I'd like to solve the questions below with repeated or conditional evaluation but I don't know how.
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 $64n*log(2,n)$ steps. For which values of $n$ does insertion sort beat merge sort?
What is the smallest value of $n$ such that an algorithm whose running time is $100n^2$ runs faster than an algorithm whose running time is $2^n$ on the same machine?
Any pseudocode would help me so much. Thank you.