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I've written a little for loop, which is going to iterate over all of the elements in the list.
让我们先看看这儿的代码，我已经写了一个循环语句,用来迭代处理数组中所有的元素。
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These are sort of the cells, if you like, in memory that are holding the elements of the list.
记忆就像是数组中的元素,我们之前说的是，我在这里开始并且比较。
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OK. So, soon as I get down to a list that has no more than two elements in it, I'm done.
不超过2个元素的列表，那就结束了,注意，这里是小于等于。
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And again, this points out something I wanted to me-- I mentioned last time, list can be heterogeneous, in the sense that the elements can be multiple different types.
这儿又指出了一点我想要告诉大家的,我上节课也提到了，就是数组是多相的,也就是说元素可以是多种类型的。
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Again. Basic premise of binary search, or at least we set it up was, imagine I have a sorted list of elements. We get, in a second, to how we're going to get them sorted, and I want to know, is a particular element in that list..
好，二分查找的基本前提，或者是我们建立二分查找的基础,我们已经有了一个排好序的元素列表，我们就需要知道如何来快速的排序,如何从列表中找到特定的元素。
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If I look for, say, minus 1, you might go, gee, wait a minute, if I was just doing linear search, I would've known right away that minus one wasn't in this list, because it's sorted and it's smaller than the first elements.
如果我要查找-1，你可能要怒了，呵呵，等一等，如果我用的是线性查找，我不会知道-1不在这个列表中,但是列表是排好序的,1又比第一个元素小。
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Hmm. Well, wait a minute. If I want to sort a list, I'll take one element, I've got to look at probably a lot of the other elements in the list in order to decide where it goes. And that suggests it's going to depend on how long the list is.
我会取一个元素，然后去查看列表,来决定要把那个元素放到哪里,这就意味着它依赖于列表的长度,对，这没什么说服力，但是事实上。
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It says, well I'm going to print out first and last just so you can see it, and then I say, gee 2 if last minus first is less than 2, that is, if there's no more than two elements left in the list, then I can just check those two elements and return the answer.
然后它计算了尾点和开始点的差,如果小于2的话,也就是说数组中的元素小于等于，我对这两个元素进行比较,然后返回结果就可以了，否则的话，我们就去寻找中值点，注意它是怎么实现的,首先这个指向一个列表的开头。
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For example, the number of elements in the list.
比方说链表中的元素个数。
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You try to design actually I'm going to come back to that in a second. It's like you're trying to use a hash function that spread things out pretty evenly. But the places you store into in those lists may have to themselves have a small list in there, and when you go to check something, you may have to do a linear search through the elements in that list.
你尝试着去设计,实际上过会儿我会回头讲解这个问题,类似于你需要用一个哈希函数,非常平均的将物体分发出去,但是在列表中你数据,映射到的地方可能会有自己的一小段列表，当你回头查找数据的时候,你可能需要在那一小段列表中做线性查找。
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b OK. In this example I'd use b. All right, as b get-- b is the thing that's changing as I go along here, but it could be things like, how many elements are there in a list if the input is a list, could be how many digits are there in a string if the input's a string, it could be the size of the integer as we go along. All right.?
好，在这个例子里我会用，因为b是一直在变的东西,但是也可能是如下情况：,如果输入是数组的话,变化的就是数组的元素数，如果输入是字符串的话,变化的就是字符串的长度，如果是integer的话,可能就是这个数的大小，对不对？
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