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They are quite distinct from each other, and you should be able to manage with that final exam without undue difficulty.
它们都各有特点,你需要在期末考之前解决所有困难。
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So it really is a dilemma which has to be solved collectively.
所以这真是进退两难，需要合力解决。
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So let's actually let you try another example of solving a problem that has to do with one of the spectrums.
下面请大家来看一下另一个例子,这次是一个需要大家解决的关于光谱的问题。
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But it grows pretty rapidly, as n goes up, and I'm going to show you an example in a second.
解决问题需要的时间会急剧增长，一会儿我会让大家看个例子的,我想大家注意的还是。
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If we weren't so pressed for time, I kinda wanna see how long we could get away with this before it gets awkward, but that, in fact, is an infinite loop t hat's hopefully deliberate.
如果有时间，我想看看,我们需要花多长时间解决这一问题，事实上，它是我故意,使用的无穷循环。
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The second point to clear up is that there's really three different issues that might interest us.
需要解决的第二点是,有三种不同的观点,也许能够引起我们的兴趣
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But what I needed to do this problem was to find these two unknowns.
但我解决这道题需要找到这两个未知量
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And we'll need a tiebreaking assumption and we'll do the obvious tiebreak.
我们需要假设一个解决平局的方法,我们确实也需要解决平局问题
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In a letter in late 1861 from the front, "Will indeed settle the question, for some years at least, as to whether union or secession, the Constitution or rebellion, shall triumph.
在一封1861年年底来自前线的信中,"会解决问题,但至少需要数年,不管是联合还是独立,宪法抑或是起义,终将有一方胜利
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Non-obvious ideas were conceived of to solve these problems of long-term risks and to get around the psychological barriers imposed by framing biases and psychological biases, in order to allow people to actually manage the risk and to get around moral hazard.
解决方法需要被研究并发掘,来处理长期风险问题,避开由于框架效应,引起的心理障碍，能够使人们真正控制风险,规避道德风险。
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It is going on for many years actually from the time of operation providr comfort with which I was involved in Northern Iraq when we realised that we would have civilian problems we need to develope civilian capacity to deal with these things.
这种状况已经持续了很多年了,从一开始在阿富汗北部,我参与的提供安慰行动,那时候我们就意识到我们缺少平民,我们需要更多的平民来解决这些问题。
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So there are formal questions that we will take up time and again.
人们又怎么对待那些资源,这些是我们需要花时间，解决的正式问题。
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So what you typically do and a hash case is you design your code to deal with that.
你所需要做的就是通过设计你的代码,来解决上面的问题。
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Now as an aside, I'll admit this is a completely useless program, much like the first couple of ones we did because why would you write a program just to solve this?
说点题外话，我承认这是一个完全无用的程序，跟我们之前写的两个程序一样,我们为什么需要写个程序来解决这个数学运算呢？
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I'm going to let t of b be the number of steps it takes to solve the problem of size b.
我会设立一个t作为,计算指数为b的时候解决问题需要的步骤数。
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I'm given an integer that's a perfect square, and I want to write a little piece of code that's going to find the square root of it. All right so I'm cheating a little, I know it's a perfect square, somebody's given it to me, we'll come back in a second to generalizing it, so what would the steps be that I'd use to walk through it?
完美平方数的整数，我想写一段代码来求这个数的平方根,好，我这儿有点儿作弊了,我知道这是一个完美的平方数了,他们给我的，我们后面会讲怎么产生这个数的，那么我想解决这个问题,需要什么步骤呢？
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> So this is just a dumb text editor called Nano, dumb in that it's very simple which is nice because it eliminates a lot of the complexities of learning a new tool when really all you wanna do is solve an actual problem.
这是NANO文本编辑器，它很简单，可以消除因学习这个新工具,而带来的许多复杂问题,你真正需要做的就是解决一个实际问题。
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t In the b even case, again I'm going to let t of b be the number of steps I want to go through.
如果b为偶数，那么我还是要用,来代表解决这个问题需要的步骤数。
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And again, I'm going to do it with a little bit of abusive notation, and it's a little more complicated, but we can kind of look at. All right?
为了解决这个问题,我还是需要滥用一点符号，这有点复杂，让我们来看看吧，好不好？
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So it turns out there's a solution to this: If you need more precision, more digits after the decimal point than a float allows, what do you go for instead?
所以这里有一个解决方案：,如果你需要比float类型允许的更高精度，小数点后更多位数,那你该用什么取代它？
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