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These things run for variable amounts of time because they take input, a list of size of some amount.
而这一段的执行时间是可变的,因为它们需要输入一个包含一些元素的列表。
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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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So, how many distinct, so again, we're talking about distinct kinetic energies, a spectrum for the element hafnium, 72 and I'll tell you here that it has a z of 72, so you don't have to spend two minutes searching your periodic table.
好，有多少分立的……还是一样，我们讨论的还是不同的动能，铪元素的光谱中出现，而且我来告诉大家铪的原子序数是，这样你就不用因为在元素周期表中找它,而花费两分钟的时间了。
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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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And so, I get some power. I get the ability to store arbitrary things, but what just happened to my complexity?
但是复杂度变了,找到第k个元素,要花多少时间呢？
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I've got to go to the first place, figure out how far over to skip, go to the next place, figure out how far over to skip, eventually I'll be out the door.
需要多长时间？,这太离谱了，因为我需要先去第一个元素,计算出下一个元素。
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I'm accessing a list. How long does it take for me to get the nth element of a list?
我取得数组的第N个元素,需要多长时间呢？
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With this, if I can assume that accessing the i'th element of a list is constant, then you can't see that the rest of that analysis looks just like the log analysis I did before, and each step, no matter which branch I'm taking, I'm cutting the problem down in half.
读取数组中的第i个元素,是个常量时间的操作的话，我也就能像以前那样得到,这个算法是对数级复杂度的分析,并且每一步不管我选择哪个区间，我都可以把问题的规模缩小一半。
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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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To get any location in memory, to get to any value of the list, I simply have to say which element do I want to get, I know that these things are stored in a particular size multiply that index by 4, add it to start, and then it's in a constant amount of time I can go to that location and get out the cell.
取得列表中的任何一个值,简单说来，想要取得列表中的任何元素,我知道这些元素存在特定的大小中,把下标乘以4，加到start上,然后定位到内存单元，并取出值就是固定的时间了,好的，如果元素以固定大小存储。
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