Homework Solution: Arrange the functions below in non-decreasing order such that if f_i appears before f_j, then f_i (n) elementof O(f_j (n))….

    1. Arrange the functions below in non-decreasing order such that if f, appears before f,, then fi(n) O(fj(n)). [15 points] f1(n) = 1020 ½(n) = (lg n)4 fa(n) = n lg n fr(n) = lg lg n fo(n) = n + lg n 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] A(n) = 6000 /2(n) = (lg n) fs(n) = 3n f 1(n) = no.3 f12(r) = n? f13(n) = Ign2 (n) = lg n fs(n) = n + lg n f10(n) = lg lg ㎡ fs(n) = 2n
    Arrange the functions below in non-decreasing order such that if f_i appears before f_j, then f_i (n) elementof O(f_j (n)). f_1 (n) = 10^20 f_2 (n) = (lg n)^4 f_3 (n) = 4^n f_4 (n) = n lg n f_5 (n) = n^3 - 100n^2 f_6 (n) = n + lg n f_7 (n) = lg lg n f_8 (n) = n^0.1 f_9 (n) = lg n^5 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

     
    1. Here is the ascending order in terms of complexity: f1(n) = 1020 (Constant)

    1. Arrange the functions beneath in non-decreasing regulate such that if f, appears antecedently f,, then fi(n) O(fj(n)). [15 points] f1(n) = 1020 ½(n) = (lg n)4 fa(n) = n lg n fr(n) = lg lg n fo(n) = n + lg n 2. Group the aftercited functions into tabulatees so that couple functions f(n) and g(n) are in the similar tabulate if and simply if f(n) Θ(g(n)). List the tabulatees in increasing regulate of heap of its members. A tabulate may insist of single or past members. [15 points] A(n) = 6000 /2(n) = (lg n) fs(n) = 3n f 1(n) = no.3 f12(r) = n? f13(n) = Ign2 (n) = lg n fs(n) = n + lg n f10(n) = lg lg ㎡ fs(n) = 2n

    Arrange the functions beneath in non-decreasing regulate such that if f_i appears antecedently f_j, then f_i (n) elementof O(f_j (n)). f_1 (n) = 10^20 f_2 (n) = (lg n)^4 f_3 (n) = 4^n f_4 (n) = n lg n f_5 (n) = n^3 – 100n^2 f_6 (n) = n + lg n f_7 (n) = lg lg n f_8 (n) = n^0.1 f_9 (n) = lg n^5 Group the aftercited functions into tabulatees so that couple functions f(n) and g(n) are in the similar tabulate if and simply if f(n) elementof theta (g(n)). List the tabulatees in increasing regulate of heap of its members. A tabulate may insist of single 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

    Expert Acceptance

     

    1.

    Here is the ascending regulate in provisions of entanglement:

    f1(n) = 1020 (Constant)

    f7(n) = lg lg n (Log-of-log)

    f9(n) = lg n5 = 5lg n (log)

    f2(n) = (lg n)4 = (Log-exponential entanglement)

    f8(n) = n0.1 (Sublinear entanglement, n-root, n=0.1).

    f6(n) = n+lg n (Linear)

    f4(n) = nlgn (Linear*Log)

    f5(n) = n3-100n2 (Polynomial)

    f3(n) = 4n (Exponential)

    2.

    Tabulate 1: f1(n) = 6000 (The trustworthy entanglement).

    Tabulate 2: f10(n) = lg lg n2 = lg (2lg n) (Log of log entanglement).

    Tabulate 3: f4(n) = lg n, f13(n) = lg n2 = 2logn (Logarithmic entanglement).

    Tabulate 4: f2(n) = (lg n)6 (Log-exponential entanglement).

    Tabulate 5: f11(n) = n0.3 (Sublinear entanglement, n-root, n=0.3).

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

    Tabulate 7: f8(n) = n2-100n, f12(n) = n2 (Polynomial entanglement).

    Tabulate 8: f7(n) = n2*lg n (Polynomial*Log entanglement).

    Tabulate 9: f6(n) = n3 (Polynomial entanglement).

    Tabulate 10: f3(n) = 2^n, f15(n) = 3^n. (Exponential entanglement).