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I have some old records and I'll see what I'm paying for my gold for the gold fillings ten years ago.
我有一些旧的记录,我可以去看看十年前,我到底补金牙时为了金子花了多少钱。
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Huh, all right. Well, there's some Indians here, but I guess we could set up camp, hang out.
哈，好吧，这儿有一些印第安人，但我想我们可以扎营，到处看看。
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And the reason I want to show you this is to notice that the recursion can be doubled.
如果我来写斐波那契数列你可以看看这儿,原因是我想让你看看这部分的递归可以翻倍。
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I brought the text with me. You can look at it now or at your leisure.
我带来了这部作品，你们可以看看，现在或者是有空时。
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Actually, so you can still read that, let me bring down and clean this board.
你们可以继续看看那句话,我先把这块黑板擦一下
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I'll even tell you what it is ahead of time.
我甚至可以让你预先看看是哪些话。
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I would look at it and know it looks nice, but I'm not going to say,
我可以去看看，知道那个很不错，但是不会说：
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and see if there's any, kind of anything in the sales or any T-shirts or trainers that I might buy.
看看有没有东西在促销或者T恤或跑鞋我可以买的。
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In either case, I take that value and multiply back by two, if it was even I get back the original number, if it was odd, I'm not going to get back the original number, so I can just check to see if they're the same.
在两种情况中，我都把结果值,再乘以2，如果x是偶数我就,得到了原来的值，如果x是奇数那么就不会得到,原来的值，因此我看看得到的值,和原来的值相等不相等就可以了。
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And I know it's kind of, you can see it on your handout, it has the rest of the pieces over here.
我可能会去求它们的长度，我知道这有点儿，你们可以在课堂手册上看看。
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And as you'll see by your handout, I've attempted tend to trace it.
你们可以看看课堂材料，我尝试着去找，了找它的起源，我能找到。
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If not, what could I do?
好，我可以先看看这个元素的值？
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And just to look ahead a little bit, you could easily imagine that I might want to not just put a statement in there, what the specs are, I might want to put some constraints. Some specific things to check for, to make sure that you're calling the code right.
这不仅是抽象的概念还有规范的概念，我们再往前看看,你可以简单的想象得到，我不仅仅是想在这里加一个声明,这些规范说明中我还想加一些约束，我们要注意一些特殊的事情。
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23456789 All right, here I gave it a big number, 123456789. And again, I don't want to bore you, but you can see what's going on here with this trend.
我给出一个大数字，又一次，我并不想令你们感到枯燥，但你们可以自己看看会发生些什么,这儿有个有趣的问题。
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So I'm going to go over here, and I'm going to type test search-- I can type and if you look at your handout, it's just a sequence of tests that I'm going to do OK. So initially, I'm going to set up the list to be the first million integers.
大家可以看看你们的课堂材料，那儿有一些我要做的实验,好，一开始我先去建立个，含有一百万个integer的数组,对，这有点儿简单,但是这给我提供了这样一个有序的数组。
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