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Although we run it on a laptop so that we can monitor its operation, the algorithm itself doesn't require a lot of computer power and could easily be run from a chip that has the capabilities of one that's already in insulin pumps or in cell phones."
VOA: standard.2010.04.15
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So I'm going to solve this by enumerate and check, which is an example of what's called a brute-force algorithm.
你懂的,所以我得靠列举和检验来解决这个问题,这就是我们说的穷举算法。
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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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Now, as obvious a statement as that is in this algorithm, it turns out that is the key to this whole problem being solved correctly without my algorithm looping infinitely.
这是此算法中很明显的一句话，也是正确解决,整个问题的关键,否则此算法就会陷入死循环。
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It couldn't have been a very complicated algorithm because it basically paired people up randomly on the campus.
这个算法不是很复杂,基本上是给校园里的人随机配对。
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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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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。
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You might remember vaguely logarithms from high school math and such but what this suggests for us , the computer scientists, is that this is certainly a smarter, a faster algorithm.
你可能还会依稀记得,高中数学里的对数,这就给了我们这些计算机科学家们，一些启示,即，这种算法更智能，更迅速。
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Obviously the algorithm is likely to depend on the size of the input, so this is not a great idea.
很明显这个算法是与我的,输入的大小相关的，因此这不是个好方法。
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And that's because that is a version of a divide and conquer algorithm.
这个想法非常重要,因为这就是分而治之算法的一个版本。
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Where those pieces, I would do the same thing with, I would divide them up into smaller chunks, and sort those. Is that going to give me a more efficient algorithm?
合并起来，而那些小列表,我又会把他们拆成更小的列表,再排序，这会给我,一个更高效的算法么？
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So this is a nice little search-- sorry, a nice little sort algorithm . And in fact, it's relying on something that we're going to come back to, called the loop invariant.
恩，这是一个很棒的小搜索，抱歉，和很棒的小排序算法，事实上，它依赖于一些我们要回顾的东西,被称作循环不变量。
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All right? Because if I don't do any swaps on a pass through the algorithm, then it says everything's in the right order.
好么？因为如果我,这一遍没有做任何交换，那么就意味着已经排好序了。
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If I'm running a quadratic algorithm, it'll take one millisecond to complete.
算法会在1毫秒内完成，如果问题的复。
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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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And so ease of implementation is actually a very compelling -- metric against which to measure-- -- do you mind toning my voice down a bit-- is a very reasonable measure against which to measure the quality of an algorithm, right.
如此简单的实现实际上是一个很牵强的,度量，与之相对的衡量是-,如果你们不介意，我降低点音量-,是一种用来度量算法质量的,合理的方法。
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They are computationally challenged, meaning, at the time they were invented, they were perfectly good sorting algorithms, there are better ones, we're going to see a much better one next time around, but this is a good way to just start thinking about how to do the algorithm, or how to do the sort.
他们是相当棒的排序算法，是有更好的算法，我们下一次,就会看一个更好的，但是开始想想,如何完成算法，或者说是如何排序,是一个好的学习方法,恩，再试试吧,如何来排序呢？
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Well, we saw the teaser in terms of that animation that suggests this merge sort algorithm when implemented by a computer is absolutely faster.
我们从前面的动画中可以看到,这个归并排序算法在计算机上实现之后,绝对比其他算法更快。
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And probably the obvious thing you'll think about is, we'll come up with a clever algorithm. And I want to disabuse you of that notion.
可能你想到的最有效的方法,就是设计一个,聪明点的算法了,这正是我想你们注意到的。
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A really nice algorithm. As I said, an example of divide and conquer.
真的很好的一个算法，就如我说的。
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PROFESSOR: Great question. So the question is, how do you choose an algorithm, why would I choose to use a pseudo-polynomial algorithm when I don't know how big the solution is likely to be, I think that's one way to think about it.
教授：问得好，所以问题是，你怎样选择算法，为什么当我,不知道解决方案会有多大的时候,我要选伪多项式算法呢，我想这是一种思考问题的方式。
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We saw this with the sock algorithm a moment ago.
我们前面看到了袜子算法。
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Because the algorithm I proposed is going to leverage this idea of recursion which recall was just a piece of jargon we tossed out at the last-- at the end of last week's lecture, last time's lecture recursion really in this context refers to the act of a function calling it's self.
因为我提出的这种算法使用了,递归的思想，这是上周课程的最后,所提出的一个术语，上次的课程中，递归是指,函数的自我调用。
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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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Where have we implemented a greedy algorithm, or have been asked to do a greedy algorithm? Well, there are not that many things you guys have been working on this semester.
现在你已经实施了一个贪婪算法,我们在哪里实施了贪婪算法,或者我们那里被要求实施贪婪算法呢？,们这学期不需要用什么功对吧？
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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。
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And we can just extrapolate in a straight line We before saw some examples where I had an algorithm to generate points, and we fit a curve to it, used the curve to predict future points and discovered it was nowhere close.
我们可以干脆用一条直线来描述它,我们之前看到在一些例子中,我用一个算法去生成一些点，然后用一条曲线对它进行拟合，然后用这条曲线来预测未来的点,最后却发现结果完全不对。
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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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At the University of Minnesota, a computer algorithm paired people up.
在密尼苏达州立大学，通过计算机算法将同学分组。
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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。
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