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And so, if you rewind the tape and play it again over and over and over again, each time you set things up the very same way they must move or transform or change or end up in the very same state.
所以,如果你将一盘磁带,反反复复地播放,每次你播放的内容,从头到尾的起承转合一定是,绝对一致的
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You really can take in everything single at a time, you can really pay attention to each piece.
你真的能够一次专注于一个作品，并理解它。
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So, the curious thing about recursion is that pretty much always can you implement this idea of doing the same thing again and again and again but with smaller bytes each time.
可见，递归算法中新奇的一点是,为了实现一个想法,你可以一遍又一遍地做相同的事情,但每次的规模都会有所减小。
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You can make multiple--you can put three or four-- the copy gets worse and worse each time, but you've got multiple copies.
你也可以复写多份，放上三四张复写纸-,不过越往下复印的效果会越差，但终归你还是有了多份副本。
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I've got a list, walk you through it an element at a time, do I look at each element of the list more than once?
你一次只能得到他的一个元素,我是不是把数组里面的每个元素，都过了大于等于一次？,你不这样认为么？大家有什么建议？
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And you do your work product and you bring it to sections and hand it in to your TA in section each time.
请完成并带好你们的作业,并在每次上课时交给你们的助教
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And each time one of these errors occurs, or you get multiple errors that compound each other, then you've got a lot of potential error introduced in these messages.
每当有误差发生,或多重误差复合叠加,然后你所得到的信息,就会包含很多潜在的误差
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This is often the way relationships start "We like each other, I'm physically attracted to each other, I-- to you, I enjoy spending time with you but I'm not making any long-term commitments.
爱情经常以这种形式开场,我们喜欢对方，享受肌肤之亲-,享受一起度过的时光,但不做长远的承诺。
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And this a time in the company where you just have to aspire with each hire to get an A rate plus person and it's easier said than done.
也就是说，在这个时代,招聘的标准就应该定为,招聘A或者A+的人,不过说起来容易做起来难。
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This time, you're a transplant surgeon and you have five patients, each in desperate need of an organ transplant in order to survive.
这次你是一名器官移植医生，你有五名病人，每名病人都急需器官移植才能存活。
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Each one of you will have a single time.
你们每一个人都将有单独的时间。
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We played a game at the very end last time, where each of you chose a number - all of you chose a number - and we said the winner was going to be the person who gets closest to two-thirds of the average in the class.
我们在上节课最后做了一个游戏,你们每个人都选了一个数字,你们所有的人都选择了一个数字,选择的数字最接近全班,平均数的三分之二的人就是赢家
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Here's another picture of it here, showing it in a little bit more detail, that you have lots of DNA in each of the cells in your body but you're not using all that DNA at any one time.
这里有一张更加详细的图片,来说明这一点,人体内每个细胞中都含有大量DNA,但并不是所有的DNA都会同时发挥作用
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Because I'm cutting down the problem in half at each time. You're right, but there's something we have to do to add to that, and that's the last thing I want to pick up on.
但是我们还需要强调一点,这是我最后想讲的一点,让我们来看看代码-实际上，让我们先来测试测试吧。
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Now, we probably could have improved the accuracy if we had spent individual time with each of you and said, well now here's a serving of this and that's -here's a serving of that.
现在,我们大概可以提高准确性了,如果我们在你们每个人身上花些时间,并告诉你们这有一份这个,这有一份那个
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OK. You can see that thing is cutting down the problem in half each time, which is good, but there's one more thing I need to deal with.
这很棒，但是我们还需要处理另外一件事情,让我们仔细来看看,我在开始做之前一直在说，应该先试验试验。
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And you can see it wrapping its way down, cutting in half at each time until it gets there, but it takes a while to find. All right.
但是这也花了一点时间来搜索，好，让我们看看100万，或者1000万是不是在数组里。
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Last time we worked through this idea of the scale and how you can build triads on each of the members of the scale.
上节课我们已经讨论过音阶中的这个概念,以及你们怎样才能在音阶的各个音上组建起三和弦。
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You want to write the specs so that everybody does in fact know what this piece of code is doing, and you're writing it each time around.
但是你得养成良好的习惯和编程风格,你得撰写规范说明从而保证,每个人都知道这段代码是干什么的。
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I just doubled the indentation each time so you can see it. So each successive call, notice what's happening. The argument is getting reduced. And we're going another level in. When we get down to this point, we're calling it with just a string of length one.
因此每次成功调用注意它的过程,我们的命题不断简化，而且我们不断深入嵌套,当我们走到这一步的时候,我们就是在调用它处理，仅有一个元素的字符串了。
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