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If it was an unordered list, we were basically stuck with linear search. Got to walk through the whole list to see if the thing is there.
如果是一个未排序的列表,基本上我们就只能使用线性搜索了,通过遍历整个列表来查看。
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So when I do the analysis, I want to think about what am I doing here, am I capturing all the pieces of it? Here, the two variables that matter are what's the length of the list, and how many times I'm going to search it?
这里，要关注的,两个变量是列表,的长度以及我要搜索的次数,这种情况下，这个算法赢了？
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OK? So the example I'm going to do, I'm going to search a sorted list.
来搜索目标元素，好，翻到课堂材料的第二页。
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And typically, I'm not going to just search once in a list, I'm going to search multiple times.
还要考虑我要如何去使用它？,我不会对一个列表只做一次搜索。
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Let's search to see though now if a million is in this list, or 10 million, whichever way I did this it must be a million, right?
不管我选哪个，数都挺大的对不对？,用嘴基本的方法，噢，花的时间有点长,好，而用二分法呢？
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We actually threw half of the list away and we kept dividing it down, until ultimately we got something of size one to search.
我们实际上将另一半的列表给抛弃了,我们接着不断的如此分解下去,直接最终我们搜索到了唯一的一个元素。
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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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I remind you, I know you're not really listening to me, but that's OK. I reminded you at the beginning of the lecture, I said, let's assume we have a sorted list, and then let's go search it.
没关系，我告诉过你在课程的开始,我们假设这是一个排好序的列表,然后才进行的搜索,那实际上有序列表从哪里来的呢？
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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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Well let's see. My fall back is, I could just do linear search, walk down the list one at a time, just comparing those things. OK. So that's sort of my base. But what if I wanted, you know, how do I want to get to that sorted list? All right?
我只能做线性搜索了,一次遍历一遍列表，一个一个比较，但如果我想要,那怎样得到有序的列表呢？,现在的一个问题是，我们排序之前？
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In binary search-- ah, there's that wonderful phrase, this is called a version of binary search just like you saw bin-- or bi-section methods, - when we were doing numerical things- in binary search, I need to keep track of the starting point and the ending point of the list I'm looking at.
就是当我们处理数字的时候，所称的二分检索，在二分法搜索中,我需要记录区间的开始点和尾点，初始化的时候就是-,问题输入的开始点和尾点，当我开始做测试的时候,我想要做的就是去取中值点。
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And the example I want to look at is, suppose I want to search a list that I know is sorted, to see if an element's in the list.
看看目标元素在不在数组里，也就是说我要去,检索一个有序的数组。
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On the other hand, am I likely to only search a list once? Probably not. There are going to be multiple elements I'm going to be looking for, so that suggests that in fact, I want to amortize the cost.
我可能就搜索一次么？,可能不是，可能我要找好多个元素,这样的情况下,我们就能分摊开销了，这告诉我们什么？这意味着。
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All right? A linear search, I start at the beginning of the list and walk all the way through it. All right, if I'm lucky and it's at the low end, If it's not, if it's at the far end, I've got to go forever, and you saw that last time where this thing paused for a little while while it actually searched a list this big.
如果很幸运就在开头,那运行起来很快，如果是在末尾,那就一直得走到头，上次看到了,如果搜索空间很大,程序都会暂停一会,好的，那我希望你们。
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We're going to call binary search, it's going to take the list to search and the element, but it's also going to say, here's the first part of the list, and there's the last part of the list, Well, it checks to see, is it bigger than two?
我们将要调用这个二分查找,它将会在列表里面搜索元素，假定这里是，列表的第一个元素,那里是列表的最后一个元素，代码内部到底做了什么？
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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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I could still do the linear case, which is order n or I could say, look, take the list, let's sort it and then search it. But in that case we said well to sort it was going to take n log n time, assuming I can do that.
我仍然可以做O的线性搜索,或者也可以以这个列表为例，我们先将其进行排序,然后再进行查找，但是在这种情况下,要花费n，log，n的时间去对其进行排序。
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