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
I am on the internet, probably every time I mark,
我上网的时候,几乎每次都会标记清楚,
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。
And I want to remind you, that block of code is a set of instructions, the same set of instructions that are going to be done each time through the loop.
我想提醒大家,这块代码是一个指令集,一个每次循环都会被执行的相同指令集,会变化的仅仅是变量的值。
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
Every time I drive the steering wheel of my car, I rub off some items. But that's OK, it's still the very same physical object.
每次我使用方向盘时,都会摩擦掉一些微粒,但没关系,它还是原来那个物体。
With each lecture we put together pre-lecture questions and post-lecture questions that the students were required to answer and they used their learning space that I told you before: Sunspace.
每次讲座我们都会给出,课前问题和课后问题,并要求学生回答,他们利用我之前谈到的,学习空间,即阳光地带。
And in each election, they would come forward and say, "we are not really a left wing party, we're a centrist party these days" And people would say, we don't believe you.
每次选举的时候,他们都会声称,我们不是一个左翼政党,我们现在是中间派,但是选民都不相信他们
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
And I guarantee you if you do those three things throughout the course that you'll do well in the course and I've said this almost every time I've given the course and nobody has ever told me that I'm wrong.
如果你们做到了这三点,我保证你们会在这门课中取得好成绩,每次开课前我都会这么给学生说,从来没有人告诉我这个说法有问题
I'll count up the number of people killed in every church that I go to visit to look at.
每次我去一个教堂里,我都会数当地记录的阵亡人数
Every time I grabbed the steering wheel to drive, I wore away thousands of atoms.
每次我开车握着方向盘,都会磨掉很多原子。
Every time I go near the podium, I find I'm drawn to it."
每次我走到讲台附近时,都会感到被它吸引"
Yeah. Log. It's a good think, but why do you think it's log? Ah-ha. It's not a bad instinct, the length is getting shorter each time, but what's one of the characteristics of a log algorithm? It drops in half each time.
对了,对数,这是个好想法,但是你们为什么认为是对数呢?,啊哈,这样的本能不错,每次长度都会缩小些,但是对数算法的特性是什么。
And in this case, we go from 8 to 4 to 2 to 1 three times and then on each iteration of this algorithm, each pass across the board I'm touching N numbers, so that means I'm doing N things, log N times.
在这个例子中,我们从8得到4,到2,再到1,是3次,在这个算法的每次迭代中,每一趟我都会操作N个数,也就是所我每次要做N步操作,一共要做,log,N,次。
I'm thinking about a problem, I'm going to show you an example in a second, first thing I'm going to do is say, what is the thing that's going to change every time I run through the same set of code?
我要解决一个问题,我马上会让大家看一个例子,第一件我要做的事情就是,弄明白每次运行同样的指令集时,每次都会改变的东西是什么?
But it turns out that because the Standard I/O Library is -lstdio so common they don't force people to type this all day long because it's just so commonly used.
由于大家都会用到标准输入输出库,因此我们不要求每次都在后面添上,可以省略。
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