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And that's the kind of instinct I'd like you to get into thinking about. So the answer here is no.
所以答案是否定的,好的，那我们能在线性时间内排序么？
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What's shown in this diagram is the progress of the developing embryo as it travels in time, down the fallopian tube.
这张图上显示的,就是胚胎发育的过程,是按照它在输卵管中移动的时间排序的
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It at least does corroborate the claim that merge sort N*log N as we argue intuitively is in fact, N log N in running time.
但这至少证实了归并排序,的时间复杂度为。
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That one's not so obvious. So let's think about this for a second. To sort a list in linear time, would say, I have to look at each element in the list at most a constant number of times.
所以让我们来思考一会,要在线性时间能排序，列表里每个元素最多被使用常数次,不一定是一次，对吧。
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The Septuagint's rationale for ordering the books is temporal.
希腊译本是按时间顺序排序的。
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OK. Today, for the rest of the lecture, we're going to take a break from the topic of algorithms, and computation, and things of the sort. And do something pretty pragmatic.
好，今天剩下的时间里，我们不再讲算法，计算和排序这些话题了,我们会做一些非常实用的事,我们主要的讲讲测试。
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I just go down the list selecting the smallest person at a time and then I repeat, repeat, repeat but when we actually did out the math or kind of reason through it, the running time, the asymptotic running time of bub-- of Selection Sort was also what?
只需要遍历列表，每次找出最小的元素,然后重复上述步骤，但从数学角度看,选择排序的时间复杂度,又是多少呢？
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Like what the heck have we been spending our time for-- our time on with Bubble Sort and with Selection Sort and in fact there's plenty of other N squared sorts that we're not even gonna bother looking at.
真见鬼，我们竟然在-,冒泡排序和选择排序上花时间,而事实上，还有很多我们根本都不想考虑的,复杂度为N平方的排序方法。
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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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On the other hand, if I want to sort it first, OK, if I want to do sort and search, I want to sort it, it's going to take n log n time to sort it, and having done that, then I can search it in log n time.
我先排序，好的，如果我想排序再搜索，我要排序，这需要花n，log，n时间排序，然后做完了，我们能花log，n时间搜索,啊，哪一种更好呢？恩，呵呵。
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Once I have it sorted I can search it in log n time, but that's still isn't as good as just doing n. And this led to this idea of amortization, which is I need to not only factor in the cost, but how am I going to use it?
一旦对其完成排序,就可以在log，n的时间内对其完成搜索,但是这样做仍然不如n的复杂度,这样做引出了耗时分摊的想法,这时不仅需要考虑耗时的因素？
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And this was just a formal way of describing the best case running time and in the case of Selection Sort, what was the best case running time?
这是描述最好情况下运行时间的,一种正式的方式,在选择排序中，最理想的运行时间是多少呢？
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So supposed that I give you 16 elements to sort, well, following the logic before, the running time involved in sorting 16 elements is gonna be twice the running time 16 of sorting 8 elements, left half and right half plus 16 - and again, a little sanity check, 16 means-- just the merge steps, right?
现在要对16个元素进行排序，根据之前的逻辑，对16个元素排序,要花的时间是对8个元素排序所花时间的,2倍，分别用于左半部分和右半部分，再加上6,这里16是-,做合并的步数，对吗？
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If I'm using algorithm that I'm now calling merge sort, T the running time involved in sorting N elements, T of N, you know, is just the same as running the algorithm for the right half, plus what's this plus N come from?
如果我用归并排序算法，对N个元素其运行时间，就等于此算法一半元素的运行时间,另一半的运行时间，再加上N，这个N是什么呢？
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And then one of the things that I suggested was that if we could figure out some way to order it, and in particular, if we could order it in n log n time, and we still haven't done that, but if we could do that, then we said the complexity changed a little bit.
这就涉及到了排序,如果可以想出一种来将其进行排序,甚至可以在n，log，n的时间内完成,虽然目前我们没做这件事,但是一旦开始做这件事,那么复杂性就是发生一些变化。
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