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Don't be intimidated. Even though it is apparently exponential, a lot of times you can actually solve it much, much faster.
别怕，即使它,很明显是指数型的，很多时候,你都能更快的解决它。
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He is very technical. He's, pretty much any question you have,
他非常专业。几乎能解决你所有的问题，
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It literally halves the amount of time it takes to solve that problem but we can actually do better.
它能把解决问题时间的缩短一半,但其实我们能做的更好。
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And we do so by a quantity called the average valence electron energy.
我们可以通过,一个叫做平均价电子能的量来解决这一问题。
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They say with the contraction in Venture Capital doesn't mean we're not going to get good solutions to the business problems we face.
他们认为风险投资上的契约并不意味着,能有好的方式来解决面临的商业困难。
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And so frequently what we try and do is, we take a new problem and map it onto an old problem so that we can use an old solution.
我们经常做的一件事就是，我们处理一个新问题时,把它归结为一个老问题,以便我们能采取老的解决方式。
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And the prospect of having a lot of time to pursue math problems of a richer and deeper sort seems fairly attractive.
要是能有时间,解决更困难更深奥的数学问题,对我相当有引吸力。
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If you can do this, you can do most of the problems you will run into.
如果你会做这个,那么你就能解决碰到的大部分题目了
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And that's how over time you resolve conflicts, not just bring people together.
这样随着时间的推移，就能解决冲突，不仅是让人们聚在一起而已。
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So in this case, the communication worked but am I right in thinking that the communication isn't such an instant solution as it was in the game we saw last time?
在这个博弈中,交流起到了作用,但是能说这和上一讲的博弈一样吗,交流并没能直接给出解决的方案
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So could you use taxes and subsidies, for example, to raise the price of foods that you think people should be eating less of, and lower the price of things you would like people eating more of?
你能通过税收和补助金的方式来解决吗,例如,抬高那些你觉得大家应该少吃,的食品的价格,降低那些你认为我们,应该多吃的食物的价格
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And she would intercept them as they came across the rickety bridge, or the low bridge, and she would ask them a few questions and ?" conclude with, "Can you write me a story? " You would help me out with my experiment if you'd just write a little story right now."
她会拦住他们,当他们分别横过摇晃的桥和低矮平稳的桥时，她会问一些问题,最后一个问题是“能为我写一个故事吗“,我将解决实验中遇到的瓶颈,如果你能立即给我写一个小故事“
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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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What does it require to be a successful mechanic, to do all the mechanics problems?
怎么才能当个成功的力学家,并能解决所有的力学问题呢
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It's definitely an opportunity for help, but particularly, as an opportunity to work with someone for just a few moments to help get you unstuck or to get you past some stumbling block that, otherwise, if you struggled with on your own, you might sink or waste even multiple hours on just something that you're not seeing.
这是一个寻求帮助的机会，特别是，作为一个与某人一起工作的机会,他们能帮助你解决问题,或帮助你越过绊脚石，否则，如果你自己单独奋斗，你可能,浪费很多时间在,你不了解的东西上。
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So that you will come away with a sense of what you can do, what you can't do, and what kinds of things you should use to tackle complex problems.
因此你们才能对,你们能做的事儿，不能做的事儿,和用何方法去,解决棘手问题有一个基本概念。
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All it could do, though, was solve those equations.
它所能做的就是解决这些方程组问题。
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Perhaps the right kind of lobotomy would do the trick.
适当的额叶切除术就能解决问题。
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in the context of a web page. And increasingly that is where the human computer interaction is, and so will you be empowered by terms and not to just to make a website per se but to make an application, something that's of interest to you, something that solves problems, something that lets you tell someone through the most electronic means possible that you saw them somewhere on campus.
以网页内容的形式表现出来,人机交互的运用将越来越多，而且你将学会编程,不仅能制作网站，还能做出应用程序，一些你感兴趣的东西，一些解决问题的手段，还有一些可以让你通过使用,现有的电子手段来分辨出,校园里面看到的一个人的东西。
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Well, I solve 2 or 3 exponential problems before breakfast every day. You know things like, how to find my way to the bathroom is inherently exponential, but I manage to solve it anyway.
你要知道如何找到,我的浴室就是一个，固有的指数型问题,但是我还是能解决它。
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Once you hear that description, it's easy to write the code, in fact. This is a place where the recursive version of it is much easier to think about than the iterative one.
实际上一旦你听到了大致描述,就能很轻松的写出代码来,在这一点上应用递归来解决问题,比用迭代要容易理解多了。
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On Thursday we'll do a more careful analysis and try and understand how I could have accomplished this seemingly magical task of solving an exponential problem so really quickly.
在周四的时候,我们会做进一步的分析,并且尝试理解我为什么,能如此快速的解决这种,看上去超复杂的指数型问题。
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Then, of course, you can do more complicated things.
接下来我们就能解决一些更复杂的问题
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That's the question we're going to try and address. If we can do this, this is good, because first of all, it removes any questions about what machine I'm running on, it's talking about fundamentally, how hard is this problem, and the second thing is, it is going to do it specifically in terms of the input. Which is one of the things that I was worried about.
这是一个我们接下来要去,尝试和解决的问题，如果我们能做到的话会很不错，因为首先，它解决了结果可能和我,运行的计算机有关系的问题，因为这从根本了告诉了，我们这个问题的复杂度，第二件事情,就是这种方法可以依据输入的大小来计算,而这正是我最担心的地方。
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So always amazing to us how we go into the problem, our eye or mind can see one class of solutions, but the math will tell you sometimes there are new solutions and you've got to respect it and understand and interpret the unwanted solutions, and this is a simple example where you can follow what the meaning of the second solution is.
解决问题的方式总能让人惊喜不已,我们的眼睛或思想可以看见一类解,但数学有时会告诉你还有新的解,你不能忽视它,而是解释这些不期而至的解,这只是一个简单的例子,由此你可以理解第二个解的意义
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I'll let you chase it through, it does work. What I want to look at is, what's the order of growth here?
我会让你们去运行这个方法的，确实能得到正确答案，我想问的是，这个解决问题的方法的增长率是什么？
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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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That's not what Game Theory is about.
这不是博弈论能解决的
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I just reduced it to a smaller version of the same problem.
我刚刚把它简化为一个更小的同类问题,这就是我可以写出能解决更短字符串的例子。
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