Question 1 Give the simplified tilde notation of each of the following formulas, and give the order of growth of each.

n (n 1) (n 2) / 24 (n 2) (lg n) (lg n + 2) n (4n +1) n^2 n (n^2 +1) / 2 + n lg n lg ((n 1)(n^2) (n 2))^3

Question 2 Determine whether the following code fragment takes linear time, quadratic time, or cubic time (as a function of n). Also give an explanation of your answer.

for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) for (int k = 0; k < n; k++) if( (i == j) && (j==k)) c[i][j][k] = 1.0; else c[i][j][k] = 0.0;