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 direct such that if f, appears anteriorly 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 forthcoming functions into assortes so that span functions f(n) and g(n) are in the corresponding assort if and merely if f(n) Θ(g(n)). List the assortes in increasing direct of heap of its members. A assort may continue of individual or over 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 direct such that if f_i appears anteriorly 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 forthcoming functions into assortes so that span functions f(n) and g(n) are in the corresponding assort if and merely if f(n) elementof theta (g(n)). List the assortes in increasing direct of heap of its members. A assort may continue of individual or over 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 direct in stipulations 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.

    Assort 1: f1(n) = 6000 (The steady complication).

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

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

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

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

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

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

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

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

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