寻找到大的ThetaTheta

2023-09-11 06:59:56 作者:十里平湖霜满天

我在一个数据结构和算法类。我想指出若f(n)是克大西塔(N)。我也必须说明大O,小O等...但我损失了大约接近这个特殊的对的方式。

  F(N)=日志*(log n)的
G(N)=日志(LOG * N)
 

据我目前了解,如果这对完成这一说法

 Θ(G(N))= {F(N):存在C_1,C_2> 0和n_0< BR>
 使得0≤C_1 G(N)≤F(N)≤C_2 G(N)对所有的n≥n_0}。
 

我的问题是,我不知道是什么日志* ,以及如何使用它。

解决方案   

我不知道日志*为

好了,看看它。不幸的是,谷歌并没有搜索符号太清楚,但谷歌搜索日志星打开了的重对数立刻和 SymbolHound ,搜索引擎不忽略符号,变成了一个 StackOverflow的帖子解释它。它也可能是在你的书或课堂笔记的地方。

重对数,记日志*(N),是时候,你需要采取的对数数 N 之前,你得到的值小于或等于1。

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要解决该问题,请考虑以下。如果你需要采取的 N 日志*(N)时间,然后得到一个值小于对数= 1多少次,你需要服用日志的对数(N)做同样的事情?

I am in a Data Structures and Algorithms class. I am trying to indicate if f(n) is Big Theta of g(n). I will also have to indicate Big O, small o, etc... but I am lost about the way to approach this particular pair.

f(n) = log* (log n)
g(n) = log( log* n )

From what I have currently learned, if this pair completes this statement

Θ(g(n))={f(n):there exists c_1, c_2 > 0 and n_0 <br>
 such that 0 ≤ c_1 g(n) ≤ f(n) ≤ c_2 g(n) for all n ≥ n_0}.

My problem is that I have no idea what log * is and how to use it.

解决方案

I have no idea what log * is

Well, look it up. Unfortunately, Google doesn't search for symbols too well, but Googling log star turns up the iterated logarithm immediately, and SymbolHound, a search engine that doesn't ignore symbols, turns up a StackOverflow post explaining it. It's also probably in your book or course notes somewhere.

The iterated logarithm, denoted log*(n), is the number of times you need to take the logarithm of n before you get a value less than or equal to 1.

To solve the problem, consider the following. If you need to take the logarithm of n log*(n) times before you get a value <= 1, how many times do you need to take the logarithm of log(n) to do the same thing?

 
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