Homework Solution: Give the asymptotic running time of each the following functions in Θ notation. Justify your…

    Give the asymptotic running time of each the following functions in Θ notation. Justify your answer. (Show your work.) Func5(n) 2for i ← n to n2 do for j ← n to i do 6 7end s end 9 return (s); en Func6 (n) 2for i ← 6 to n2 do while (j < 222) do j(1.5)j 6 7end s end 9 return (s);
    Func5(n) 2for i ← n to n2 do for j ← n to i do 6 7end s end 9 return (s); en Func6 (n) 2for i ← 6 to n2 do while (j

    Expert Answer

     
    1) here the first loop executes n times

    Give the asymptotic present period of each the aftercited functions in Θ notation. Justify your response. (Show your effect.)

    Func5(n) 2control i ← n to n2 do control j ← n to i do 6 7purpose s purpose 9 recompense (s); en Func6 (n) 2control i ← 6 to n2 do time (j < 222) do j(1.5)j 6 7purpose s purpose 9 recompense (s);

    Func5(n) 2control i ← n to n2 do control j ← n to i do 6 7purpose s purpose 9 recompense (s); en Func6 (n) 2control i ← 6 to n2 do time (j

    Expert Response

     

    1)

    here the primary loop executes n periods
    control each external loop the secret loop executes i periods
    and control each intermediate loop the secret most loop executes i^(1/2) periods

    Hence the sum estimate of periods the loop is performed in stipulations of n is as follows:
    n*n*n^(1/2) that is n^(5/2)

    Hence the entanglement is O(n^(5/2))

    2)

    Here externalmost loop executes n^2 – 6 periods
    control each external loop secret loop executes 2i^2 periods.
    Hence the sum estimate of periods the loop is performed in stipulations of n is as follows:

    n^2 – 6 * 2n^2.
    Ignoring the invariable the entanglement conquer be n^4