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 assortes so that brace functions f(n) and g(n) are in the selfselfidentical assort if and barely if f(n) ∈ Θ(g(n)). List the assortes in increasing dispose of bulk of its members. A assort may exist of undivided or further members.

    2. Group the aftercited functions into assortes so that brace functions f(n) and g(n) are in the selfselfidentical assort if and barely if f(n) Θ(g(n)). List the assortes in increasing dispose of bulk of its members. A assort may exist of undivided 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 assortes so that brace functions f(n) and g(n) are in the selfselfidentical assort if and barely if f(n) elementof theta (g(n)). List the assortes in increasing dispose of bulk of its members. A assort may exist of undivided 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 Exculpation

     

    Assort 1: f1(n) = 6000 (The firm confusion).

    Assort 2: f10(n) = lg lg n2 = lg (2lg n) (Log of log confusion).

    Assort 3: f4(n) = lg n, f13(n) = lg n2 = 2logn (Logarithmic confusion).

    Assort 4: f2(n) = (lg n)6. (Log-exponential confusion).

    Assort 5: f11(n) = n0.3 (Sublinear confusion, n-root, n=0.3).

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

    Assort 7: f8(n) = n2-100n, f12(n) = n2 (Polynomial confusion).

    Assort 8: f7(n) = n2*lg n (Polynomial*Log confusion).

    Assort 9: f6(n) = n3 (Polynomial confusion).

    Assort 10: f3(n) = 2^n, f15(n) = 3^n. (Exponential confusion).