有没有什么情况下你更喜欢O(log n)时间复杂度而不是O(1)时间复杂度?还是O(n)到O(log n)
你能举个例子吗?
有没有什么情况下你更喜欢O(log n)时间复杂度而不是O(1)时间复杂度?还是O(n)到O(log n)
你能举个例子吗?
当前回答
人们已经回答了你的确切问题,所以我要回答一个稍微不同的问题,人们来这里时可能会想到这个问题。
许多“O(1)时间”算法和数据结构实际上只需要预期的O(1)时间,这意味着它们的平均运行时间是O(1),可能仅在某些假设下。
常见的例子:哈希表,“数组列表”的扩展(也就是动态大小的数组/向量)。
在这种情况下,您可能更喜欢使用保证时间绝对受对数限制的数据结构或算法,即使它们的平均性能可能更差。 一个例子可能是平衡二叉搜索树,它的运行时间平均较差,但在最坏的情况下更好。
其他回答
A more general question is if there are situations where one would prefer an O(f(n)) algorithm to an O(g(n)) algorithm even though g(n) << f(n) as n tends to infinity. As others have already mentioned, the answer is clearly "yes" in the case where f(n) = log(n) and g(n) = 1. It is sometimes yes even in the case that f(n) is polynomial but g(n) is exponential. A famous and important example is that of the Simplex Algorithm for solving linear programming problems. In the 1970s it was shown to be O(2^n). Thus, its worse-case behavior is infeasible. But -- its average case behavior is extremely good, even for practical problems with tens of thousands of variables and constraints. In the 1980s, polynomial time algorithms (such a Karmarkar's interior-point algorithm) for linear programming were discovered, but 30 years later the simplex algorithm still seems to be the algorithm of choice (except for certain very large problems). This is for the obvious reason that average-case behavior is often more important than worse-case behavior, but also for a more subtle reason that the simplex algorithm is in some sense more informative (e.g. sensitivity information is easier to extract).
我在这里的回答是,在随机矩阵的所有行的快速随机加权选择是一个例子,当m不是太大时,复杂度为O(m)的算法比复杂度为O(log(m))的算法更快。
给已经好的答案锦上添花。一个实际的例子是postgres数据库中的哈希索引和b树索引。
哈希索引形成一个哈希表索引来访问磁盘上的数据,而btree顾名思义使用的是btree数据结构。
大O时间是O(1) vs O(logN)
目前不鼓励在postgres中使用哈希索引,因为在现实生活中,特别是在数据库系统中,实现无冲突的哈希是非常困难的(可能导致O(N)最坏情况的复杂性),正因为如此,使它们具有崩溃安全性就更加困难了(在postgres中称为提前写日志- WAL)。
在这种情况下进行这种权衡,因为O(logN)对于索引来说已经足够好了,而实现O(1)非常困难,而且时间差并不重要。
人们已经回答了你的确切问题,所以我要回答一个稍微不同的问题,人们来这里时可能会想到这个问题。
许多“O(1)时间”算法和数据结构实际上只需要预期的O(1)时间,这意味着它们的平均运行时间是O(1),可能仅在某些假设下。
常见的例子:哈希表,“数组列表”的扩展(也就是动态大小的数组/向量)。
在这种情况下,您可能更喜欢使用保证时间绝对受对数限制的数据结构或算法,即使它们的平均性能可能更差。 一个例子可能是平衡二叉搜索树,它的运行时间平均较差,但在最坏的情况下更好。
对于安全应用程序来说,这经常是这样的情况,我们希望设计算法缓慢的问题,以阻止某人过快地获得问题的答案。
这里有几个我能想到的例子。
Password hashing is sometimes made arbitrarily slow in order to make it harder to guess passwords by brute-force. This Information Security post has a bullet point about it (and much more). Bit Coin uses a controllably slow problem for a network of computers to solve in order to "mine" coins. This allows the currency to be mined at a controlled rate by the collective system. Asymmetric ciphers (like RSA) are designed to make decryption without the keys intentionally slow in order to prevent someone else without the private key to crack the encryption. The algorithms are designed to be cracked in hopefully O(2^n) time where n is the bit-length of the key (this is brute force).
在CS的其他地方,快速排序在最坏的情况下是O(n²),但在一般情况下是O(n*log(n))。因此,在分析算法效率时,“大O”分析有时并不是您唯一关心的事情。