换个角度来思考下为什么是对数级的。
It's got that property of, it cuts things in half.
但你们是正确的，是对数级的,它有这样的效率是因为他每次能把问题减半？
Thank you. I mean, I know I sort of said it to you, but you're right. It's logarithmic, right?
这两段是圣诞颂歌,本质都是级进
Those are two Christmas carols that are very conjunct in nature.
你要百依百顺才能从用户那里得到一个输入,这个输入可能只是一个,语言优先级。
You have to jump through hoops just to ask the user for a piece of input which should be really the thing a language prioritizes.
改变以指数级发生。
Change happens exponentially.
我还能怎么办？谢耳朵大侠，85级的血精灵，东部王国的英雄，像烈日下的尸骸一样被扒光了。
What choice did I have? The mighty Sheldor, level 85 blood elf, hero of the Eastern kingdoms, has been picked clean, like a carcass in the desert sun.
那么我可以得出一个相当大的上界，我们可以给一个指数级增长的上限。
I could get a really big upper bound, this thing grows exponentially.
所有能量级都是负数，因为它是一个束缚系统,在这里我从n等于1讲起。
All the energies are negative because it is a bound system. I start up here with n equals one.
现在在后面，我违反了把main函数放在上面的优先级,可能那是可以宽恕的。
Now downside of this, well, I've just now violated my preference for having main up top, maybe that's forgivable.
怎么回事？莱纳德，我是一个3级战士了。
What's going on? Leonard, guess what? I'm a level-three warrior.
寻找的是能够最大程度地帮助自己发展的入门级工作。
you're looking for that first entry-level job that's going to help develop you the best that you can.
这很好的表明了这是，对数级复杂度的问题，我马上就要解释。
This case, I reduced the size of the problem in half.
杂度是指数级的呢？,有人猜猜么？
And if I'm running an exponential algorithm, any guesses?
我们刚刚发现了一个罕见的低级地震群，在内华达州的法尔科。24小时之内发生了23次小地震，都很小，震级在2.0级到2.6级。
Now, we got a rare low-level seismic swarm out in Falco, Nevada. Twenty-three small quakes, all tiny 2.0 to 2.6 in the last twenty-four hours.
全体战斗员进入一级备战。
Combatant commands are now at Defcon 1.
在现实世界中，你可能想说，如果你去电影院看R级电影，“你有18岁吗？,或者你跟随你的父母亲来的吗？“
You might want to say in the real world, if you go to a movie theater for this R-rated movie, "Are you 18 and over or are you with a parent?"
我们发现存在着不同,当级进混合着跳进时,也许正是这样的处理突出渲染了,贝多芬第五交响曲中的不安氛围
We have the difference between conjunct music with the and disjunct music and that perhaps adds to the unsettled quality of the beethoven Fifth Symphony.
你得组个至少5人的队去，1个35级的医师。
You need to be in a group of at least five for that quest and one should be a level 35 healer.
看一下能量级图表中,多电子原子的部分。
And this is the energy level diagram for multi-electron atoms.
那你想不想知道沃罗威茨先生曾经偷偷登录我的魔兽争霸账号，然后把我一个八十级的术士名字由谢耳朵改成了没耳朵。
Would you be interested in knowing that Mr. Wolowitz once snuck onto my World of Warcraft account and changed the name of a certain level-80 warlock from Sheldor to Smeldor?
所以我们会使用互联网实现随需视频么，那会成为杀手级应用么？会有数百万人,就在他们想看的时候看到视频么？
So will we be using the internet for video on-demand, will that be the killer app? Will millions of people wide watch this video right when they want to watch it?
我不是大师，但是我们能从零开始吗?零级。 不，这没有东西是零级的。
Well, I'm not a master, but let's just start at zero. Level zero. No. There is no such thing as level zero.
让一个个体对国家级的事务进行干预，这是我们需要反思的。
To have an individual engaging in these state level interventions should give us all pause.
没事，是我，佩妮，听着，我现在25级了，然后到了紫莲花沼泽，对吧？
No danger, look, it's just me, Penny. Listen, I got to level 25 and reached purple lotus swamp, right?
