recursive algorithm performs 2 recursive calls. Assume the first recursive call is of size at most 70% the original input size, and the second call is of size at most 25% of the original input size. In addition, the algorithm performs O(n) additional work after making these recursive calls. What is the big-Oh run time of this algorithm

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;...

Explain the halting condition for the recursive binary search and why all recursive algorithms need one.

Give an account of the stopping condition for the recursive binary search, and elaborate on why such a condition is required of all recursive algorithms.

Devise a recursive algorithm for finding n! mod m where n and m are positive integers.

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.

Give a recursive algorithm for computing na, where n is a positive integer and ais a real number.

Give a recursive algorithm which takes as input a sequence of numbers and returns the minimum (i.e., smallest) member in the sequence. Your algorithm should not use an iterative loop. FindMin (al, a2,..., an) If (length (alan) = 1), Return (_A_) m: FindMin (al an-1) // The recursive call If (an S m) Else End-if Return (_B__) Return (_C_)

The n-th harmonic is the sum of the reciprocals of the first n natural numbers given by: 17 1.1 1 1 H1 =Σ =1+=+=+ - 2 3 4 k=1 k +. + n (i) Write a recursive algorithm of this function returning, H, with nε N. (ii) Give a recurrence relation for the number of divisions the recursive algorithm calculates for an input n & N. iii) Solve the recurrence relation and give the O(n) of the algorithm.

Give an account of the stopping condition for the recursive binary search, and elaborate on why such a condition is required of all recursive algorithms.

A recursive algorithm is applied to some data A = (a1,..., am) where m≥ 2. The running time T is characterised using the following recurrence equations: T(2) = c when the size of A is 2 T(m) = T(m-1) + 2c otherwise Determine the running time complexity of this algorithm.

Use Binary Search, Recursive (Algorithm 2.1) to search for the integer 120 in the following list (array) of integers. Show the actions (execution) step by step. No code needed. Solution: 12 34 37 45 57 82 99 120 134 1. Compute the middle index from initial low (1) and high (9) indices: mid = Continue... A