It's a time of technological innovation, tremendous technological innovation, so much technological change that half the time it frightened people.
这还是个技术革新的时代,空前的技术革新,如此多的技术涌现,以至于人们有时候是对其感到恐惧的
Machiavelli said in that famous chapter 25, that the prince, if he is lucky, will master fortuna about half the time, only about 50% of the time.
马基雅维利在有名的第25章里说,君主,如果他幸运的话,可以在一半的时间里掌握命运,仅仅是50%的时间。
The style of warfare that emerges in this period, apparently for the first time, is what we call the hoplite phalanx and each half of that needs to be explained.
显然,这个时期第一次出现了,一种独特的战争形式,那就是重步兵方阵,我来给大家分别解释下这两个词
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。
So supposed that I give you 16 elements to sort, well, following the logic before, the running time involved in sorting 16 elements is gonna be twice the running time 16 of sorting 8 elements, left half and right half plus 16 - and again, a little sanity check, 16 means-- just the merge steps, right?
现在要对16个元素进行排序,根据之前的逻辑,对16个元素排序,要花的时间是对8个元素排序所花时间的,2倍,分别用于左半部分和右半部分,再加上6,这里16是-,做合并的步数,对吗?
The second half of the book turns in somewhat different, certainly equally important directions, but would take us much more time than the time we have allotted to deal with.
巨著的后半篇幅,转向不同,但绝对同等重要的方向,可所需花费的时间,将远超过我们课堂所订的时间。
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