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Don't be intimidated. Even though it is apparently exponential, a lot of times you can actually solve it much, much faster.
别怕，即使它,很明显是指数型的，很多时候,你都能更快的解决它。
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And so when we say something is exponential, we're talking about in terms of the number of bits required to represent it.
所以当我们说某些东西，是指数增长的我们指的,就是代表它的比特数。
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So let's understand: what is the nature of exponential function so that we can understand the power of one?
让我们先理解指数函数的本质,以便理解“一“的力量？
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He said that is going to equal one minus the exponential.
一根共价键中,离子百分数等于。
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This is an example of an exponential growth process and you're familiar with processes like these.
这是一个指数增长的过程,你们应该都很熟悉的
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And in fact, if you look at the top figure it looks as exponential or, quadratic isn't even growing at all.
它看上去是指数型的,而幂次型的看上去,根本没有增长。
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And I won't go through it, but what you can see is it's more or less, it is in fact, exponential.
我不想全讲一遍,但是你们可以看到。
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So if you think about the way something like, say, Mapquest works, and last week in recitation you looked at the fact that shortest path is exponential.
所以如果你想想电子地图，还有上周学的列举法,你就会发现一般最简单的方法,都是指数递增的。
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Or just have the good intentions without the effort that's necessary to bring about a positive exponential function.
还是只有好的意图但不付出,必要的努力发挥正面指数函数的作用。
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And what we want to do then, is we want to basically come up with, how do we characterize the growth-- God bless you-- of this problem in terms of this Quadra-- sorry, terms of this exponential growth.
现在我们想要做的就是,我们怎么来量化增长率呢？,在这个问题中也,就是框架-对不起是，输入指数的增长。
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We have seen log, linear, quadratic, and exponential.
平方级的和指数级复杂度的方法，再说一遍，可能会有些常量。
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There's a tendency for people to say, oh this problem's exponential, I can't solve it.
人们往往会说，哦这是个指数型的问题我没法解决它。
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Well, I solve 2 or 3 exponential problems before breakfast every day. You know things like, how to find my way to the bathroom is inherently exponential, but I manage to solve it anyway.
你要知道如何找到,我的浴室就是一个，固有的指数型问题,但是我还是能解决它。
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Because in "Pay it Forward", they capture this very idea of human networks as exponential functions.
电影“让爱传出去，深刻地描述了,人类网络是指数函数的观点。
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So I haven't done magic, I've given you a really fast way to solve a knapsack problem, but it's still exponential deep down in its heart, in something.
所以我并没有施魔法，我已经告诉了你,一种快速解决背包问题的方法了,但是某些方面它的核心仍然是指数增长的。
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And you really, wherever possible, want to avoid that exponential algorithm, because that's really deadly. Yes.
比你的电脑的性能增长的快多了，并且大家无论何时，都要避免去用指数级的函数。
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And finally, we saw an example of an exponential algorithm, those Towers of Hanoi.
最后，我们来看一个,指数算法的例子，汉诺依塔的例子。
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Again, misleading-- fail to understand it because we don't understand the nature of exponential change.
再一次，误导…,没有理解指数函数，因为我们不理解,指数变化的本质。
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On Thursday we'll do a more careful analysis and try and understand how I could have accomplished this seemingly magical task of solving an exponential problem so really quickly.
在周四的时候,我们会做进一步的分析,并且尝试理解我为什么,能如此快速的解决这种,看上去超复杂的指数型问题。
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For most people, it seems extraordinary because people don' understand the nature of exponential function and therefore don't understand the nature of the power of one.
很多人会觉得不可思议,因为他们不懂指数函数的本质,也不懂“一“的力量。
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And if I'm running an exponential algorithm, any guesses?
杂度是指数级的呢？,有人猜猜么？
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You see how really fast exponential growth is?
你看到指数增长有多恐怖了吧？
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We don't like exponential algorithms, or at least you shouldn't like them, because they blow up quickly. And we saw some examples of that. And unfortunately, some problems are inherently exponential, you're sort of stuck with that, and then you just have to try be as clever as you can.
我们并不喜欢指数算法，至少你不应该喜欢，因为他们会,爆炸式的增长，我们将看到,这样的例子，不幸的是，一些问题先天是指数型的，你会被它们稍稍的卡住,然后你就得尽可能的发挥你聪明才智了。
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To illustrate the exponential nature of human networks, let's look at smiles.
为了说明人类网络的指数本质，我们来以笑为例。
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One of the interesting properties of cells that are in exponential growth is that the time to increase the cell number by a factor of 2 is always the same.
细胞有一个有趣的性质,那就是在指数增长阶段,细胞增长的速度,永远是以二为底数来增长的
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We also looked at exponential.
我们还看了指数分布。
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Because we underestimate the growth of exponential function.
因为我们低估了指数函数的增长。
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Log? Linear? Exponential? Quadratic?
对数？线性？指数？平方？
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We've seen log, we've seen linear, we've seen quadratic, we've seen exponential.
我们看过了对数级的，线性的，二次平方的，指数级的算法。
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This is one of these properties of this kind of exponential growth.
这就是这种,指数增长问题的特性。
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