How to calculate n log n = c

Question

I have a homework problem for my algorithms class asking me to calculate the maximum size of a problem that can be solved in a given number of operations using an O(n log n) alg

Answer 1

the O notation only gives you the biggest term in the equation. Ie the performance of your O(n log n ) algorithm could actually be better represented by c = (n log n) + n + 53.

This means that without knowing the exact nature of the performance of your algorithm you wouldn't be able to calculate the exact number of operations required to process an given amount of data.

But it is possible to calculate that the maximum number of operations required to process a data set of size n is more than a certain number, or conversely that the biggest problem set that can be solved, using that algorithm and that number of operations, is smaller than a certain number.

The O notation is useful for comparing 2 algorithms, ie an O(n^2) algorithm is faster than a O(n^3) algorithm etc.

see Wikipedia for more info.

some help with logs