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Each child had no other health problem.
VOA: special.2009.01.13
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We do expect the majority of the students to tackle, as you'll see tonight when the PDFs go online at 7 PM, the so called standard edition of each problem set.
我们希望你们大部分能解决这些问题，你将会看到我们下午7点钟,会把PDF放到网上去，也就是每套问题的标准版本。
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It implies that this algorithm is calling itself again and again, and again, and on each time the size of the problem I'm trying to sort is being divided by what?
这就说明此算法会一次又一次地调用自己,每次我要排序的问题规模大小,会除以多少呢？
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So let us put the guns aside and speak words of wisdom to each other so that we can come to a more amicable solution to the problem."
VOA: standard.2009.12.21
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And I'm going to show you an example in a 1 second, just to drive this home, but notice the characteristics. In the first two cases, the problem reduced by 1 at each step.
在前面两个例子里,每一部问题的规模缩小了,不管是迭代的还是递归的，这表明这个问题的复杂性可能是线性的。
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And so they each had to present... Each one wrote a term paper on one problem.
那么每个学生都要。,每名学生都要就一个问题写期末论文。
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The problem with the Blue Sky Laws was that they were each state done separately and it was hard for states to manage what were, basically, national businesses.
蓝天法的问题在于,各州的法律都是分开制定的,由各州政府去处理,然而全国性的问题却无从解决
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Well it kind of depends on what you think is driving the problem, and each of these things suggest a different level, different types of things you might do.
这取决于你对产生这个问题的原因的理解,不同的理解决定着你可以采取的,行动的层次和方式
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Now that--If the only language you've ever heard is English, that's going to seem like a really weird example of a problem because you're listening to me speak and in between each of my words you're hearing a pause.
如果你只接触过英语,那么刚才的问题就看上去非常奇怪了,因为你在听我讲话,而你会在我所说的单词之间听到一个停顿
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And that's what these will be for on a weekly basis for each of the remaining problem sets.
这就是为那些每周剩余的习题集,而打好基础的。
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OK. You can see that thing is cutting down the problem in half each time, which is good, but there's one more thing I need to deal with.
这很棒，但是我们还需要处理另外一件事情,让我们仔细来看看,我在开始做之前一直在说，应该先试验试验。
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Because I'm cutting down the problem in half at each time. You're right, but there's something we have to do to add to that, and that's the last thing I want to pick up on.
但是我们还需要强调一点,这是我最后想讲的一点,让我们来看看代码-实际上，让我们先来测试测试吧。
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For those do we offer what we call hacker editions of each of the problem sets.
对于我没提出的黑客问题,的黑客版本的同学。
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Typical characterization, not all the time, but typical characterization, is an algorithm that reduces the size of a problem by one, or by some constant amount each time, is typically an example of a linear algorithm.
我们学习过了线性算法，它的典型特征，不是通用的,但是比较典型的特征是，它是逐一减小问题的大小的，或者说是每次减小常数的大小。
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> So now that might not have felt like the fastest algorithm but think about what you could have done with that algorithm in each iteration, much like the phonebook up front here, you literally split that problem in two because on each iteration roughly half of you were sitting down and then another half and then another half.
虽然这并不是最快的算法,但如果把这种算法每次迭代,就像刚才查电话簿一样，你便将这个问题一分为二了,因为每一次迭代后只有一半坐下来,以此类推。
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Log n Log n, because at each stage I'm cutting the problem in half. So I start off with n then it's n n/2 n/4 n/8 over two n over four n over eight.
因为总共有多少层？,因为在每一层，我都是把问题分解成两半,因此以n开始，然后是。
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With this, if I can assume that accessing the i'th element of a list is constant, then you can't see that the rest of that analysis looks just like the log analysis I did before, and each step, no matter which branch I'm taking, I'm cutting the problem down in half.
读取数组中的第i个元素,是个常量时间的操作的话，我也就能像以前那样得到,这个算法是对数级复杂度的分析,并且每一步不管我选择哪个区间，我都可以把问题的规模缩小一半。
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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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