August 2017
Intermediate to advanced
360 pages
8h 35m
Chinese
Content preview from 算法技术手册（原书第2 版）
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24
｜
第
2
章
那么在比较两个
256
位的数字时，性能又如何呢？比较两个
1024
位的数字又如何呢？
我们认为，在长度
k
固定的前提下，比较两个
k
位数字的操作可以在常数时间内完成。
这么认为的前提是问题的规模（即
x
、
y
的值）不得超过
k
。由
k
的倍增所导致的额外费
用也被认为是
O
(1)
的性能。
2.4.2 对数级算法的性能
酒保和顾客打了一个
10 000
美元的赌。酒保说：“我会从
1~1 000 000
中挑选一个秘密
数字，你有
20
次的机会来猜这个数字。每次猜完，我会告诉你结果是高了、低了，还
是猜中了。如果你能在
20
个问题之内猜到我的秘密数字，我给你
10 000
美元，否则你
给我
10 000
美元。”你会打这个赌吗？回答当然是应该打，因为你能够稳赢。表
2-1
给
出了范围为
1~8
的示例场景。表中展示了如何通过一系列的询问，每次将候选数据缩减
一半。
表
2
-
1
：在
1
~
8
之间猜数字的示例行为
数字 第一次猜的数字 第二次猜的数字 第三次猜的数字 第四次猜的数字
1 是 4 吗
？
是 2 吗
？
肯定是 1
！
高了 高了 你赢了
2 是 4 吗
？
是 2 吗
？
高了 你赢了
3 是 4 吗
？
是 2 吗
？
肯定是 3
！
高了 低了 你赢了
4 是 4 吗
？
你赢了
5 是 4 吗
？
是 6 吗
？
肯定是 5
！
低了 高了 你赢了
6 是 4 吗
？
是 6 吗
？
低了 你赢了
7 是 4 吗
？
是 6 吗
？
是 7 吗
？
低了 低了 你赢了
8 是 4
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.