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What do you think? Even with these glasses on, I can see no hands up, any suggestions? Somebody help me out.
戴着眼镜我也能看出来没人举手，有想法么？大家来帮帮我吧，你们对这个算法的增长率是怎么认为的？
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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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The idea behind all these algorithms is that what's ultimately important is how many comparisons you ultimately need to make.
这些算法的思想是,你最终需要做多少次的比较,这才是真正重要的。
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So don't get too caught up in understanding the methods or statistics in a particular study or anything like that.
所以没必要过于纠结,非要去理解,某项研究的分析和算法
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Therefore, for simple branching programs, the length of time, the complexity the code, is what we would call constant.
因此，对于简单的分支程序，运行的时间长度，算法的复杂度，也就是我们说的常数。
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And so the fact that in this whole slide here, this algorithm for sorting, I'm using the verb sort.
在这个排序算法中,我用到了一个动词排序。
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And you can look at it, and let's in fact take a look at it to see what it does.
你们看一看那个算法,看看到底它做了什么。
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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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And the obvious question I could start with is, and suppose I ask you, how long does the algorithm implemented by this program take to run?
我开始这个话题的第一个问题是，假设我问你，由这个算法实现的程序大概,要运行多久才能给出答案？
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So now that we begin to have this ability to express strings in memory, to understand what they are, we can start to apply actually real-world algorithms to them.
现在我们开始用这个技能来在内存中表达字符串,来理解它们是什么，我们可以开始,我们可以对其使用实际的，现实生活中的算法。
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But if it watches you over some amount of time just like it's been for years with advertisements, can this kind of algorithm, this kind of process presumably improve?
但是如果它像关注广告一样,花费一些时间关注你，这些算法和进程，想必会提升吧？
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It's 33, 32, it's only 32 times and you can check that math at home but here lies the power of algorithmic thinking, of computational thinking as they say.
你需要33，32，对，32次,你也可以在家里自己计算，但数学算法的力量是无穷的，这就是科学家们所谓的计算机思维。
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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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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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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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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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And then the things I have to ask is how much of a division do I want to do?
如果可以这么做，那么分治算法是个好的选择,接下的问题就是我需要把问题分成多少份？
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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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It's a problem, as you'll see, designed to give you some practice at dealing with some of the, dare I say, more theoretical concepts we've covered in class.
这种问题会让你在处理我们,课堂上并没有讲到的更多,理论概念这方面上有更多实践,这种问题就像算法复杂度一样。
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So as you can see, as we escalate the problem difficulty, the difference between the good method and the not quite as good method gets bigger and bigger and bigger.
如你所见，当我们处理更复杂的,问题的时候，优良的算法,和并不那么好的算法之间的,差异会变的越来越大，这一点很重要。
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So in fact, over the next thirty or forty minutes we're going to show you a set of examples of sort of canonical algorithms, and the different classes of complexity.
在接下来的三四十分钟里面,我们将要讲一系列的,权威算法，以及不同种类的复杂度问题。
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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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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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And I'll remind you, we saw a set of algorithms and part of my goal was to get you to begin to recognize characteristics of algorithms that map into a particular class.
我要提醒你们的是，我们看了很多算法,我的目标之一是让你们开始,意识到算法们的特性,并且能够一一映射到特定的分类中。
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So, the curious thing about recursion is that pretty much always can you implement this idea of doing the same thing again and again and again but with smaller bytes each time.
可见，递归算法中新奇的一点是,为了实现一个想法,你可以一遍又一遍地做相同的事情,但每次的规模都会有所减小。
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Just contrast this for a brief moment to something like Selection Sort which from the get go had a ridiculous amount of redundancy comparing the same damn numbers again and again, and again.
这就与其他的排序算法形成了鲜明的对比,比如选择排序,它会一次又一次地做,多余的比较。
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One of the things we want to help you do is identify the different classes of algorithms, what their costs are, and how you can map problems into the most efficient class to do the computation.
我们想要教会你们的事情之一就是,学会辨别不同种类的算法，它们的代价是怎么样的，以及怎么样把问题映射到,最有效的算法种类中去做计算。
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Usually what I want to talk about is what's the smallest size class in which this function grows? With all of that, what that says b is that this we would write is order b.
通常我们想要的是,方法增长时最贴切的描述,也就是说，在这个问题上,算法关于。
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Because if you did what I suggested with the list, the time to look up the key would be linear in the length of the list. You'd have to look at each element until you found the key.
字典是用一种很神奇的，叫做散列法的算法,来实现的，后面我们将,会学到一点关于。
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