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And I don't know why, but since time immemorial that is the way computer scientists have drawn trees.
叶子是在最下面的，我不知道为什么,但从记事以来他们就是这么画树的,这也许就是为什么我们。
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Our next pattern is one of my favorites. It's the "I think" pattern.
下面一个是我最喜欢的句型之一，那就是“I think”句型。
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where one person is, in a sense, ] seeing another without being seen.] She was starting down, Looking back over her shoulder at some fear.
某种意义上来说，这就是一个人看着，另一个，不被看到的时候],她想下来，转过头惊恐地望着下面。
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And I'll also remind you, and we're going to see this in the next example, we talked about looking at the worst case behavior. In these cases there's no best case worst case, it's just doing one computation.
我还要提醒大家的就是，我们也会在下一个例子里发现者一点，我们谈到了要去考虑最坏的情况,在下面这些例子里,没有好情况坏情况之分，就只是一次运算。
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So that's where it's easy to get lost, but let's see if these lines in the picture help us stay on track.
这就是容易迷惑的地方，下面看看,这幅图中的这些线能否帮助我们追踪。
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So, this is first ionization energy, let's think about second ionization energy.
那么，这就是第一电离能，下面让我们来想一想第二电离能。
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Well, Plato's very next argument attempts to persuade us that indeed we do have reason to believe that the soul is one of the prior-existing pieces.
柏拉图下面一个论证就试着,说服我们有理由相信,灵魂原来就是存在的
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Here is the power of linearity.
下面就是线性的威力。
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They're called flats if they're down below.
如果在下面,它们就是降调
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And here's why.
下面就是原因。
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And I want to show you one more example of that, in the scene where Humbert and Lolita have reached the hotel, the Enchanted Hunter. This is on page 118 near the bottom.
我想再举一个例子，就是亨伯特和洛丽塔,到达Enchanted，Hunter，饭店的那场，这在118页下面。
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This has been one of the major reasons for explaining the function of the phalanx as I will explain it to you.
而我下面所要解释的方阵的作用,也就是问题的答案
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pV=RT p plus a over v bar squared times v bar minus b equals r t. All right if you take a equal to zero, these are the two parameters, a and b. If you take those two equal to zero you have p v is equal to r t.
我们就回到,也就是理想气体,状态方程,下面我们来看看,这个方程。
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One other remark before we leave this, in the game we played last time, in the investment game, one feature of that game was that the more you thought other people were going to invest, the more you wanted to invest.
在继续讲下面的内容前,我再多说几句,上一讲的投资博弈有一个特征,就是如果你越认为大家会投资,你就越想投资
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Merge sort takes this idea of divide and conquer, and it does the following: it says let's divide the list in half.
归并排序以如下的步骤使用了分治思想：,把列表分成两半：,下面就是分治。
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Let's move on to the last topic in terms of this first exam, which is thinking about the idea of isoelectronic atoms, or isoelectronic ions. And isoelectronic is very straightforward, it just means having the same electron configuration.
下面我们继续讲第一次考试的最后一个主题，也就是等电子原子，或等电子离子的概念，“等电子的“是非常直接的表达，它的意思就是具有相同电子排布的。
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When I ran it up here, with the old Fib, and we printed the result, and I ran it with Fib 1 down here.
当我运行到这里，也就是老的Fib函数，我们打印这个结果，当我在下面调用Fib1时,也打印了结果。
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And it's called divide and conquer for the obvious reason. I'm going to divide it up into sub-problems with the hope that those sub-problems get easier. It's going to be easier to conquer if you like, and then I'm going to merge them back. Now, in the binary search case, in some sense, this is a little bit trivial.
因此被称为分治的原因就这么简单,将一个问题分解成一些子问题,并希望这些子问题解决起来比较方便,正如你希望的，求解的过程也会变得简单,下面就是把结果合并起来,现在，在二分搜索的例子里,从某些方面来说，这有点微不足道。
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But notice what this does. The first thing it does is, it says, let's check and make sure x is greater than or equal to 0. If it isn't, notice what's going to happen. None of that block is going to get executed, and it's going to come down here and print out a useful piece of information, which says, hey, you gave me a negative number. I don't know how to do this.
做的是和以前一样的事情,但是注释它做了什么，第一件做的事情就是,程序说，要去检查并且确信x是大于等于0的，如果不是的话，请注意会发生什么,下面的代码都不会被执行,程序会到这里来然后显示一些有用的信息,信息会说，嘿，你给了我一个负数,我不知道该怎么弄这个了。
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So, this raises kind of an interesting question in terms of what the difference is between these two cases, and we're talking about numbers of energy.
那么，到这里就出现了一个很有意思的问题,那就是下面这两种情况的区别在哪里？,当然我们关心的是能量的多少。
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If I want to try and decide how to tackle a problem in an iterative matter, here the steps I'm going to go through. First thing I'm going to do, is I'm going to choose a variable that's going to count.
但是这就是我对它的观点,如果我试着去以迭代的方式,解决一个问题的话,下面是我应该采取的步骤,第一件要做的事情。
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Rhythm is simply these patterns, usually repeating patterns, of longs and short that get superimposed as they set up above the basic beat underneath.
节奏就是一些长短模式,通常是反复出现的,与下面的基本节拍叠加在一起
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And that gets me to the final question.
下面就是最后一个问题了。
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It's going to add the other pieces in.
下面要做的就是把其它的添加进去。
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Yeah, this is not a bad time for me to remind you that in one of Plato's dialogues, Socrates says the Greeks sit like frogs around a pond and that pond is the Aegean Sea.
下面引用一下,柏拉图记录的一段对话,苏格拉底说希腊地形,就像一群青蛙围着一个池塘,而那池塘就是爱琴海
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