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. 2. 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. [15 points] fi (n) = 6000 /2(n) = (lg n) (n)3 f(n) n lg n fs(n) = n -100n f 1(n) = no.3 f12(n) = n? f13(n) = Ign2 (n) = lg n fs(n) = n + lg n f10(n) = lg lg ㎡ fs(n) = 2n
    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

    Expert Answer

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

    Group the aftercited functions into adjustes so that couple functions f(n) and g(n) are in the corresponding adjust if and barely if f(n) ∈ Θ(g(n)). List the adjustes in increasing appoint of body of its members. A adjust may insist of individual or further members.

    2. Group the aftercited functions into adjustes so that couple functions f(n) and g(n) are in the corresponding adjust if and barely if f(n) Θ(g(n)). List the adjustes in increasing appoint of body of its members. A adjust may insist of individual or further members. [15 points] fi (n) = 6000 /2(n) = (lg n) (n)3 f(n) n lg n fs(n) = n -100n f 1(n) = no.3 f12(n) = n? f13(n) = Ign2 (n) = lg n fs(n) = n + lg n f10(n) = lg lg ㎡ fs(n) = 2n

    Group the aftercited functions into adjustes so that couple functions f(n) and g(n) are in the corresponding adjust if and barely if f(n) elementof theta (g(n)). List the adjustes in increasing appoint of body of its members. A adjust may insist of individual or further 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

    Expert Response

     

    Adjust 1: f1(n) = 6000 (The perpetual 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).