But that's also nice, it lets you see how the recursive thing is simply unwrapping but the complexity in terms of the amount of time it takes is going to be the same.
它让我们看到了,在复杂度依照时间总数来看,没有变化的情况下,递归是怎么一步步的展开的,我欠你一个糖,谢谢。
Be careful, and this is going to be especially complicated and confusing when we get to quantities that have a more obscure meaning like entropy.
大家要小心,如果需要测量的物理量,如熵,没有很明确的意义,那么着可能变得很复杂。
There is now no preference--well it could be-- there are lots of complexities in the tax law but, basically, dividend policy really is irrelevant now.
这就没有偏好差别了,税法中仍有很多复杂条款,但基本说来,是否推行股利政策与此无关
So you can hear, the triplet being inserted, so a triplet is simply insertion of three notes in the place of two, not more complicated than that.
大家听到,插入了三连音,三连音只是简单地,在原来两个音符的位置上换成三个音,没有更复杂的概念了
Now we can think about the fourth period, and the fourth period is where we start to run into some exceptions, so this is where things get a teeny bit more complicated, but you just need to remember the exceptions and then you should be OK, no matter what you're asked to write.
现在我们可以考虑第四周期,而且在第四周期,我们会遇上一些特例,所以事情有,一点复杂,但是你只需要记住,这些特例然后就没有问题了,无论你被要求写什么。
Although I don't quite understand--I should say, there's many things about how the fighting went on which we can only attempt to imagine because we just don't have films of ancient hoplite battles, I'm sorry to say.
虽然我有时也很困惑,比如说,战场上瞬息万变,情况非常复杂,由于没有古代重步兵白刃战的影像资料,我们只能猜想战场上发生了什么,真的是很遗憾
We'll talk about how your normal valves function inside your heart and how your heart couldn't work in the way that it did if it didn't have valves that were doing a very complex operation many many times a day.
我们会讨论,正常的瓣膜在心脏中如何工作,以及没有这个,每天不停完成很多复杂任务的心脏瓣膜,心脏为什么,就不能正常工作了
And that's just a way of reminding you that we want to think carefully, but what are the things we're trying to measure when we talk about complexity here? It's both the size of the thing and how often are we going to use it? And there are some trade offs, but I still haven't said how I'm going to get an n log n sorting algorithm, and that's what I want to do today.
这只是在提醒你们我们要仔细的思考问题,但是当我们在讨论复杂性的时候,我们到底要衡量哪些东西?,是列表的大小和对其进行查找的频率吗?,这里面临一些取舍,但是我还没有说明,怎样得到一个n,log,n复杂度的排序算法,并且这是我今天想要讲的内容。
The brain perceives all of this complex information and it processes it and it extrapolates from it the beat, but again nobody in music-- except the bass drum player in a marching band-- nobody in music ever does anything except just play the beat.
我们的大脑感知了所有复杂的信息加工后,推算出了拍子,不过没有人,除了军乐队的低音鼓手,没有人在音乐里仅仅只是打鼓点
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