Select the equation below that provides a solution to the following recurrence: T(n)-2T(n/3)+1 T(1)-1
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- Solve the recurrence relations shown below. a. T(n)={4T(n−1)+1if n>11if n=1T(n)={4T(n−1)+1if n>11if n=1 -- b. T(n)={3T(n/3)+4nif n>11if n=1Given the following code snippet, find the following:1) Recurrence relation of func (x,y) when x>0 and length of y is n.T(x,n) = T(_) + O(_) (Just fill in the blanks)For 2-3, consider worst-case scenario and initial value of y as [1]2) Time complexity of func (x,y)3) Auxiliary Space Complexity of func (x,y)Determine Big O for the following recurrence relations using the Master Theorem if applicable, otherwise use Repeated Substitution. Show your work. Simplify the answer. a) T(n) = 1T(n) = 9T(n/3) + n b) T(n) = 1T(n) = 2T(n - 1) + 1 Master Theorem when n=1 when n>1 when n=1 when n>1 For T(n) = A T(n/B) + O(nk) where A 3 1, B > 1
- 3. Solving RecurrencesGive asymptotic upper and lower bounds for T(n) in each of the following recurrences.Assume that T(n) is constant for n ≤ 2. Make your bounds as tight as possible, andjustify your answers. (1) T(n) = 4T(n/4) + 5n(2) T(n) = 5T(n/4) + 4n(3) T(n) = 25T(n/5) + n2Data Structures and Algorithms Solve the following recurrence relations. x(n) = x(n − 1) + 5 for n > 1, x(1) = 0 x(n) = x(n − 1) + n for n > 0, x(0) = 0 x(n) = x(n/2) + n for n > 1, x(1) = 1Given the following code snippet, find the following:1) Recurrence relation of func (x,y) when x>0 and length of y is n. Express in the form below:T(x,n) = T(?) + O(?)For 2-3, consider worst-case scenario and initial value of y as [1]2) Time complexity of func (x,y)3) Space Complexity and Auxiliary Space Complexity of func (x,y)
- Running Time Analysis: Give the tightest possible upper bound for the worst case running time for each of the following in terms of N. You MUST choose your answer from the following (not given in any particular order), each of which could be reused (could be the answer for more than one of a) – f)): O(N2), O(N3 log N), O(N log N), O(N), O(N2 log N), O(N5), O(2N), O(N3), O(log N), O(1), O(N4), O(NN), O(N6)Consider the following recurrence relation: T(n) = 5*(T(n/5)) + 2 with n = 5^k, and T(1) = 1 We have: T(5^0) = T(1) = 1 T(5^1) = T(5) = 5*(T(5/5)) + 2 = 5 * T(1) +2 = 5 *1 +2 = 7 T(5^2) = T(25) = 5*(T(25/5)) + 2 = 5 * T(5) +2 = 5 * 7 + 2 = 37 T(5^3) = T(125) = 5*(T(125/5)) + 2 = 5 * T(25) +2 = 5 * 37 + 2 = 187 etc....... Find rule of T(5^k) = ?What is the recurrence relation of maximum subarray sum problem by using Divide and Conquer approach CHOOSE ANY ONE OPTION 1.T(n) = 7T(n/2) + n 2.T(n) = 8T(n/2) + n 3.T(n) = 2T(n/2) + n 4.T(n) = T(n/2) + n
- Suppose that f(n) satisfies the divide-and-conquer recurrence relation f(n) = 3f(n/4)+n2/8 with f(1) = 2. What is f(64)?Consider the following recurrence relation: T(n) = 5*(T(n/5)) + 2 with n = 5^k, and T(1) = 1 We have: T(5^0) = T(1) = 1 T(5^1) = T(5) = 5*(T(5/5)) + 2 = 5 * T(1) +2 = 5 *1 +2 = 7 T(5^2) = T(25) = 5*(T(25/5)) + 2 = 5 * T(5) +2 = 5 * 7 + 2 = 37 T(5^3) = T(125) = 5*(T(125/5)) + 2 = 5 * T(25) +2 = 5 * 37 + 2 = 187 etc....... Find T(5^k) = ?(a) For each of the following recurrences, give an expression for theruntime T (n) if the recurrence can be solved with the Master Theorem.Otherwise, indicate that the Master Theorem does not apply.(i) T (n) = T (n/2) + T(n/2) + T(n/2) + n2(ii) T (n) = 0.5T (n/2)+ 1/n(iii) T (n) = 3T (n/3) + n(iv) T (n) = 4T (n/2) + nlogn