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Come on, you know, representing sets of integers, this is pretty dumb. Suppose I want to have a set of characters. How could I do that?
你知道的，表示整数的集合,这好傻啊,假设我有一组字母的集合？
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Remember what range does, it gives me a set or a collection or a tuple of integers from 0 up to 1 - is the last value, so it's going to give me everything from 0 up to the total number of heads.
我将要在这个循环范围内加上鸡的数量,记住循环范围的目的,它给了我一个从一开始的整数集合,或者数组,这是最后的值。
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So, a couple of weeks ago we proposed to swap two integers, and we couldn't at the time.
那么，几周前，我们提出交换两个整数，然而在那时，我们办不到。
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So, for example, in this case, I had lists that I knew were made out of integers.
那么，比如在这个例子里，我有一个我知道。
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In the case of integers it was easy.
情况非常简单，在字符的例子中。
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So, for example: in this case, my list is a bunch of integers. And one of the things I could take advantage of, is I'm only going to need a finite amount of space to represent an integer.
列表是一系列整数,要注意的这里的优势能够,用有限的空间来表示整数,例如，如果我想要操作。
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The answer is I can't. OK, in the simple case of integers I can, but in the case of something more complex like faces or fingerprints or passwords for that matter, it's hard to design a hash function that has completely even distribution, meaning that it takes any input into exactly one output spot.
答案是我不能，好吧,在简单的整数的例子中,我可以做到，但是在一些更复杂的场景中,比如面部，指纹，密码相关的问题中，很难设计一个哈希函数具备完全平均的分配,也就是说，做到对任一输入，可以准确地得到相应的唯一输出,因此在一个哈希问题中。
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And in fact, now let me ask those two questions about this piece of code. First question is, for what values of integers-- we're going to assume integers-- but for what values of x does this code terminate? And the second question is, for what values of x does it give me back the right answer?
实际上，让我关于这块代码问两个问题,第一个问题是，对于什么样的整数值，我们会假设是整数,对于x的什么值程序,会最终终止？第二个问题是,对于x的什么值程序,会返回正确答案？
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So the integers are totally ordered the reals are totally ordered lots of things are, the rationals are totally ordered.
对正数来说,这样的序列是排好序的,对实数也是如此,对很多事情都是如此。
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So we've seen one example of this, this idea of walking through all the integers looking for the square root.
现在计算机速度很快了，我可以把这个数字设的更大点,计算机会去很快的做这个事情。
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I think one of the classic ones for strings is called the Rabin-Karp algorithm. And it's simply the same idea that you have a mapping from your import into a set of integers.
我认为字符串哈希,最经典的是Rabin-Karp算法,它只是简单的相同概念,你有一个映射关系将你的输入映射成一组数字。
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Well the idea of a hash, in fact, what's called a hash function is to have some way of mapping any kind of data into integers.
我要怎么做？实际上想法还是哈希,通过一个哈希函数,把任何种类的数据都映射成整数。
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OK. And I'm going to look to see, is a particular element inside of that list, and again, I'll remind you, that's just giving me the integers from zero up to 9999 something or other.
一个又大又长的列表吧，好的,我打算查找列表中的一个特定元素，我会告诉你，我用的是0到大概是,9999左右的整数。
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As you see here, some of the elements are strings and some of the elements are integers.
你也看到了，这儿的一些元素,是字符串一些元素是integer类型。
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All right. I want to return to some non-scalar types. So we've been looking, the last couple of lectures, at floating pointing numbers and integers.
好，我们现在回到一些,非基本类型的话题来，我们在过去的几节课里,一直在研究浮点数类型和integer类型。
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And keep going, until the square of one of those integers is greater than or equal to - sorry, just greater than x. OK, why am I doing that? When I get greater than x, I've gone past the place where I want to be.
如果还是比x小的话，跳到3，这么继续下去,直到一个整数的平方大于或者等于,对不起，是大于x，好,为什么我要这么做呢？,让我得到的整数的平方和。
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Now I'm putting count in double quotes, not to make it a string, but to say, this is count generically. It could be counting one by one through the integers, it could also be taking a collection of data and going through them one by one. It could be doing counting in some other mechanism.
现在我把count用双引号标起来，不是说把它命名为一个字符串，而是说，这是一个通用的计数器,它可能是每一次减1的整数,也可能是拿一个集合的数据然后,一个一个的访问它们,也可能是以某种机制来计数。
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First of all, two parameters. It's OK. All it says is, when I call this, I need to pass in two parameters for this to work. All right? Now, if I want to use that, I'm going to use a second piece of code here, called Barnyard. I'm going Barnyard to read in a couple of values, convert them into integers, and then I'm going to use solve to get a solution out.
注意我得到了什么,第一，两个参数,它的意思就是我调用这个函数，我得给它输入两个参数，明白了吗？,现在如果我要使用它我得用,这里的第二段代码，也叫,我将读入一组值，将它们转化为整型,然后我会用solve得到一个解决方案。
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