# Homework Solution: Group the following functions into classes so that two functions f(n) and g(n) are in the same class if and only if f(n) e…

Group the following functions into classes so that two functions f(n) and g(n) are in the same class if and only if f(n) ∈ Θ(g(n)). List the classes in increasing order of magnitude of its members. A class may consist of one or more members. Group the following functions into classes so that two functions f(n) and g(n) are in the same class if and only if f(n) elementof theta (g(n)). List the classes in increasing order of magnitude of its members. A class may consist of one or more members. f_1 (n) = 6000 f_2 (n) = (lg n)^6 f_3 (n) = 3^n f_4 (n) = lg n f_5 (n) = n + lg n f_6 (n) = n^3 f_7 (n) = n^2 lg n f_8 (n) = n^2 - 100n f_9 (n) = 4n + squareroot n f_10 (n) = lg lg n^2 f_11 (n) = n^0.3 f_12 (n) = n^2 f_13 (n) = lg n^2 f_14 (n) = squareroot n^2 + 4 f_15 (n) = 2^n

Class 1: f1(n) = 6000 (The constant complexity).

Group the subjoined functions into adjustes so that couple functions f(n) and g(n) are in the selfselfselfcorresponding adjust if and singly if f(n) ∈ Θ(g(n)). List the adjustes in increasing ordain of heap of its members. A adjust may halt of undivided or past members. Group the subjoined functions into adjustes so that couple functions f(n) and g(n) are in the selfselfselfcorresponding adjust if and singly if f(n) elementof theta (g(n)). List the adjustes in increasing ordain of heap of its members. A adjust may halt of undivided or past members. f_1 (n) = 6000 f_2 (n) = (lg n)^6 f_3 (n) = 3^n f_4 (n) = lg n f_5 (n) = n + lg n f_6 (n) = n^3 f_7 (n) = n^2 lg n f_8 (n) = n^2 – 100n f_9 (n) = 4n + squareroot n f_10 (n) = lg lg n^2 f_11 (n) = n^0.3 f_12 (n) = n^2 f_13 (n) = lg n^2 f_14 (n) = squareroot n^2 + 4 f_15 (n) = 2^n

Adjust 1: f1(n) = 6000 (The faithful complication).

Adjust 2: f10(n) = lg lg n2 = lg (2lg n) (Log of log complication).

Adjust 3: f4(n) = lg n, f13(n) = lg n2 = 2logn (Logarithmic complication).

Adjust 4: f2(n) = (lg n)6. (Log-exponential complication).

Adjust 5: f11(n) = n0.3 (Sublinear complication, n-root, n=0.3).

Adjust 6: f5(n) = n+lg n, f9(n) = 4*n+√n, f14(n) = √(n2+4) (Linear complication).

Adjust 7: f8(n) = n2-100n, f12(n) = n2 (Polynomial complication).

Adjust 8: f7(n) = n2*lg n (Polynomial*Log complication).

Adjust 9: f6(n) = n3 (Polynomial complication).

Adjust 10: f3(n) = 2^n, f15(n) = 3^n. (Exponential complication).