大概在音乐史上,最为级进的旋律,是我们第一堂课上撇过一眼的,贝多芬的《欢乐颂》
And possibly the most conjunct of all melodies in the history of music was the melody that we looked at very briefly in the first gathering, and that is Beethoven's famous Ode to Joy.
最上面一级，AAA，最先给付，最低级，B级，最后给付，最先承担违约。
The highest level, AAA, is getting paid first. The lowest rated, B, is getting paid last, taking on defaults first.
首先，情感是基本机制,设定目标及事务优先级,我们将谈论很多关于宇宙的话题,在这堂课和下堂课。
The first is this, that emotions are basically mechanisms that set goals and priorities and we're going to talk a lot about in this class and the next class about universals.
教授是该领域的,明星级领头思想家。
Taught by a star who was a leader thinker in this area.
威胁分析？马苏德·沙马尔，塔里克·尤哈尼奥斯曼·艾哈迈德，亚辛·赛义德，激进穆斯林大师级软件工程师。
Threat analysis? Massoud Shammar, Tariq al Juhani, Osman Ahmed, Yasin Said. Radicalized Muslims, masters level software engineers.
才3级就觉得自己发财了，真是个新手。
Level three, and she thinks she's rich. What a newb.
周六夜要从嗨翻升级成史诗级啦。
Saturday night just went from crazy to epic!
对数级复杂度的算法就是指,通过一系列常量级步数的操作,可以将问题的规模。
A log algorithm typically is one where you cut the size of the problem down by some multiplicative factor.
它是一个保守系统,所以所有的能量级都是负值。
It is a conservative system so all the energies are negative.
致命纳得! 速度8级、防御力16级。丑陋双头龙, 隐匿性11级，攻击性加倍。
The Deadly Nadder! Speed 8, armor 16. The Hideous Zippleback. Plus 11, stealth, times 2.
我告诉了你们这是一个对，数级的算法，这是很棒的,我们来一起看看这个算法到底做了什么。
We started off talking about binary search, and I suggested that this was a log algorithm which it is, which is really kind of nice.
灭绝级的事件太多了，比恐龙灭绝之前还多。
There were more than a dozen extinction level events before even the dinosaurs got theirs.
那是什么？我们会把卖不出的B级BB级和BBB级的债券堆在一起。
What is that? This is where we take a bunch of B's, BB's and BBB's that haven't sold, and we put them in a pile.
点它就是了，祝贺你，你现在是一个3级的战士了。
Just click on them. Yeah, congratulations. You are now a level-three warrior.
那我怎么办呢？把没卖掉的鱼，就好比是BBB级债券全部扔掉承受损失吗？
So, what am I going to do? Throw all this unsold fish, which is the BBB level of the bond, in the garbage and take the loss?
如你所见，甚至平方级复杂度的方法。
So you can see, even the quadratic ones can blow up in a hurry.
当然不该，你才 25级，这些匈牙利人，他们把你当龙的诱饵。
Of course it's not. You're only a level 25. These Hungarians, they're just using you for dragon fodder.
从最低能量到级最高能量级都是这样,而这是占据的函数。
Lowest energy to highest energy and it is a function of occupancy.
好，然后说到指数级，正如你所见，典型的例子是,我讲一个问题分解成为,两个更小规模的子问题。
OK. And then the exponentials, as you saw is when typically I reduce the problem of one size into two or more sub-problems of a smaller size.
对数级的，这太重要了，接下来我要给你们看个例子。
OK. There's some constants in there, but this is order log b.
如果没听到答案的同学,答案是对数级的？
OK. What would you guess the order of growth here is? Yeah. Why? Good. Exactly. Right?
上升半音级是什么
What's a half step above D?
这就是能量级图表大致的模样。
This is what the energy level diagram looks like.
这个图表，看起来很烦，很无趣，但是它很有用,有非常明确的规定,譬如，当你写代码时，就会涉及操作符的优先级。
This chart, very boring and uninteresting but useful to say there are very well defined rules as to when you're writing code, what operators, like what syntax should get evaluated first.
猛烈凶魇，火力15级。恐怖龙，攻击性8级、毒性12级。
The Monstrous Nightmare. Firepower 15. The Terrible Terror. Attack 8, venom 12.
假入我们一秒钟运算十亿次，我们已经看过了对数级，线性增长的。
Let's suppose n is 1000, and we're running at nanosecond speed.