Consider the following recursive algorithm Algorithm Qtn) Input: a positive integer n it n 1 Freturn 1 else return Q(n-1)+2 -1 1) Set up a recurence relation for this function's value and solve it to determine what this algorithm computes 2) Setup a recurence relation for the munber of multiplication made by this algorithm and solve it to find the total number of multiplications that are esecuted.

DESIGN YOUR OWN SETTING Devise your own setting for storing and searching the data in an array of non-negative integers redundantly. You may just describe the setting without having to give an explicit algorithm to explain the process by which data is stored. You should explain how hardware failures can be detected in your method. Once you have described the setting, make sure to include the following: Write a pseudocode function to describe an algorithm where the stored data can be searched for a value key: if the data is found, its location in the original array should be returned; -1 should be returned if the data is not found; -2 should be returned if there is a data storage error Include a short commentary explaining why your pseudocode works Describe the worst-case and best-case inputs to your search algorithm Derive the worst-case and best-case running times for the search algorithm Derive the Theta notation for the worst-case and best-case running times Maximum word count for…

Another recursive algorithm is applied to some data A = (a₁, ..., am) where m = 2* (i.e. 2, 4, 8,16 ...) where x is an integer ≥ 1. The running time T is characterised using the following recurrence equations: T(1) = c when the size of A is 1 T(m) = 2T (2) + c otherwise Determine the running time complexity of this algorithm.

* Axiomatic Proof Prove the following program for integer division (x/y): { x>= 0 ^ y>0 } q := 0; r := x; while y <= r do   begin   r := r - y;   q := q + 1;   end { y > r ^ x = r + y * q }