty familiar widget of little gadget that you might see on most websites today, but my God, what an uninteresting problem to solve ourselves.
这是一个大家都很熟悉的小工具,现在在大多数的网站上都可以看到，天哪，如果我们自己解决这样的问题那将是多么无趣！
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We need to think about solutions to this, right from the start of the class, and we already talked about something.
从一上课开始,我们就应该开始,思考这些问题解决方案,现在我们已经谈论了一些了
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Here, the problem is solved by injecting it directly into the cell, shown here, and then that's one issue with gene delivery.
现在,这个问题已经通过,将其直接注入细胞的方法解决了,图上这里,这只解决了基因输送的一个问题
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Now I've shortened it a little bit by saying, ah, we've run out of weight, we're OK.
现在我会简短一些说，啊，我们装不下了，问题解决。
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Now, I want to do one concrete problem where you will see how to use these derivatives.
现在我要解决一个具体的问题,从中你会明白如何运用这些导数
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So we've got a chord progression.
现在我们把和弦进行的问题解决了。
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So what is shown here is the potential solution to potentially read out neural signals dragged from the brain and use these signals after some interpretations or decrypting if you will to drive prosthetic arms or computer cursors on the screen.
大家现在看到的是一种可能的解决方案,有助于解读病人大脑发出的神经信号,同时在经过翻译或者解码之后,使用这些信号，驱动假臂,或者电脑屏上的光标。
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Because, if Iraq spreads if you can't get peace between Israelis and Palestinians, and that conflict continues, conflict in Lebanon, conflict with Syria Then you have the Iraq War turning into complete chaos.
如果伊拉克问题蔓延,或是如果不能解决巴以冲突，or，indenpendently，如果冲突加剧，黎巴嫩问题，叙利亚问题,伊拉克战争现在已经发展到一团糟。
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What I though I'd do is just tease you with some visuals if you haven't gotten to the point of playing with the staff solution so the themes of problem set 3 are two-fold.
如果你们还没达到使用解决方案的程度,那现在我能做的就是用一些图形为你们梳理一下,习题集3的主题,是两方面的。
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Now, what we saw last time is there's a brute force solution.
现在，我们上次,看过穷举法解决方案。
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So now I have this right hand side of the 4-cup problem.
现在就解决4个杯子问题中的右半部分。
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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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For those perhaps familiar with some of the jargon do we introduce what we call link lists and hash tables and tries, increasingly sophisticated data structures, that allow us to solve problems that are much bigger and much more interesting than the very familiar one that we started with here.
那些对编程的术语较熟悉的同学,我们会教授,链接列表，哈希表，以及日益复杂的数据结构,以便帮助我们解决其他的,比现在所学的更大也更有趣的问题。
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So the problem of infectious disease prevention and treatment isn't solved yet, you know this, right?
传染病预防和治疗的问题,现在仍然没有解决,你们应该了解,对吧
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Now as for all these data sizes, let's close one outstanding question.
现在为了这些数据量，让我们先结束一个未解决的问题。
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That gets us to the smart thief. Why is this thief smart? Because she took 600. And she learned 600 that in fact there is a good way to solve this problem. And that's what we're going to talk about next. And that's something called dynamic programming.
现在我们要当聪明的贼,这个贼为什么聪明呢？,因为它选择了,它知道这事实上是解决这个问题的好方法,这就是我们接下来要讲的,也就是动态编程。
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Now, we are done because now we can ask how high does it go, and you go back to your y of 1 is 15+10-5, which is what?
现在问题解决了,因为我们可以算出,最高点的高度,你回到这个式子,求出y=15+10-5,是多少
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STUDENT: So, how do you come to a conclusion as to which you should use then, if you can determine the size based on solution, or based on input, so how do you decide?
学生：所以，你怎样决定你该用,哪个来算呢？现在如果你可以选择是，基于解决方案的大小，还是基于输入的大小，你应该怎样决定呢？
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So now we're left with a problem that's but 500 pages large and so what might a human do now to find Mike even more closely?
现在我们只用翻500页就能解决问题了,接下来，怎么做才能离Mike这个名字更近一步？
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The algorithm on mine professed to be implementing now is this thing.
这个算法现在要,解决的就是这个问题。
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Typically up till now, we've looked at things that can be done in sublinear time. Or, at worst, polynomial time. We'll now look at a problem that does not fall into that. And we'll start with what's called the continuous knapsack problem.
至今为止我们已经处理过,亚线性问题，最多也就是多项式问题,我们现在要看的问题则是不能用这些解决的,我们将要开始讲连续背包问题。
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Once I've got that, you notice I can now define a polar point, same way. Notice I've now solved one of my problems, which is, in each one of these cases here, I'm creating both x y and radius angle values inside of there.
你们注意到我现在可以，定义一个极坐标点了，以同样的方式,请注意到现在，我已经解决了我的问题之一了，也就是，在这些例子中的每一个,我在里面都创建了x，y值。
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First of all, two parameters. It's OK. All it says is, when I call this, I need to pass in two parameters for this to work. All right? Now, if I want to use that, I'm going to use a second piece of code here, called Barnyard. I'm going Barnyard to read in a couple of values, convert them into integers, and then I'm going to use solve to get a solution out.
注意我得到了什么,第一，两个参数,它的意思就是我调用这个函数，我得给它输入两个参数，明白了吗？,现在如果我要使用它我得用,这里的第二段代码，也叫,我将读入一组值，将它们转化为整型,然后我会用solve得到一个解决方案。
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