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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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Our friend Schr?dinger told us that if you solve for the wave function, this is what the probability densities look like.
我们的朋友薛定谔告诉我们,如果你用波函数来解决，你就会知道这些概率密度看上去的样子。
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The notion here is that you can get a globally optimal solution from locally optimal solutions to sub-problems.
这里的概念是你可以通过,子问题的局部最优方案,得到全局优化解决方案。
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So let's actually let you try another example of solving a problem that has to do with one of the spectrums.
下面请大家来看一下另一个例子,这次是一个需要大家解决的关于光谱的问题。
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In week zero, when we tore the phonebook in half and half and half we were recursing through that problem.
当我们将电话簿划分为一半又一半的时候,其实就是利用递归在解决问题。
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The poem then tries out different answers, answers that alternately explore transcendental and secular solutions.
该诗试图给出不同的回答，答案分别探索,超验和世俗的解决方法。
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That was an interesting situation where the project of one group of students was in fact a great solution for the product of another group of students.
这种情况很有趣,一组学生的项目,实际上就是另一组学生,推出的产品的解决方案。
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One solution for that is to get a copy of a textbook I wrote called Basic Training in Mathematics.
解决办法之一,就是买一本我编写的教材,书名叫《数学基础训练》
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Whatever you want to do; check your email, publish tweets, go shopping or whatever, it can be solved by this one box.
无论你想做什么;,查收邮箱，发布推特状态，网上购物等等，都可以通过这个搜索框解决。
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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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And that makes it for me a very exciting time to study this because the problems aren't solved in the way that bridge building is largely a solved problem now.
对于我而言,这是一个非常激动人心的时代,因为一百年前桥梁建设中难以解决的问题,在今天都得到了解决
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Very difficult problems, but in my judgement, all solvable if we generate the country in the kind of bipartizan political cooperation and political courage that will be necessary to fix them.
这些问题很不容易解决，但我认为,不是不能解决，只要我们,以这种两党制的合作形式治理国家,还要有治理它们的政治勇气。
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For all students, what we want to do is we want to give you an understanding of the role computation can and cannot play in tackling technical problems.
对所有学生来讲，我们想做的就是,给你们关于计算在能否解决技术问题中,所扮演角色的,认识。
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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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We just go through the list top to bottom, left to right, and cross names off as we go.
我们会从上到下，从左到右看那个问题清单，如果解决了就把名字擦掉。
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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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Now, as obvious a statement as that is in this algorithm, it turns out that is the key to this whole problem being solved correctly without my algorithm looping infinitely.
这是此算法中很明显的一句话，也是正确解决,整个问题的关键,否则此算法就会陷入死循环。
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OK, and you can see that this thing ought to unwrap, it's going to keep extending out those multiplications until gets down to the base case, going to collapse them all together.
好，你可以看到这种方法,是怎么解决的,他一层层的将乘法展开一直到最底层,然后将他们一起乘起来。
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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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And they were kind enough to send us this magnetic tank which we'll call forth from the computer solutions to a series of problems that would occur on a simulated flight to the planet Saturn.
他们很友善，送给我们这个有磁性的水槽,用于计算机解决一系列,土星模拟飞行中,可能出现的问题。
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OK. Binary search is perhaps the simplest of the divide and conquer algorithms, and what does that mean? It says, in order to solve a problem, cut it down to a smaller problem and try and solve that one.
好了，二分搜索也许是,最简单的分治算法，这意味着什么？,也就是说，为了解决一个问题,把它切割成小的问题,然后再来一个个解决。
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But in terms of SI units, which become much more useful if you're actually trying to use intensity in a problem and cancel out your units, we're just talking about joules per second is what intensity is.
但是用国际单位制，这个变得越来越有用了,如果你实际上在使用强度,来解决问题和约化单位，我们仅仅讨论每秒钟的焦耳,这就是强度。
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It's a long sequence of instructions, it starts at the beginning, walks through, may jump around a little bit, but eventually comes down at the end. It's okay for the things you're doing for the early problem sets.
这是一长串指令，从开端开始，向前步行，偶尔来回跳一会儿,但是最终会走到结尾,这些足以解决最初级的问题。
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Like how can you possibly figure that out with actually compelling a machine to do it for you and sure enough we chatted for a few moments, I kind of gently pointed out well it's kind of like problem 7 last year.
就好像去逼计算机为你做这件事,就能解决问题一样,我们确实谈过这个问题，我委婉地告诉他,这种情况与我们去年讲过问题7类似。
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So what you typically do and a hash case is you design your code to deal with that.
你所需要做的就是通过设计你的代码,来解决上面的问题。
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In a help session what he might do typically is solve between four and eight problems that illustrate the key principle being talked that week.
在帮助课程中他一般会,解决4到8个问题,来阐明那一周教的关键原理。
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So you see a problem like this in the real world; you see a problem on campus you might want to solve.
在现实生活中你会遇到这样的问题;,在学校里看到这种问题时，你会想要去解决它。
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So this is very similar, this is a kind of recursive thinking we talked about earlier, where we take our problem and we make it smaller we solve a smaller problem, et cetera.
我们则跳过比猜想数小的那个区间,然后我们重复这一过程,跟之前我们讲过的，递归思想非常类似,我们解决问题的时候,先把问题一步步变小，然后解决小问题。
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> Indeed. So there is a solution and that is the solution.
>，的确，这里有解决方案，那就是一个解决方案。
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So yes, f is a float, but that solution is too late; we need to fix the problem sooner.
是的，f是一个浮点数，但是那个解决方案太迟了;,我们应该在次之前把问题解决。
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