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So I'm going to solve this by enumerate and check, which is an example of what's called a brute-force algorithm.
你懂的,所以我得靠列举和检验来解决这个问题,这就是我们说的穷举算法。
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It will probably quit at some point because of space issues, unless I'm writing an algorithm that is using no additional space.
其中一个的时候，它会一直运行下去,它可能在某一处因为空间问题退出,除非我写了一个。
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And so one of the things we'll look at today is how can we leverage an algorithm, how can we implement an algorithm that at least at first glance the second time we've now seen it feels so obviously better.
因此，今天我们要学习的一点就是,我们怎样才能影响一个算法，怎样实现一个算法,使你在第二次看它时会觉得,至少比你第一次看到它时更好。
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and we like log algorithms, because they're really fast. A typical characteristic of a log algorithm is a pro-- or sorry, an algorithm where it reduces the size of the problem by a constant factor.
并且我们也很喜欢对数算法,因为它很快,对数算法的典型特性是高速，哦，抱歉，是他能以常数因子的速度,降低问题的大小，很明显。
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A really nice algorithm. As I said, an example of divide and conquer.
真的很好的一个算法，就如我说的。
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And so ease of implementation is actually a very compelling -- metric against which to measure-- -- do you mind toning my voice down a bit-- is a very reasonable measure against which to measure the quality of an algorithm, right.
如此简单的实现实际上是一个很牵强的,度量，与之相对的衡量是-,如果你们不介意，我降低点音量-,是一种用来度量算法质量的,合理的方法。
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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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Typical characterization, not all the time, but typical characterization, is an algorithm that reduces the size of a problem by one, or by some constant amount each time, is typically an example of a linear algorithm.
我们学习过了线性算法，它的典型特征，不是通用的,但是比较典型的特征是，它是逐一减小问题的大小的，或者说是每次减小常数的大小。
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So the running time of the problem where the input is T of size N as expressed here formulaically, T of N, the running time of an algorithm, given an input of size N. You know what?
因此一个输入为N的问题的运行时间,在这儿的公式表示为，如果输入为N，那么此算法的运行时间,是多少呢？
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