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A log algorithm typically is one where you cut the size of the problem down by some multiplicative factor.
对数级复杂度的算法就是指,通过一系列常量级步数的操作,可以将问题的规模。
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It implies that this algorithm is calling itself again and again, and again, and on each time the size of the problem I'm trying to sort is being divided by what?
这就说明此算法会一次又一次地调用自己,每次我要排序的问题规模大小,会除以多少呢？
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And by that, I mean, not how much memory do I need to store the size of the input, it's really how much internal memory do I use up as I go through the computation?
需要占用多少内存,我意思并不是，存储输入需要多少内存,而是当我完成这个？
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It's deliberate that a lot of the examples in lecture are fairly short and bite-size so that you can actually focus on pulling out the key ideas without getting distracted by line and lines of code.
很多的演讲中的例子,是短小的,因此你们可以集中于提取其中的主要思想,而不是被一行行的代码给分心。
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Another way of saying it is, if I, for example, 10 increase the size of the input by 10 10 the amount of time increases by 10.
另一种说法就是，例如，我把输入的规模增加0,解决花费的时间也会增加。
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and we like log algorithms, because they're really fast. A typical characteristic of a log algorithm is a pro-- or sorry, an algorithm where it reduces the size of the problem by a constant factor.
并且我们也很喜欢对数算法,因为它很快,对数算法的典型特性是高速，哦，抱歉，是他能以常数因子的速度,降低问题的大小，很明显。
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Now. You might look at that and say, well that's just a lot like what we had over here Right? We had some additive constant plus a simpler version of the same problem reduced in size by 1.
现在你可能会看着这个说，这很像我们以前做过的,对不对？我们用一些附加的常量,加上问题的另外一个规模缩小了1的,简化版本来代替这个问题本身。
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And small is not derogatory here, by the way, it just says the size of things you're going to be able to do.
顺便一提，这里的小并不是贬义，只是代表你有能力做的,事儿的规模而已。
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So, I'm now multiplying by the result of calling the size of operator, which we've seen before.
现在我乘以运算符的大小,之前我们看到的。
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OK. So to do this, we're going to have to do a couple of things. All right, the first one is, what do we mean by input size?
好，为了实现这种方法我们,有些事情要做，第一件事情就是，当我们说到输入的大小的时候代表了什么呢？
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Typical characterization, not all the time, but typical characterization, is an algorithm that reduces the size of a problem by one, or by some constant amount each time, is typically an example of a linear algorithm.
我们学习过了线性算法，它的典型特征，不是通用的,但是比较典型的特征是，它是逐一减小问题的大小的，或者说是每次减小常数的大小。
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N Well, here is a list of size N. How many times can you divide a list of size N by 2, right?
这是一个大小为N的列表，将一个大小为,的列表除以2需要几次呢？
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To get any location in memory, to get to any value of the list, I simply have to say which element do I want to get, I know that these things are stored in a particular size multiply that index by 4, add it to start, and then it's in a constant amount of time I can go to that location and get out the cell.
取得列表中的任何一个值,简单说来，想要取得列表中的任何元素,我知道这些元素存在特定的大小中,把下标乘以4，加到start上,然后定位到内存单元，并取出值就是固定的时间了,好的，如果元素以固定大小存储。
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