-
We started off talking about binary search, and I suggested that this was a log algorithm which it is, which is really kind of nice.
我告诉了你们这是一个对，数级的算法，这是很棒的,我们来一起看看这个算法到底做了什么。
-
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。
-
Linear algorithms tend to be things where, at one pass-through, you reduce the problem by a constant amount by one. If you reduce it by two, 1 it's going to be the same thing.
有问题么？,线性复杂度的算法，当进行了一个,常量级步数的操作的时候，将问题的规模缩小了一个。
-
It's a good sign that this is logarithmic, and I'm going to come back in a second to why logs are a great thing.
为什么对数级复杂度是个好事情，让我们再来看一个算法,噢，抱歉是让我们再来看两个算法。
-
If I'm running a linear algorithm, it'll take one microsecond to complete.
算法会在1微秒内完成，如果是一个平方级的方法。
-
We've seen log, we've seen linear, we've seen quadratic, we've seen exponential.
我们看过了对数级的，线性的，二次平方的，指数级的算法。
-
Yeah. Is the last one there?
对数级复杂度的算法的优势对不对？
-
It is certainly possible, for example, that a quadratic algorithm could run faster than a linear algorithm. It depends on what the input is, it depends on, you know, what the particular cases are. So it is not the case that, on every input, a linear algorithm is always going to be better than a quadratic algorithm.
一个二次平方级复杂度的算法,当然也是可能跑的比线性复杂度算法快的,这取决于，你知道的，输入以及特定的案例，因此并不是对于每个输入,线性复杂度就一定会,比二次平方级复杂度的算法的表现要好,只是通常来说是这样的。
-
And as a consequence, it is log.
因此这是对数级复杂度的算法。
-
With this, if I can assume that accessing the i'th element of a list is constant, then you can't see that the rest of that analysis looks just like the log analysis I did before, and each step, no matter which branch I'm taking, I'm cutting the problem down in half.
读取数组中的第i个元素,是个常量时间的操作的话，我也就能像以前那样得到,这个算法是对数级复杂度的分析,并且每一步不管我选择哪个区间，我都可以把问题的规模缩小一半。
应用推荐