Question

3. (20 points) Algorithm Analysis and Recurrence There is a mystery function called Mystery(n) and the pseudocode of the algorithm own as below. Assume that n 3* for some positive integer k21. Mystery (n) if n<4 3 for i1 to 9 5 for i-1 to n 2 return 1 Mystery (n/3) Print "hello" 6 (1) (5 points) Please analyze the worst-case asymptotic execution time of this algorithm. Express the execution time as a function of the input value n. Derive a recurrence for the running time (2) (5 points) Solve the recurrence in 3(1) by providing a tight upper and lower bound solution. Show the rational of how to solve the recurrence.
pleas answer asap

Answer 1

From the current pseudo code ,we get the recurrence relation as -T(n) = 9T(n/3) + n

Masters Theorem for dividing function is as :

T(n) = aT(n/b) + f(n)  where f(n) is of form nklogp(n)

Solution for these equation by masters theorem is as

1. if a > b^k, then T(n) = θ(n^log_ba)
2. if a = b^k, then
   (a) if p > -1, then T(n) = θ(n^log_ba log^p+1n)
   (b) if p = -1, then T(n) = θ(n^log_ba loglogn)
   (c) if p < -1, then T(n) = θ(n^log_ba)
3. if a < b^k, then
   (a) if p >= 0, then T(n) = θ(n^k log^pn)
   (b) if p < 0, then T(n) = θ(n^k)

Hence for the current code ,we get the soln as :O(n²)