Wednesday, September 18, 2019

algorithms - How to find the inverse of $nlog n$?

So I'm on chapter $1$ of introduction to algorithms & at the end the book proposes a problem: here



The answers are there & I was able to work through most of them myself despite my lack of math skills by finding the inverse of the $f(n)$'s in the leftmost column. For instance, the $n^3$ has an inverse of $\sqrt[3]{n}$ but what is the inverse for $n \log_2 n$?



However, there is $n\log_2n = 1000000$ microseconds which I cannot figure out how to find the inverse of ($n = 62746$). I'm writing python code so that way I don't screw up my calculations as I move through the table but I have no idea how to find this.



I'm not very math savvy so if you use notation, can you please name it so I can google it?



If it's not possible to reverse engineer - can someone please explain how was $62746$ calculated for that row/column combination?




Thank you for your help.

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