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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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they come to law firms and we get to help them solve the problem.
他们会到事务所来寻求帮助，我们则帮他们解决问题。
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Therefore, we have the chance to innovate and to solve those problems. So, I think there are hopes for that.
因此，我们有机会进行创新来解决这些问题,那就是希望之所在。
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So, let's think about it, and let's think about what we're actually doing when we solve this.
确实更有效率的解决了问题,好，接下来让我们来想想,看我们实际上是怎么来解决这种问题的。
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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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We can understand something that's fully random and work out the statistics and be comfortable with that to some degree.
我们能够理解一些,充满随机性，然后通过统计分析来解决的问题,而且一定程度上我们对此也很熟悉。
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So let me turn to a different approach to solving the question, answering the question,which one should we believe?
所以让我用另一个方法来解决这个问题，回答该相信哪一个理论的问题？
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Mine is to demonstrate over and over how little mathematics you need to get the job done.
我的方法就是,反复演算,用最少的数学来解决问题
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If you'd like to sit down with one of us more intimately and more sort of tranquilly, and work through problems for more than just a couple minutes at a time.
如果你希望和我们其中一个人坐下来，更亲密的,更平静的，每次用几分钟的时间,来解决问题。
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I think India does have a democratic building mechanism in addressing some such issues.
我认为印度是有一个民主体制,来解决这类问题的。
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It puts together the experience with tobacco and the experience with diet, to talk about how countries might see this problem coming and doing something about it.
它把发生在香烟和饮食上的,事情放在一起进行对比,讲述了国家是如何发现问题,并做一些事情来解决问题
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And Thorndike noted that cats do not solve this problem through insight.
桑代克注意到,小猫并不会通过顿悟来解决这一问题。
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Partly because I think it's a good exercise, but also I don't want this class to be a class where you sit there, with your cup of Willoughby's coffee if needed to keep awake, and you watch me solve models because that's not how you learn.
一方面是由于我认为这是个好的锻炼机会,此外,我也不希望这个课程,变成你们坐在这,用威洛比咖啡来保持清醒,一边看我解决问题,因为你们不应那样学习
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We've had a great deal to do with it, but of course we still haven't the slightest idea what it is.
我们花了很大的功夫来接解决这个问题，但我们仍然一点都不知道语言是什么。
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The survivors had to figure out a new way to do things and they didn't do anything new in a hurry.
幸存者们必须想出一条新路子,来解决问题,但他们匆忙之间并没有新举措
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The real issue is to figure out how to build constructs out of this that tackle particular problems, but the fundamental basics of computation are just captured in that set of mechanisms.
坏消息是当然这不是真的,真正的问题是怎么来,构建解决特定的问题的这些结构，但是运算的最基本的东西,仅仅体现在机制集里。
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We want to write a piece of code that helps these guys out, so I'm going to show you an example.
通过写一段代码,来解决一个这样的问题，接下来让我们来看个例子。
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So when you're trying to think about is this a problem that I can solve with dynamic programming, these are the two questions you ask.
所以当你想知道能否,用动态编程来解决这个问题时,你可以问自己两个问题。
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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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All right. So it's fun, and I got a little bit of applause out of it, which is always nice for me, but I also showed you how to think about it recursively.
好，挺有趣的，我也得到了一点掌声，这让我挺高兴的，但是我想让大家明白,怎么用迭代的思想来解决这个问题。
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Well, things can be fixed by a little trick called global variables.
好的，问题可以通过,一个叫做全局变量的东西来解决。
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I want to try to understand in that lecture-- help us to understand how this works and how we're getting solutions--possible solutions to these problems.
在那节课我会,帮助大家了解这是如何发挥作用的,以及我们是如何找到,可行性方案来解决目前的问题
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So what can we do to solve this?
来解决这个问题，我们能怎么做？
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Next time down I've got eight versions.
我可以用替代来解决这个问题。
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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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If we make--If we solve the problem of boredom setting in with progressive memory loss and radical personality changes, maybe boredom won't set in, but it's not anything that I especially want for myself.
如果用持续失忆,和剧烈人格变化来解决无聊的问题，也许不会产生无聊，但那不是我特别想做的事。
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It is going on for many years actually from the time of operation providr comfort with which I was involved in Northern Iraq when we realised that we would have civilian problems we need to develope civilian capacity to deal with these things.
这种状况已经持续了很多年了,从一开始在阿富汗北部,我参与的提供安慰行动,那时候我们就意识到我们缺少平民,我们需要更多的平民来解决这些问题。
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Non-obvious ideas were conceived of to solve these problems of long-term risks and to get around the psychological barriers imposed by framing biases and psychological biases, in order to allow people to actually manage the risk and to get around moral hazard.
解决方法需要被研究并发掘,来处理长期风险问题,避开由于框架效应,引起的心理障碍，能够使人们真正控制风险,规避道德风险。
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t In the b even case, again I'm going to let t of b be the number of steps I want to go through.
如果b为偶数，那么我还是要用,来代表解决这个问题需要的步骤数。
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So I'm going to solve this by enumerate and check, which is an example of what's called a brute-force algorithm.
你懂的,所以我得靠列举和检验来解决这个问题,这就是我们说的穷举算法。
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