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And when you have an optimal substructure and the local solutions overlap, that's when you can bring dynamic programming to bear.
当你得到一个最优子结构,但局部解决方案有重跌时，你就可以引入动态编程,来解决这个问题了。
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So study this, master this pattern as well as the other patterns, and you really can master English step by step.
因此，学习掌握这个句型以及其他所有的句型，你就可以一步一步说一口流利的英语。
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Our friend Schr?dinger told us that if you solve for the wave function, this is what the probability densities look like.
我们的朋友薛定谔告诉我们,如果你用波函数来解决，你就会知道这些概率密度看上去的样子。
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Okay? So when you say that what you're doing is scientific in a context of this sort, you are making yourself vulnerable.
对吧？，所以在这种情况下你说自己所做的是科学的时,你就使自己站不住脚了。
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Once you can see it and once you can step back from it, then you can also decide, "This pass is my filter. This pass is my constraint.
一旦你看到了它，一旦你能退一步思考它，你就能决定，这么走可以去伪存真，这么走会遇到困难。
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But suppose if you think about death you just get too depressed and you can't live life to the fullest.
但假设如果你考虑了死亡,你就变得抑郁,你就没法尽情地活。
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Then things suddenly blow up on you, but you'll recover and you'll figure something out and then you'll move from there.
然后突然间爆掉了，但是你会修复好自己而且解决问题,然后你就能从那个经济低谷走出来。
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If you knew only the third derivative of the function, you can have something quadratic in t without changing the outcome.
如果方程里有三阶导数,你就可以引入一个二次项,但是结果却不会变
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Finally, and this is the last thing I'll say: If you take another person's perspective, you'll care more about them.
最后我要说的是：,如果你从别人的角度看问题，你就会更关心他们。
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You get a vaccine for chicken pox, it gets injected, and sometime later you're going to be protected against it.
当你拿到水痘疫苗,并注射入体内后,一段时间之后,你就可以免于感染
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You put some inputs in, it has a contract that says if you put the right kind of inputs in you'll get a specific output coming out, but you don't have to know what's inside of that box.
你可以将输入一些内容,它相当于一个条件合约,如果你的输入是正确的，你就能得到特定的输出,但是你不知道盒子里面有些什么。
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You've got to pretty much take that chalk, and make a slurry out of it, put water, and dry it back up, put in a mold, and then you can have the chalk again, but you can't just glue it back together.
你得尽可能地收集它的碎片，把它做成粉浆，加水然后风干，放进模具，然后你就能重新得到这支粉笔，但是你不能简单地把它粘起来。
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Carter You just repeat the same reasoning again and again, and you eventually get down to 1.
你就一直重复刚才的过程,最终你会得到1
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So, if you can't immediately know, and you don't all have periodic tables in front of you, so that's fine, but if you have a periodic table in front of you, you need to be able to count valence electrons, so work on that if it doesn't come naturally to you in terms of figuring that out.
如果你不能马上想到，而且你手上没有周期表，那还好，但如果你面前有一张周期表，那你就得具备从中查出价电子个数的能力，如果你不能自然而然地想到,请在这方面多下点功夫。
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If you know that you're dying for the reason of others to live.
抽签前你就知道，你可能抽到牺牲自己救别人。
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Then also you'll be asked to do identifying information if you print it out from the program itself, but if you go up to your web browser print option and print from that particular thing then you can do it and no identifying information will be necessary.
如果你想直接从网上打印分析结果,就得提供个人信息,但是,如果你用浏览器中的打印选项,只打印营养分析结果,你就可以打印文件而无需提交个人信息
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But then you start seeing the results and you start seeing how your body changes and you start, you know,
但是接着你就开始看到成果，你开始看到你身体的变化，你就开始，嗯，
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But you'll see that once you get to final projects frankly, you're not gonna want to implement everything from scratch.
但是一旦你得出了最终方案，你就不会愿意利用框架去,实现任何功能了。
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That is a maximum If you are sharing your time and energy during this period on Tuesday afternoons, or the arch-field don't work so think carefully about that.
让大家充分发挥自己的能力,如果每周二下午这段时间,你都有时间，精力也很充沛，就可以来上这门课，不过这样你就没时间参加实践活动了,所以请仔细考虑吧。
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so you get a good idea of, like, what you knew how to do and what you couldn't do. So.
你就能明白你现在会做什么，以及不能做什么。
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Maybe you should leave before it gets too dark, so that you don't have to walk too far.
也许你该在天黑之前就动身回去了，这样你就不用走那么远了。
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As I say, red tends to be chosen, but then if you get lab experiments showing that that particular color of gas blue is somehow or another sort of more invasive of your consciousness than red is, then you move away from the arbitrariness of the choice of red as a color.
所以人们就倾向于选择红灯，但是如果你想用实验证明,比如说烟蓝色或者,其他任何另一种颜色比红色更加醒目，那么你就忽视了颜色选择上的任意性。
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And so you get to build your own special purpose programming language that helped you solve your problems in biology or finance or whatever,
你读过的类型都可以,所以你就可以让编程语言按照你的,特殊用途去解决你的生物学,财务或者任何类型的问题，
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And if your answer is no, your answer will be no, then you just know you can't use this equation here.
如果不是，那就不能，你就知道，你不能用这个方程了。
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When you serve on a board, you are in a fiduciary role; you are there to protect shareholders and that's the concept.
一旦你进入了董事会,你就成为了受托人,你的存在就是为了维护股东的利益,就是这样
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When you think about the possibility of bare survival of the scrubbed, clean,erased soul,you see that survival wasn't really everything you wanted.
当你想到，存活下去的仅是被清洗过的灵魂，你就会发现存活下去对你来说并无关紧要。
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If you look at it that way, then you're violating another one of Locke's treatises, which is that you can't take anything from anyone else.
如果你这么想的话，你就违反了,洛克的另一个论点，就是你不能拿走他人的财产。
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So, cognitive dissonance will lead you then to think that what you are giving it up for has some value and then you establish a liking for it.
这样认知失调就会让你想到,你为之付出代价的东西一定是有价值的,然后你就会喜欢上它。
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So David, you're about to go, you realize you've got this coordination problem, so you phone Nina up and you can say whatever you like, so what would you say to Nina?
大卫你来吧,你觉得最好事先能联系稳妥,所以你就给妮娜打了个电话,你会对她说点什么呢
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