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And the basic idea was that we had some sort of a line and we knew the answer was somewhere between this point and this point.
去学习的二分搜索是有联系的,这种方法的基础思想,是我们有一个线性的序集,我们也明白答案在其中的某一段区间。
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The line is totally ordered. And what that means, is that anything here is smaller than anything to its right.
这个线性区间是有序的,也就是说两者相比,大的在小的的右边。
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But the second slice, strategies 45 through 67, getting rid of those strategies involves a little bit more.
但是排除45到67的第二个区间时,还牵涉到了别的内容
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So, our detection devices are a little bit limited here today, we're actually only going to be using our eyes, so that means that we need to stick with the visible range of the electromagnetic spectrum.
我们今天所有的探测仪器十分有限，实际上我们要用我们的眼睛来观测，这意味着我们只能看到,电磁谱中的可见光区间。
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So, you can see the term structure doesn't go up between overnight and three months.
从隔夜拆借利率到三月远期利率这段区间内,利率期限结构没有上扬
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But, there's a whole range in between.
在中间有一个完整的区间。
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The force may taper off, the force may not be given by a straight line, but for modest deformations, every spring will have a linear regime in which the force is linearly proportional to the stretching.
它产生的力可能会渐渐消失,力的曲线可能不是一条直线,而有轻微的弯曲,每个弹簧都有一个线性区间,在这一区间内,力和伸长量是线性关系
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Then if I'm looking for the square root of something less than 1, I know it will be in my region, right?
如果我要求平方根的数小于,我就知道我们的答案应该,在0-1这个区间了，对不对？
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It was over here. Because the square root of a quarter is not smaller than a quarter it's bigger than a quarter. Right?
答案超出了这个区间,因为0。25的平方根会比0。25大,是应该比0。25大对不对？
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So this is very similar, this is a kind of recursive thinking we talked about earlier, where we take our problem and we make it smaller we solve a smaller problem, et cetera.
我们则跳过比猜想数小的那个区间,然后我们重复这一过程,跟之前我们讲过的，递归思想非常类似,我们解决问题的时候,先把问题一步步变小，然后解决小问题。
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What they are trying to determine is how wide is the band of outcomes.
他们想,确定收益区间的跨度。
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So over here, my best response is to choose Middle.
所以在这个区间内我最佳对策是中
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And when I do this test, what I want to do, is say I'm going to pick the middle spot, and depending on the test, if I know it's in the upper half, I'm going to set my start at the mid point and the end stays the same, if it's in the front half I'm going to keep the front the same and I'm going to change the endpoint.
如果我知道目标数可能，再比中值点大的区间里，我可能就会把开始点设为中值点,而尾点不变，如果在小的那个区间里,就保持开始点不变而把尾点设为中值点，你们可以看到这儿的代码,就是这么做的,对不对？它是怎么做的？
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So the basic idea was fine, but I failed to satisfy the initial condition that the answer had to be between the lower bound and the upper bound. Right?
因此基础的思想是对的，但是程序没能满足,正确答案在给定的区间内这个条件,对不对？
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Well, what-- where did I tell my program to look for an answer?
好，我设置我的程序去,哪个区间找答案来着？
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In binary search-- ah, there's that wonderful phrase, this is called a version of binary search just like you saw bin-- or bi-section methods, - when we were doing numerical things- in binary search, I need to keep track of the starting point and the ending point of the list I'm looking at.
就是当我们处理数字的时候，所称的二分检索，在二分法搜索中,我需要记录区间的开始点和尾点，初始化的时候就是-,问题输入的开始点和尾点，当我开始做测试的时候,我想要做的就是去取中值点。
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So it wasn't on the region.
因此答案并不在这个区间。
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You have discrete random variables, like the one I just defined, or there are also--which take on only a finite number of values-- and we have continuous random variables that can take on any number of values along a continuum.
就像刚定义的,是一个离散型随机变量,随机变量还可以有无限种取值,也就是连续型随机变量,随机变量可以取某一区间的一切值
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And that idea was, we make a guess in the middle, we test it so this is kind of a guess and check, and if the answer was too big, then we knew that we should be looking over here. If it was too small, we knew we should be looking over here, and then we would repeat.
这些有理数是有序排列的,然后我们的想法是,首先在中间取个数作为猜想数，然后对这个猜想数进行验证，如果由猜想数得到的答案太大,我们知道应该跳过，比猜想数大的那个区间，如果太小的话。
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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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So we're throwing away all of the strategies less than 5/4 for Player I and bigger than 6/4 for Player I, which is 1? for Player I and similarly for Player II.
这样我们又剔除了,参与人小于5/4大于6/4的策略,参与人I只有1?的区间,同理可证参与人II
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Half of the returns are within a spread of a half-percent.
半数基金收益都集中于0.5%大小的区间
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Notice the printout here.
这次搜索的区间。
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And I'll remind you, what I'm printing out there is first and last, with the range I'm looking over, and then just how many times the iteration called.
我要打印出来的是，每次的区间,也就是first和last指向的值，以及重复多少次了。
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