I have question that comes from a algorithms book I’m reading and I am stumped on how to solve it (it’s been a long time since I’ve done log or exponent math). The problem is as follows:
Suppose we are comparing implementations of insertion sort and merge sort on the same
machine. For inputs of size n, insertion sort runs in 8n^2 steps, while merge sort runs in 64n log n steps. For which values of n does insertion sort beat merge sort?
Log is base 2. I’ve started out trying to solve for equality, but get stuck around n = 8 log n.
I would like the answer to discuss how to solve this mathematically (brute force with excel not admissible sorry 😉 ). Any links to the description of log math would be very helpful in my understanding your answer as well.
Thank you in advance!
http://www.wolframalpha.com/input/?i=solve%288+log%282%2Cn%29%3Dn%2Cn%29
(edited since old link stopped working)