Section 2.2 Asymptotic Order of Growth

An algorithm's worst-case running time can be tested quantitatively by computing its algorithmic upper and lower bounds. To prove that an algorithm has an asymptotic upper bound of n² we can imagine one whose worst-case running time T(n) is f(n) = pn²+qn+r. We can prove that this function is O(n²) with the inequality T(n)=pn²+qn+r⇐p²+q²+r²=(p+q+r)n² thus T(n)⇐cn² where c = p+q+r