Do the following problems:

a) Explain in your own words, what each of the following mean: (Be sure to use the rules of complexity, complexity algebra). (x1) 4n + 6 ~ O(n2 ); (x2) 5n2 3n + 6 ~ (n) (x3) 5n2 3n + 6 ~ (n2 ) Say: f(n) has complexity [O(g(n)) | (g(n)) | (g(n))].

b) For f(n) = n^5/4 + 6n, g(n) = 50n^5 + n^2 + n, indicate whether f(n) ~ O(g(n)), f(n) ~ (g(n)), or f(n) ~ (g(n)). Explain.

c) For f(n) = 2^ n , g(n) = 3 ^n , indicate whether f(n) ~ O(g(n)), f(n) ~ (g(n)), or f(n) ~ (g(n)). Explain.

d) What is the run time complexity, based on N, of the following code fragment? for (i = 0; i < N; i++) for(j = 0; j < N; j++) for (k = 0; k < N; k++) cin >> A[i][j][k];