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 under in non-decreasing manage 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 collocatees so that span functions f(n) and g(n) are in the identical collocate if and simply if f(n) Θ(g(n)). List the collocatees in increasing manage of lump of its members. A collocate may rest of individual or further 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 under in non-decreasing manage 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 collocatees so that span functions f(n) and g(n) are in the identical collocate if and simply if f(n) elementof theta (g(n)). List the collocatees in increasing manage of lump of its members. A collocate may rest 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 Solution

     

    1.

    Here is the ascending manage in provisions of complication:

    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 complication)

    f8(n) = n0.1 (Sublinear complication, 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.

    Collocate 1: f1(n) = 6000 (The fixed complication).

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

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

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

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

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

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

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

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

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