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And when you have an optimal substructure and the local solutions overlap, that's when you can bring dynamic programming to bear.
当你得到一个最优子结构,但局部解决方案有重跌时，你就可以引入动态编程,来解决这个问题了。
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because then you can solve new problems on midterms and what not if you understand the conceptual part.
因为这样你可以解决中期的新的问题，如果你不理解的话，就不好说了。
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And so you get to build your own special purpose programming language that helped you solve your problems in biology or finance or whatever,
你读过的类型都可以,所以你就可以让编程语言按照你的,特殊用途去解决你的生物学,财务或者任何类型的问题，
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If you're unsure about that, check out, of course, chapter three in the textbook, where these issues are addressed.
当然,如果还不确定,可以看看课本的第三章,这些问题都提到了
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You can look at old exams, you can look at your homework, that's the kind of questions you can expect.
你可以看看古老的考试，你看看你的作业，那就是你所期待的问题。
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Our bulletin boards of sorts, discussion forums, where you can not only browse discussions, questions that your classmates have asked, you can certainly ask questions of your own.
在我们的电子公告牌，论坛，你们不仅可以浏览其他人的讨论，你的同学们所问的问题，你们当然也可以问你们自己的问题。
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And that's when, if you had everybody come to the theater for a big debate about something, you could still have people voting on certain things that the city might decide to do, although they couldn't rule themselves completely by themselves.
所以当时，如果所有人到剧院,对某一问题进行辩论，还是可以通过投票,决定某些事情，虽然他们无法进行完全的民主统治。
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But what is the commonality about getting to that question, because I think, maybe you can correct me if I'm wrong here, campus life in some ways is about that question.
但说到刚才的问题，不同学校对此共性是什么，因为，要是我说错了您可以纠正我，校园生活在某些方面是和这个问题有关的。
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How much energy are you going to get out, and how far are you going to be able to drive a car with this expansion, let's say, so that's the problem.
你能获得多少能量，利用这次膨胀,你可以把你的车开出多远，比如说这就是问题所在。
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So, if you're at hanging your exam from high school on the fridge and you want to make it look more impressive, you could just rewrite the question as that, and essentially you're answering the same thing.
所以如果你把你的高中测试题,挂在冰箱上,而且想让它看起来更难忘，你仅仅重新写出这个问题就可以了，本质上你是在做相同的事情。
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Earlier theories-- it's wonderful to have scientific theories that you can use to handle these problems, which you cannot demonstrate any fact for whatsoever.
更早些的理论...,幸好我们还有些科学理论,可以用来处理这些问题,这些没有实例,可以证明的问题
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There were some problems with that deal and I just give you one news report on that, but you can follow it if you're interested.
那项交易里存在很多问题,而我仅仅给了你一段关于它新闻报道,不过如果你对此感兴趣你可以去追查一下
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The next phase, concrete operations, from seven to twelve, you can solve the conservation problem, but still you're limited to the extent you're capable of abstract reasoning.
下一阶段,具体运算阶段,七到十二岁,儿童可以解决守恒问题,但儿童的抽象推理能力仍然有限
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So to imply that now you can eat all you want, you have an issue to free ticket if you will, some people might consider not the right message.
假如说现在你可以吃任何你想吃的东西,这里面存在一个免费门票的问题,有些人对营销信息的理解并不正确
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Now, I want to ask a question that we're going to need to think about, the two of you sitting up front here, when I was asking you how you responded to it. Can we have a moral response to this novel?
现在，我想要问你们一个我们将要思考的问题，就你们俩吧，坐在前面的，当我问你们如何回应,我们可以对这部小说有一个道德反思吗？
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I think that book will give you all the basic principles you need in calculus of one variable, more variables, elementary complex numbers, maybe solving some problems with vectors and so on, which you're going to get into.
我想那本书会给你所需的所有基本知识,包括一元和多元微积分,简单的复数运算,可以解决一些与矢量有关的问题,而这正是你们将要学的
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It will soften your speech so that you can pose the question without offending the other person.
它会很好地柔化你的言辞，这样你就可以在不冒犯其他人的情况下提出自己的问题。
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So you see the problem for consciousness now is not just a single problem.
所以大家现在可以看到意识的问题,并不是一个的问题。
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So once you look at Star Festival then you can think about the questions you have to answer and then question maybe the same thing I ask myself: who am I? While maybe some other questions.
所以当你看“七夕“的时候,你可以考虑你必须要回答的问题,这个问题有可能是我问自己的那个同样的问题：,我是谁？或者其它的问题。
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That's not hard; you have it right in front of you.
并不难回答的问题，可以从你面前的那张纸上找到答案。
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You can talk about it as much as you like, but as long as you're going to go home and still drive your Hummer and have sixteen hot showers a day, we're still going to have high carbon emissions.
你可以在减排问题上一直高谈阔论,但当你回家时,你仍然会开着你的悍马,每天洗十六次热水澡,我们依然在大量排碳
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So if you run into a problem set that just, you don't get, all right? Seek help. Could be psychiatric help, could be a TA. I recommend the TA.
所以如果你碰到了一个,你不懂的问题，好么？求助，可以是精神科，可以是一个助教，我推荐助教。
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I want to show you how easy it is to change the code. But, notice, once I've added this I actually have a problem. This is now an under-constrained problem. I have more unknowns than I have equations.
我加上这个条件后,我马上面临一个问题了,这就是现在是一个非约束性问题了,我的未知数比方程数多,你从代数中可以知道。
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And actually, a question that might come up, I just explained, the sodium channel, you might say, well, how do potassium channels work then, because I can understand how you can filter something big out, but how do you filter out something small.
实际上，可能大家会问一个问题，我刚解释过，钠离子通道，你可以说，好吧，那么钾离子通道该如何起作用呢，因为我可以理解你是如何把大东西过滤掉的，但是你如何把小东西过滤掉呢？
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Everything should be pretty self-explanatory and if you have any questions you can just contact me or ask me questions after class.
这些材料应该都很容易理解,如果有问题的话,可以在课后提问或和我联系
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And, if you have trouble balancing equations, you can look in section 2.11 in the text.
如果你在配平方程式方面有问题，你可以看看课本中的2。11节。
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To some extent we can tell whether you're solving a moral dilemma versus something else.
在某种程度上,我们可以看出,你是否正在解决道德两难问题,而不是在解决别的问题
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If you decide to opt in by a pass fail, I just need to sign your white study card or if you wanna decide before the 5th Monday, just grab the pink slip and I can sign that and you can turn that in at any point and I'm happy to chat during break today or after class if you have any questions or concerns.
如果你上我们的课程只是要一个分数，那么我只需要在你的白卡片上签个名就可以了,或者说，如果在第五周的周一前还没考虑好，把你的解聘书拿来，只要我签个字,任何时候你都开以离开我的教室,当然，如果你有任何问题和疑虑,我也很高心和大家做课下交流。
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The way the physics works is you will find some laws of motion in mathematical form, you put in the initial conditions of whatever, you solve the equations, and the answer that comes, you have no choice.
在物理问题中,你可以用数学方法得到运动定律,你代入初始条件,然后解方程,获得答案,你别无选择
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stay there because who knows, there are 20 million other things I might have said, but instead let me give you the opportunity to ask questions that you would like to raise, particularly if you want to ask about how they fought, as long as we have a phalanx here we might as well use it if we need too.
你们先别走,因为,谁知道还有什么呢,我还有一肚子的东西想给你们讲,但最好还是留给你们,一些提问的机会,尤其是关于战斗的问题,讲台上正好有一列方阵可以用来讲解
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