And in fact, one of the lessons you may already be realizing with P sets is that things seem to take twice, three times, four times longer than you actually might think.
从习题集中你可能已经得出的一个教训就是,程序所花的实际时间往往是你开始以为的两倍,三倍,四倍甚至更长。
What have we done over the last three or four lectures? We've started introducing you to classes of algorithms. Things that I'd like you to be able to see are how to do some simple complexity analysis.
我们在过去三节或四节课中讲了什么?,我开始向你们,介绍算法的类型,我想你们知道的是,如何做一些简单的复杂度分析。
I've assigned a full two weeks to the Republic, which would be four lectures, but because I wanted to do some other things with the course as well, I had to cut the Republic by one lecture, and now I'm paying for that today.
我会分配两周的时间来消化《理想国》,等同四堂讲课,但因为我想要,加一些内容到课堂来,所以我必需砍掉《理想国》的一堂课,今天我要付出代价。
They're irrational numbers and these irrational numbers like to move to rational numbers; they like to move to consonances; they like to move to intervals that are based on things such as two to one and three to two or maybe four to three.
它们是无理数,而这些无理数想要变为有理数,它们想变成和谐音,就要根据一些比率改变音程,比如二比一,三比二,或四比三的比率
Down here, I've just got two things to merge, and then I've got things of size two to merge and then things of size four to merge. But notice a trade off. I have n operations if you like down there of size one.
但是n的大小是不同的,是吗?在这里我们只要合并两个元素,然后是合并长度为2的列表,接下来是合并长度为4的列表,但是观察一下之间的权衡关系。
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