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Whereas in the linear case, I make it ten times bigger, it takes ten times longer to run. OK.
它要占用原来十倍的时间去运行，我一直在说还有一件事情没有讲，这是我要强调的最后一件事。
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I've got to do another pass. Huh. Sounds like a linear number of times I've got to do- oh fudge knuckle.
冒到最后去，还得再做冒泡,呵，听起来我要做线性次的时间-,哦，胡说八道。
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Remember, we don't do a one-to-one correlation, because p x and p y are some linear combination of the m plus 1 and m minus 1 orbital.
记住，我们不需要把它们一一对应，因为ｐｘ和ｐｙ轨道是,ｍ等于正负１轨道的线性组合。
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In particular, we're going to look at a particular version of this that we're going to call the linear city model.
我们来从一个特殊的角度看一下,我们称之为线性城市模型
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Further, the nucleus is assumed to be the seat of the essential part of the mass of the atom, and to have linear dimensions exceedingly small compared with the linear dimensions of the whole atom."
进一步的，核被认为是,原子主要质量所在的地方，和整个原子线性尺度相比,核具有很好的线性尺度“
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Something like this. That would be perfectly fine interpolation. All right, we choose to have a linear interpolation.
这种插值的方法也是完全可行的,好，现在我们决定使用，线性插值的方案。
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The force may taper off, the force may not be given by a straight line, but for modest deformations, every spring will have a linear regime in which the force is linearly proportional to the stretching.
它产生的力可能会渐渐消失,力的曲线可能不是一条直线,而有轻微的弯曲,每个弹簧都有一个线性区间,在这一区间内,力和伸长量是线性关系
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The Mycenaean kings we know, thanks to the Linear B tablets, were referred to, the singular once again is Wanax, and the plural is Wanaktes.
迈锡尼王正如我们,从B类线形刻板所知的,在古希腊语中被称为瓦纳克斯,复数是Wanaktes
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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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Linear algorithms tend to be things where, at one pass-through, you reduce the problem by a constant amount by one. If you reduce it by two, 1 it's going to be the same thing.
有问题么？,线性复杂度的算法，当进行了一个,常量级步数的操作的时候，将问题的规模缩小了一个。
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The power of linearity is F=k1+k2 if I come across f of x, y, z equals k1 plus k2, if it is a linear equation, I don't have to go and solve it all over again.
线性的威力是,一个方程，如果它是个线性方程，那么我就不用再去解他了。
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Because if you did what I suggested with the list, the time to look up the key would be linear in the length of the list. You'd have to look at each element until you found the key.
字典是用一种很神奇的，叫做散列法的算法,来实现的，后面我们将,会学到一点关于。
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So, we'll start by taking a look at constructive interference, and another way to explain this is just to say again, molecular orbitals are a linear combination of atomic orbitals.
我们先来看一看相长干涉，另外一个解释它的方法就是说，分子轨道是原子轨道的组合。
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The reference points are water freezing or boiling, and the interpolation is linear and then that morphed into the Kelvin scale as we're going to see later.
参考点是水的冰点和沸点,插值是线性的,随后它被发展成为开氏温标,我们之后会看到。
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Right? If that was the case in that code, then my complexity is no longer log, because I need linear access for each time I've got to go to the list, and it's going to Lisp be much worse than that.
这里的复杂度不再是对数的了，因为每次在列表中，查找需要线性访问,可能还要糟糕,其实，有些编程语言，如。
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If I'm running a linear algorithm, it'll take one microsecond to complete.
算法会在1微秒内完成，如果是一个平方级的方法。
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Now there many ways I can connect these two points together. The simplest way is to draw a straight line. It's called the linear interpolation. My line is not so straight, right here. You could do a different kind of line.
最简单的办法是,像这样画一条直线,这叫线性插值,不过我的这条线画得不太直，你也可以用别的办法,比如一条抛物线。
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And this is what they had expected that there would be no relationship, but instead here they saw that there was a linear relationship not to the intensity and the kinetic energy of the electrons, but to the intensity and the number of electrons.
另外一个实验,他们预期这两者没有关系,但他们看到的不是,光强和电子动能的,线性关系，而是光强,和电子数的线性关系。
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This has nothing to do with linear regression.
这跟线性回归没什么关系。
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How long does it take me to find the k'th element? Linear. Because I've got to walk my way down it. OK? So in this case, you have linear access. Oh fudge knuckle.
线性的！因为我得从头,向下走一步步走,所以这里是线性访问，哦，有问题了吧。
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Think about this compared to a linear search.
线性查找总是从开头开始遍历。
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Now this happens to be what we would call a linear process, because the number of times I go around the loop is directly related to the size of the argument. If I double 2 the argument, I'm going to double the number of times I go around the loop. If I increase it by five, 5 I'm going to increase by five the number of times I go around the loop.
这恰好是我们会成为,线性复杂度程序的一个例子,因为我要执行循环的次数是,和输入的参数的大小直接相关的,如果我将这个参数乘以,那么我就要将进行循环的次数也乘以2了，如果我把参数加上,那么循环的次数也要加上5了。
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That's it. Again, these other p dxy dyz - or the d x y, d y z, those are going to be those more complicated linear combinations, you don't need to worry about them.
同样，这些p轨道,或者，它们是一些,很复杂的线性组合，你们，不用管它。
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So this isn't-- OK. And you're also close. It's going to be linear but how many times do I go through this?
每次能丢掉一半，所以这里不是-,好的，但你也很接近了,他可能是线性的，但我得遍历多少次呢？
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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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You can choose a linear interpolation or quadratic, but you've got to choose it.
你可以选择线性插值或抛物线型插值,但你总要做出选择。
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We have to make sure that, in fact, that operation is not linear.
事实上，操作不是线性的，那让我来解释下这一点吧。
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Does it make sense to think we could do this in less than linear time? You know, it takes a little bit of thinking. What would it mean do I see a hand way at the back, yes please? Thank you.
你要稍微想一想，这意味着什么？,那儿是有人举手么？后面的,请你来回答吧,谢谢你，小伙子,你让我体会到我上课的价值。
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Again, we're going to take the linear combination of those p atomic orbitals and make what are called pi or some more sigma molecular orbitals.
同样的，我们需要得到,原子p轨道的线性组合,然后组成我们所说的,π分子轨道或者sigma分子轨道。
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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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