3. Design a dynamic programming algorithm for the Longest Alternating Subsequence problem described below: Input: A sequence of n integers Output: The longest subsequence where the numbers alternate between being larger and smaller than their predecessor The algorithm must take O(n) time. You must also write and explain the recurrence. Example 1: Input: [3, 5, 4, 1, 3, 6, 5, 7, 3, 4] Output: [3, 5, 4, 6, 5, 7, 3, 4] Example 2: Input: [4, 7, 2, 5, 8, 3, 8, 0, 4, 7, 8] Output: [4, 7, 2, 5, 3, 8, 0, 4] Write in Pseudocode, please

A. Construct a RECURSIVE solution for following iterative solution to find a value in a circular-linked list B. Analyze the runtime complexity (correctly explain the scenario, show how much work would be done, and represent the work using asymptotic notations, i.e. big O),  of the given iterative solution and  your recursive solution for the best case scenario and the worse case scenario. C. prove the correctness of your recursive solution by induction /**@param value - a value to search for@return true if the value is in the list and set the current reference to itotherwise return false and not updating the current reference*/public boolean find(T value){  if(this.cur == null)    return false; //get out, nothing is in here    Node<T> tmp = this.cur; //start at the current position  if(tmp.data == value)    return true; // found it at the starting location   tmp = tmp.next; //adv. to next node, if there is one  while(tmp != cur) {  if(tmp.data == value){    this.cur = tmp;…

A problem called S reduces to a problem called T if a T solver can be used as a subroutine to solve S. In pseudocode: Solves(...): ... SolveT(...) ... Assuming that this reduction is correct, answer the following questions regarding what the reduction tells us. If we know that an algorithm exists for solving Problem S, what does that tell us about Problem T? [ Select] If we know that an algorithm cannot exist for solving Problem S, what does that tell us about Problem T? [ Select] If we know that an algorithm exists for solving Problem T, what does that tell us about Problem S? [ Select ] [ Select ] An algorithm cannot exist for solving Problem S,r solving Problem T, what does that tell us about Nothing An algorithm exists for solving Problem S

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.