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So we can see what it's doing is it runs. So let's try fib it here with Fib of 6.
我们可以看到它在,运行的时候做了什么,让我们试试。
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fib So if I think about computing Fib of I'm going to be computing that a lot of times.
所以如果我想计算,我得算上很多次。
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The even better news is that Fib instead of 25 calls, it was only 11 calls.
更好的消息是,上次调用了25次，这次只调用了11次。
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And the memo will be a dictionary that maps me from a number to Fib of that number.
这个memo就是我从一个fib数,到另一个fibs数的记录字典。
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fib So I'll create Fib 1, fib1 which has the same arguments as Fib.
所以我将会创建和，有相同参数的。
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When I ran it up here, with the old Fib, and we printed the result, and I ran it with Fib 1 down here.
当我运行到这里，也就是老的Fib函数，我们打印这个结果，当我在下面调用Fib1时,也打印了结果。
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fib Roughly speaking, the analysis of fib is actually quite complex, of a recursive fib.
简单的说,递归的fib的分析实际上非常复杂。
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And I've done fib of 5, which is a small number. If we look at some other things, for example, let's get rid of this.
我已经计算了fib，这是一个小数，如果我们看看其它的东西,例如，让我们放开这个。
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And then I'll call fast Fib and it returns the result it has.
然后我会调用快速Fib函数,然后它会返回它的结果。
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So, as we would hope, fib=8 That right? That right, everybody?
正如我们期望的那样，对的吗？，Fib，of，6，happens，to，be，8。,对的吗，回答一下？
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But first I'm going to have, let's look at what fast Fib does and then we'll come back to the next question.
但首先我将会，让我们看看快速fib算法,做了些什么然后,我们再来讨论下一个问题。
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And let's see what happens if we call fib of 5.
让我们看看我们调用Fib会怎么样。
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fib I don't think so.
是等于8吗？，Should，Fib，of，6，be，8？,我不这么认为。
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Before we do that, or as you do that, let's look at Fib 1. The key thing to notice about Fib 1 is that it has the same specification as Fib.
我们做之前，或者当你在思考的过程中，让我们看看Fib，1，Fib1重要注意的,关键的一点就是,他和Fib的格式描述是一样的。
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Because Fib of is? What?
因为fib的值是？什么？
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I have used divide and conquer, as we seen before, to recursively break it into smaller problems. But the smaller problem of fib of 4 and the smaller problem of fib of 3 overlap with each other.
正如我们之前看到的，我已经进行了划分,并且递归性的把它分解为更小的问题,但是fib的简化问题,和fib的简化问题会相互重叠。
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So I'm going to have something called fast Fib.
我将要运行的是快速fib算法。
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Here fib got called 177 times.
这个fib函数被调用了177次。
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Now, fortunately, Fib of 0 is short.
现在，幸运的是fib很短。
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