Question1

Given the code in the following algorithm, write the summations that represent the running time of the code and solve the summations to find an approximate running time. You must show all your work without doing a line-by-line analysis. begin algorithm (1) x=0; (2) for (i=n^2; i<=n^2+5; i++) (3) for (j=4; j<= n; j++) (4) x=x+(i-j); // execution cost is c. (5) return x; end algorithm

Question 2

Use the Big-Oh definition to prove the following asymptotic statement. 5n^2 - 3n + 20 = O(n^2):