The formal approach to determining the big-O complexity of an algorithm is to set up recurrence relations and solve them. The recurrence relation for the Linear Search algorithm is defined by: I. T(n)=T(n-1)+1 II. T(n) = 2T(n/2)+1 II. T(n)=T(n-1)+Theta(n) IV. T(n)=2T(n/2)+Theta(n) V. None of the above Ov O II

Solving recurrences using the Substitution method. Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Solve using the substitution method. Assume that T(n) is constant n ≤ 2. Make your bounds as tight as possible and justify your answers. Hint: You may use the recursion trees or Master method to make an initial guess and prove it through induction a. T(n) = 2T(n-1) + 1 b. T(n) = 8T(n/2) + n^3

Time comp.

Consider the following algorithm that uses a sorted list of n elements (alist). What is the worst case runtime of this algorithm? for each element in alist    1. ask the user for an input, call it value    2. search value in alist using binary search    3. if value exists in alist, print "successful"       otherwise print "unsuccessful"      Question options: a. O(log n) b. O(n) c. O(n log n) d. O(2^n) e. O(n^2) f. O(1)

Solve the following recurrences using recursion tree method and write the asymptotic time-complexity. 1. T(n) = 3T (n/4) + n^22. T(n) = T (n/5) + T(4n/5) + n3. T(n) = 3T(n − 1) + n^4 4. T(n) = T (n/2) + n^2

Consider the following recursive algorithm, where // denotes integer division: 3//2 = 1, 5//2 = 2, etc. F(n):if n <= 1:    returnF(n//2)for i from 0 to n    for j from 0 to n//2        print(i+j)    Let function T(n) denote the running time of this algorithm. Derive T(n) and prove its worst case timecomplexity

I was told the answer is (n lg n) but I am not sure.

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T(n)=4T(n/2+2)+n. Use the substitution method to verify your answer.

Use the recursion tree method to solve the following recurrence T(n) by finding the tightest function f(n) such that T(n) = O(f(n)). T(n) ≤ 4.T(n/3) +0(n³)