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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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Well, however we settle that issue, notice there's still one other assumption that all these positions still have in common.
不管我们如何解决这个问题，我们都会发现有一个假定,是这些观点都共有的。
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We all have our version of trying to wrestle with this: if God knows what you're going to do tomorrow, to what extent does it make sense to say that what you do tomorrow you do freely?
我们都有自己试图解决这个问题的方式：,如果上帝压根儿就知道我们明天要做什么，那么，说着明天会自由的从事自己想做的事情,究竟又有什么意义呢？
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Again, same kind of reasoning says, given some value x, I happened to pick a small one here, what's an easy way to do this? Well, let's just start at one. That's my variable I'm going to change and check.
好，尤其是，让我们到这里来,让我给大家看看第二个例子,让我把这个注释掉，这是我要解决的，第二个问题，假设我想找到一些整数的,所有除数，我想要找出来这个数的所有的除数。
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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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And although some psychologists and philosophers think they've solved it, most of us are a lot more skeptical.
尽管一些心理学家和哲学家认为,他们已经解决了这个问题,但大多数仍持有怀疑的态度
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But then also a little bit about your history, where you come from, some of your experiences which have helped you or informed your opinions on this very difficult issue that the entire world really is spending a lot of time trying to work on.
然后再谈谈你们各自的经历，你们从何而来，谈一些你们自己的经历,一些帮助过你们，或形成了你们,就这个复杂问题的观点,这个全世界都在投入大量时间试图解决的问题。
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One reason it's been harder to identify stem cells is that they're so rare; the other reason is that it's hard to identify the characteristics of them and it's taken many years to work this out.
干细胞难以识别的原因之一是,这些细胞很少,另一个原因就是,干细胞的特征性蛋白难以识别,我们花了好多年去解决这个问题
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So that would suggest that education is probably not going to get the job done, because that's not the main driving reason because most people know that they shouldn't eat so much junk food, but education is what we default to when we think about what to do.
所以你们可能认为,教育并不能解决这个问题,因为这不是主要原因,大部分人都知道不该吃那么多垃圾食品,教育是思考解决方法时被忽略了的
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And the god Aruru is told that she must deal with Gilgamesh Aruru Aruru is on the board.
上帝便派女神Aruru去解决这个问题,屏幕上的是。
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Newton says F = ma, so to make it a useful result of this problem, we know the mass of this guy.
牛顿指出 F = ma,这对于解决这个问题很有用,我们知道这个物体的质量
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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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So if I try to apply the same logic, well how can I divide and conquer this problem.
如果我想要用同样的逻辑，那么怎样划分,并解决这个问题呢？
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Indeed, to get at that question, the first thing we're going to have to think about is what are we?
事实上，要解决这个问题，我们首先要考虑的是，我们是什么？
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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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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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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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We call that a base case. It's basically the simplest possible solution to the problem.
我们说这是一个基础案例,这是这个问题最简单的解决方案。
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You want to take a new problem and say, what does this most look like?
当你要解决一个新问题时，你应该想想这个问题看起来和什么最类似？
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So if I were to solve this problem, here's the way I would do it. I would say, first thing I want to do, is I want to input a value for the base as a float.
如果我想要解决这个问题，这就是我要解决它的方式了，第一件我要做的事情就是要,输入一个浮点数作为三角形的底。
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That's certainly one way to do it, but for computers that's not necessarily the easiest way. So another way of solving it is to do something we already saw last time, which is basically, why not simply enumerate all possible examples and check them?
将一个等式代入另一个等式，这当然是一种办法,但是对电脑来说这绝对不是一件简单的事,所以解决这个问题的办法，正如我们上一次看过的,非常基本？
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Just to think about how I would break that problem up.
然后想想该怎么,解决这个问题。
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And then remember how you solve this 'cause otherwise completely useless exercise.
记住我是怎么解决这个问题的，否则就是一次,无意义的演练了，对吧。
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Let's see if we can figure out how to do this.
看看我们能否解决这个问题。
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We want to capture this idea of problem solving.
我们想抓住解决问题的这个想法。
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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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So you can actually say, how do I know which methods are associated with the class? For that, we can call dir. And what it does, is it gives me back a listing of all the things, dir all the methods, that are associated with it.
我们开始建立类了，我们得到了这些方法,因此实际上你可以说，我怎么知道，哪些方法是关联与这些类的？,为了解决这个问题，我们可以调用，这个方法的作用。
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I'm given an integer that's a perfect square, and I want to write a little piece of code that's going to find the square root of it. All right so I'm cheating a little, I know it's a perfect square, somebody's given it to me, we'll come back in a second to generalizing it, so what would the steps be that I'd use to walk through it?
完美平方数的整数，我想写一段代码来求这个数的平方根,好，我这儿有点儿作弊了,我知道这是一个完美的平方数了,他们给我的，我们后面会讲怎么产生这个数的，那么我想解决这个问题,需要什么步骤呢？
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So how would we go about solving this problem if I told you not only was there a maximum weight, but there was a maximum volume. Well, we want to go back and attack it exactly the way we attacked it the first time, which was write some mathematical formulas.
有些时候两个都重要,所以如果我告诉你这里不仅有,最大重量还有最大容量，我们应该怎么解决这个问题呢？,好了，我们想回过来然后,和第一次一样看看这个问题。
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