-
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。
-
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。
-
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
-
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。
-
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。
-
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。
-
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。
-
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。
-
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？
-
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。
-
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。
-
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。
-
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。
-
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？
-
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。
-
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。
-
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。
-
OK. Binary search is perhaps the simplest of the divide and conquer algorithms, and what does that mean? It says, in order to solve a problem, cut it down to a smaller problem and try and solve that one.
好了，二分搜索也许是,最简单的分治算法，这意味着什么？,也就是说，为了解决一个问题,把它切割成小的问题,然后再来一个个解决。
-
Now you might say, wait a minute. Thing's ordered, if I stop part way through and I throw away half the list, doesn't that help me? And the answer is yes, but it doesn't change the complexity.
如果我在半路上停下来,然后不去遍历剩下的数组了,这会有帮助么？答案是有帮助，但这没法改变算法的复杂度，因为我们之前怎么说来着？
-
And then we're going to turn to the question of efficiency. How do we measure efficiency of algorithms? Which is going to be a really important thing that we want to deal with, and we'll start it today, it's undoubtedly going to take us a couple more lectures to finish it off.
然后我们会回头继续讨论效率问题,我们如何计算算法的效率？,我们处理这些问题的时候,最重要的事情是什么？,我们今天要去讨论这个问题，毫无疑问我们要用,挺多节课来学习这个。
-
All right, having said that, let's do some examples. I'm going to show you a sequence of algorithms, they're mostly simple algorithms, that's OK.
好，让我们开始看例子吧,我将会给大家讲,一系列的算法，这些都是挺简单的算法。
-
Alright, so we can implement any number of algorithms using this thing because the basic mechanism I have here is a comparator.
好了，利用它我们可以实现,很多种算法,因为在此我用到的基本原理是一个比较器。
-
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。
-
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。
-
What you're much better at doing is saying how do I take the problem I've got and map it into a class of algorithms about which I know and use the efficiencies of those to try and figure out how to make it work.
当你碰到问题的时候,更好的方法是把遇到的问题映射,到已经设计好的算法中去,并用这些算法来提高效率,来保证问题得到解决。
-
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。
-
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？
-
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。
-
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。
应用推荐