Finding the value of n in nlog(n)

  • Thread starter Thread starter -A-
  • Start date Start date
  • Tags Tags
    Value
AI Thread Summary
To solve the inequality c1*n^2 < c2*n*log(n) or the equation nlog(n) = k, one cannot find an exact analytic solution. Instead, graphical methods can be employed to estimate values of n by plotting the functions involved. The Lambert W function provides a way to approach an analytic solution for equations involving nlog(n). This function is useful for expressing solutions in terms of known constants. Understanding these methods is crucial for tackling complexity questions in computational contexts.
-A-
Messages
5
Reaction score
0

Homework Statement



Pretty simply, if you have an inequality like c1*n^2<c2*n*log(n), how do you find the values of n for this without plugging in diifferent values and substituting? Or a question like nlog(n)=k where k is a constant.

Homework Equations


Umm...thats it.


The Attempt at a Solution


I just plugged in solutions or thought I'd use MATLAB or something. This isn't actually my homework, but it comes up a lot in complexity questions, and I need to know hot to solve it.
 
Physics news on Phys.org
There is no analytic way to solve the above question. But you could ballpark the answer by drawing graphs. nlog(n) = k => log(n) = 1/n. Draw both graphs and find out the answer.

Or you could solve this problem using the Lambert W function, which is about as close you can get to an analytic solution.

http://en.wikipedia.org/wiki/Lambert_W_function
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Sum of Infinite Series: Finding the Value of S
Replies
10
Views
3K
Is ceil(n/k) equal to floor((n-1)/k) + 1 for positive integer values of n and k?
Replies
2
Views
4K
What's the standard deviation of values in the histogram bar
Replies
2
Views
2K
How can I find the value of n when given a polynomial equation?
Replies
8
Views
2K
Solve Summation Change of Index: Find $\sum_{k=0}^{n} k^2$
Replies
2
Views
2K
How many values of k can be determined, such that
Replies
1
Views
1K
Finding a and d from the Sum of an Arithmetic Series
Replies
2
Views
2K
How Do You Solve Complex Number Equations in Quadratics and Exponentials?
Replies
39
Views
5K
Max Value of a_n: Find n for Maximum Value
Replies
29
Views
3K
Given f(N) as digital signal, find f(2N -1)
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top