應(yīng)用數(shù)學(xué)專(zhuān)業(yè)外文翻譯-其他專(zhuān)業(yè)-在線瀏覽
2025-03-24 11:08本頁(yè)面
【正文】 the best we can do？ That is， how many moves are necessary and sufficient to perform the task? The best way to tackle a question like this is to generalize it a bit. The Tower of Brahma has 64 disks and the Tower of Hanoi has 8； let39。ll see repeatedly in this book that it39。s easy to see how to transfer a tower that contains only one or two disks. And a small amount of experimentation shows how to transfer a tower of three. The next step in solving the problem is to introduce appropriate notation： NAME ANO CONQUER. Let39。s rules. Then T1 is obviously 1 , and T2 = 3. We can also get another piece of data for free, by considering the smallest case of all： Clearly T0 = 0， because no moves at all are needed to transfer a tower of n = 0 disks! Smart mathematicians are not ashamed to think small,because general patterns are easier to perceive when the extreme cases are well understood(even when they are trivial). But now let39?！?9。=39。 we haven39。re not too alert. But after moving the largest disk for the last time, we must trans fr the n?1 smallest disks (which must again be on a single peg)back onto the largest； this too requires Tn?1 moves. Hence Tn ≥ 2Tn—1+1， for n 0. These two inequalities, together with the trivial solution for n = 0, yield T0=0； Tn=2Tn—1+1 , for n 0. () (Notice that these formulas are consistent with the known values T1= 1 and T2= 3. Our experience with small cases has not only helped us to discover a general formula, it has also provided a convenient way to check that we haven39。d like a nice, neat, closed form for Tn that lets us pute it quickly， even for large n. With a closed form, we can understand what Tn really is. So how do we solve a recurrence? One way is to guess the correct solution, then to prove that our guess is correct. And our best hope for guessing the solution is to look (again) at small cases. So we pute, successively, T3 = 23+1= 7。 T5 = 215+1= 31。 this is called the basis. Then we prove the statement for n n0,assuming that it has already been proved for all values between n0 and n?1, inclusive。 task hasn39。re still dutifully moving disks,and will be for a while, because for n = 64 there are 264?1 moves (about 18 quintillion). Even at the impossible rate of one move per microsecond, they will need more than 5000 centuries to transfer the Tower of Brahma. Lucas39。ll frequently skip stages I and 2 entirely, because a mathematical expression will be given to 武漢科技大學(xué)本科畢業(yè)論文外文翻譯 5 us as a starting point. But even then, we39
范文總結(jié)相關(guān)推薦
鄂ICP備17016276號(hào)-1