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So this is a thing, Week Number Four, saw very commonly, which was -- this is something we saw commonly and there's a couple of issues here.
所以这是一件事，第四个，一般的分解，那是我们讲解的东西,这里有好几个问题。
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OK. And then the exponentials, as you saw is when typically I reduce the problem of one size into two or more sub-problems of a smaller size.
好，然后说到指数级，正如你所见，典型的例子是,我讲一个问题分解成为,两个更小规模的子问题。
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And the difficulty with that approach, even if we break the question, whether not there're souls, the difficulty at the approach was that it seems as though the soul could constantly be changing while the personality who might call stays the same.
这种前提的难点在于，即使我们将问题分解，先不管灵魂是否存在，难点还在于,似乎灵魂可以,不断地改变，而人格,这个重要的方面，却保持不变。
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So things that are good candidates for divide And conquer are problems where it's easy to figure out how to divide down, and the combination is of little complexity.
因为适合用分治算法解决的问题,最好是能够简单的将问题进行分解,并且合并的过程不是非常的复杂,只要比线性方案要小。
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Our goal is to take problems and break them down into these computational steps, these sequence of instructions that'll allow us to capture that process.
我们的目标是得到问题,然后将问题分解为这些计算步骤，这些指令集,可以让我们看到这个过程。
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I just kept sub-dividing down until I got really easy problems, and then I combine them back.
我不断的进行子分解,直到得到简单的问题，然后我再把它们合并回去。
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You really want to get the power of dividing things up, but if you end up doing a ton of work at the combination stage, you may not have gained anything.
你真的想得到分解问题的能力,但是如果在合成的某个阶段,你需要做大量的工作，你可能得不到任何东西。
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The second question I want to ask is what's the base case? When do I get down to a problem that's small enough that it's basically trivial to solve? Here it was lists of size one. I could have stopped at lists of size two right. That's an easy comparison.
第二个问题是什么是基础条件？,我要将问题分解到何时才使得问题,小到可以解决的基本问题？,这里是当列表的长度为1有时候,我也可以在长度为2的时候停止分解,那是一个非常简单的对比。
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And it's called divide and conquer for the obvious reason. I'm going to divide it up into sub-problems with the hope that those sub-problems get easier. It's going to be easier to conquer if you like, and then I'm going to merge them back. Now, in the binary search case, in some sense, this is a little bit trivial.
因此被称为分治的原因就这么简单,将一个问题分解成一些子问题,并希望这些子问题解决起来比较方便,正如你希望的，求解的过程也会变得简单,下面就是把结果合并起来,现在，在二分搜索的例子里,从某些方面来说，这有点微不足道。
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Notice what happens.
这是分解问题的好方法。
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And that may generalize again and it keeps going until you either get back to Adam and Eve, I guess. I don't think they were born in the US as far as I know, or you find somebody who satisfies that definition or you find that none of your parents actually are in that category.
降低到我的父亲或者母亲,是不是天生的美国公民呢,这个问题可以继续向下分解,你甚至可以追溯到亚当和夏娃的时候,据我所知它们并不是出生在美国的,或者你要么找到一个符合定义的人,要么发现你的父母都不满足条件。
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Log n Log n, because at each stage I'm cutting the problem in half. So I start off with n then it's n n/2 n/4 n/8 over two n over four n over eight.
因为总共有多少层？,因为在每一层，我都是把问题分解成两半,因此以n开始，然后是。
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I have used divide and conquer, as we seen before, to recursively break it into smaller problems. But the smaller problem of fib of 4 and the smaller problem of fib of 3 overlap with each other.
正如我们之前看到的，我已经进行了划分,并且递归性的把它分解为更小的问题,但是fib的简化问题,和fib的简化问题会相互重叠。
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