Design a reduction algorithm that solves the below problem;                                                               Describe your algorithm with clear pseudocode, and mention the time and space efficiency class of your algorithm in terms of the size of the input Also, identify the pre/post-processing steps Problem: input: a list L of comparable objects output: an element of L that appears more than once in L, or None if no such element exists

Subject - Design & Anal algorithms Please complete all the questions together.  Thank you in Advance. Consider the following pseudocode for bubblesort:bubblesort(A, n)for i from 1 to n − 1for j from n to i + 1if A[j] < A[j − 1]swap(A[j], A[j − 1])(a) What is the loop invariant for bubblesort?(b) State briefly a proof of correctness.(c) Derive concisely the worst-case running time of bubblesort as a function of the input array sizen? Show your work!(d) Derive concisely the best-case running time as a function of n. Show your work!

A sequential search of a sorted list can halt when the target is less than a given element in the list. Define a modified version of this algorithm and state the computational complexity, using big-O notation, of its best-, worst-, and average- case performances.

The circular array queue implementation increased the dequeue operation's performance from O(n) to O(1) by doing away with the requirement to move array items. Adding or removing members from a list can occur anywhere along its length, not simply at the front or back, thus this is not true.