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I'm dividing it in half and half, and half and half, but each time I do that there's this merging process.
我将其划分为一半又一半，每次我还要做的就是合并的过程。
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And by the time I'm a million and a half, I no longer remember what was happening in oh, back, back.
等我活到150万年，我不记得,很久以前做过什么。
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OK. You can see that thing is cutting down the problem in half each time, which is good, but there's one more thing I need to deal with.
这很棒，但是我们还需要处理另外一件事情,让我们仔细来看看,我在开始做之前一直在说，应该先试验试验。
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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。
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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
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If the rate of population growth of the United States between 1820 and 1850 had sustained over time, we'd have today approximately one and a half billion people in the United States.
如果在1820至1850年间,美国人口增长率保持下去的话,今天我们的美国,就会拥有近十五亿人口
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And a couple of the communards-- one is a woman that you'll read about later, called Louise Michel, who spends half her time in exile in London, who was an anarchist, basically, was very important, along with Elisabeth Dmitrieff.
巴黎公社中的一些社员,你们之后会在阅读材料中读到她,她叫路易斯·米歇尔,她半辈子的时间都被放逐于伦敦,她是无政府主义者,更关键的是因为,她与伊丽莎白·德米特里耶夫的观点一致
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So you're right that you could have made your decision back in the locker room, or you could have made the decision at half time, but ultimately what matters We gonna hope that goes away.
你完全可以在,回到更衣室时才做出决定,也可以在中场休息的时候做决定,但最重要的是,希望这讨厌的声音不会再出现了
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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？
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In fact, it took the same number of steps as it did in the other case, because each time I'm cutting it down by a half.
因为每次我都把问题的规模,缩小一半，这很棒，好，接下来让我们这么做。
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Because I'm cutting down the problem in half at each time. You're right, but there's something we have to do to add to that, and that's the last thing I want to pick up on.
但是我们还需要强调一点,这是我最后想讲的一点,让我们来看看代码-实际上，让我们先来测试测试吧。
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And you can see it wrapping its way down, cutting in half at each time until it gets there, but it takes a while to find. All right.
但是这也花了一点时间来搜索，好，让我们看看100万，或者1000万是不是在数组里。
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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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I divide them in half one more time.
我要做什么？，再一次的将这些列表进行分半。
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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。
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OK. We wanted to finish up that section, we're now going to start on a new section, and I want to try and do one and a half things in the remaining time. I'm going to introduce one topic that we're going to deal with fairly quickly, and then we tackle the second topic, it's going to start today, and we're going to carry on.
我们该结束这一段了，现在我们要开始新的课程，我在接下来的时间里要做1。5件事情,我首先会很快的对一个我们,要学习的课题,进行一个介绍，然后再进入第二个话题，今天我们只是开始这个话题，以后还要继续讲。
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