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Cut the problem in half. Cut the problem in half again. And that's a typical characterization of a log algorithm.
是每次除以特定的量,将问题减一半，再减一半,如此，这就是对数算法的典型特性。
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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's an example of a very common tool that's going to be really useful to us, not just for doing search, but for doing a whole range of problems. That is, in essence, the template the describes a log style algorithm.
不仅仅是做搜索,还可以解决一整类问题,本质上，这个模板就描述了,对数形的算法,我们一会再回来。
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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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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。
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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。
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In the log case, it's divide by an amount.
而在对数算法中。
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Yeah. Is the last one there?
对数级复杂度的算法的优势对不对？
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We also saw a logarithmic algorithm.
我们也看过对数算法。
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And as a consequence, it is log.
因此这是对数级复杂度的算法。
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Yeah. Log. It's a good think, but why do you think it's log? Ah-ha. It's not a bad instinct, the length is getting shorter each time, but what's one of the characteristics of a log algorithm? It drops in half each time.
对了，对数，这是个好想法,但是你们为什么认为是对数呢？,啊哈，这样的本能不错，每次长度都会缩小些,但是对数算法的特性是什么。
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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。
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Perhaps more importantly, how to recognize a kind of algorithm based on its properties and know what class it belongs to. This is a hint. If you like, leaning towards the next quiz, that you oughta be able to say that looks like a logarithmic algorithm because it's got a particular property. That looks like an n log n algorithm because it has a particular property.
也许更重要的是,如何根据一个算法的特点将其辨别出来,并且知道它属于哪一类算法,这是一个提示，就对于接下来的测验来说,如果你喜欢你可以说它看起来像一个对数算法,因为它有一个特定的性质,那个看起来像一个n，log，n的算法,因为它有一个特定的性质。
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