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Each test comes in advance with a prep sheet telling you how to get ready for that particular test.
每次测试前都会给你们考点,那里面会告诉你如何备考
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Every time we go for dinner, you're always talking while you're chewing.
每次我们出去吃饭，你总是一边咀嚼着满嘴的食物，一边不停说话。
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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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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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Every time you are finding out a different force that's acting on a body with different origin.
每次你都会发现不同来源的力,作用在物体上
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Well, for the answer to that we have to go back to ancient Greek music theory, and when you read about this--it's really turgid stuff-- but believe it or not, I teach a course on this at the graduate level.
这个,要回答那个问题,恐怕要追溯到古希腊的音乐理论,每次读这些都会云山雾罩的,不管你信不信,我曾在研究生中开过这个课程
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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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if you don't want to use that, you can also derive it as we did every time, it should intuitively make sense how we got there. But the exams are pretty short, so we don't want you doing that every time, so we'll save the 2 minutes and give you the equations directly, but it's still important to know how to use them.
吸收的和发射的，如果你不想用公式,你也可以每次都向我们这样推导它,很直观的就能得到结果，但考试时间很短，我们不希望你们每次都推导,所以我们会直告诉你，让你节省2分钟，但知道如何应用它十分重要。
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If you go to the dining hall you know, the portions-- one person serves themselves this much of a food and another serves themselves another, and then when you go to a restaurant there are variations on how much you get served of things, and so it's very hard to estimate portions for people.
如果你去食堂,摄入量是指,一个人吃了自己的那部分食物,或其他人吃的他们的那一部分,当你去餐厅,每次吃多少是变化的,因此估算每个人的摄入量是很难的
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Well, if you're youngster and every time you see a problem,
嗯，如果你小的时候，每次一看到难题，
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If you start with only one, you have two pieces of DNA, then you'll get 2 to the Nth fragments after N cycles because each cycle you're doubling the number.
如果你从仅仅一个DNA开始,你有两条DNA链,经过N次循环后,就得到二的N次方个DNA片段,因为每次循环都使其数量翻倍
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But you don't want to have to run it a long time, every time you have a hypothesis.
但是你不必每次有一个假设，都要去运行很长时间。
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Anyone? How many times can you tear a 4 billion page phone book in half?
谁知道？,40亿页纸每次对半撕，你能撕多少次？
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If you'd like to sit down with one of us more intimately and more sort of tranquilly, and work through problems for more than just a couple minutes at a time.
如果你希望和我们其中一个人坐下来，更亲密的,更平静的，每次用几分钟的时间,来解决问题。
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Again, if you didn't hear it, the answer was it's log.
因为每次我可以把这个问题的规模，缩小一半，你答对了。
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We don't always want to go and solve the Schrodinger equation, and in fact, once we start talking about molecules, I can imagine none of you, as much as you love math or physics, want to be trying to solve this Schrodinger equation in that case either. So, what Lewis structures allow us to do is over 90% of the time be correct in terms of figuring out what the electron configuration is.
我们并不想每次都去解薛定谔方程，而且实际上，一旦我们开始讨论分子，我可以想象,你们中没有一个人，不管你有多么热爱数学或物理，会想去解这种情况下的薛定谔方程,总之，路易斯结构能让我们,有超过，90%，的概率判断出正确的,电子排布。
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Not to harp on the mathematical features of this, but cubing, AX*X*X you know, if you're starting to do AX star, X star, X, every time you want to cube some value in a program, it just feels like this is going to get a little messy looking, if nothing else.
不要总是说这个的数学特性，但是体积，你们懂的，如果你开始做，在一个程序中，每次你想算几个数值的体积，感觉它就变得,有一点凌乱的，如果没有其他的。
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The standard library, that first line of code, it's not strictly necessary but any time you use a function, a tool that someone else wrote that lives in that so called library, you do need that include line as we'll see.
标准库函数--第一行代码，严格来说，不是每次都要写的，但是一旦你调用某个别人写，的函数，而这个函数又恰巧位于标准库里面,你就要像我们看到的这样，把它include进去。
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But for now, it's probably simpler just always use the curly braces just to get into the habit.
但是现在，简单起见，你可以,养成每次都使用花括号的习惯。
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You won't always draw out every single possibility that you have to start with.
你都可以这样做,大家并不需要每次都把所有可能的结构都写出来。
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The printout is simply telling me, what are the ranges of the search.
你可以看到这个方法每次都将，原问题的规模缩小了一半。
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Every time you see a square bracket, put a paren in. All right?
每次你看到一个方括弧，你就得在此添加一个圆括弧，明白了吗？
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> So now that might not have felt like the fastest algorithm but think about what you could have done with that algorithm in each iteration, much like the phonebook up front here, you literally split that problem in two because on each iteration roughly half of you were sitting down and then another half and then another half.
虽然这并不是最快的算法,但如果把这种算法每次迭代,就像刚才查电话簿一样，你便将这个问题一分为二了,因为每一次迭代后只有一半坐下来,以此类推。
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So, certainly the CS50 Library designed to be dynamic and, in fact, any time you call get string, we are, in fact, ; allocating a chunk of RAM but it's not coming from the stack; it's actually coming from this portion of memory called the heap.
所以，Cs50库是动态设计的，实际上，每次你调用GetSting时，我们分配一块内存，但它不是来自栈;,而是来自于叫做堆的,内存的一部分。
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