a. Write pseudocode for a divide-and-conquer algorithm for finding the position of the largest element in an array of `n` numbers. b. What will be your algorithm's output for arrays with several elements of the largest value?
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- For each of the algorithms unique 1 and unique2, which solves the element uniqueness problem, perform an experimental study on the same computer to determine: 1) What are these two algorithms doing here? Are they doing the same thing or not? 2) Which algorithm is faster and why? 3) Can you come up with an even faster algorithm? If so, what is it? /** Returns true if there are no duplicate elements in the array.*/ public static boolean uniquel (int[] data) { int n = data.length; for (int j 0; jSee the pseudo-code of the Binary Search using recursion below. Fill in the XXXX and YYYY in the code Algorithm BinarySearch (A,v,low,hi) Input: array A indexed from low to hi with items sorted from smallest to largest. We are searching for the item v Output: returns a location index of item v in array A; if v is not found, -1 is returned. if (low > hi) then return (-1); mid = (lo + hi)/2; if (A[mid] = v) then == return(mid); if (A[mid] < v) then return(BinarySearch(A, XXXX ,hi, v)); else return(BinarySearch(a, lo, YYYY, v)); О а. ХX: lo+1, YҮҮ: hi O b. XXXX: mid, YYYY: mid О с. ХXXX: lo, YYYY: hi O d. XXXX: lo+1, YYYY: hi-1 O e. XXXX: mid+1. YYYY: mid-101... ""Implementation of the Misra-Gries algorithm.Given a list of items and a value k, it returns the every item in the listthat appears at least n/k times, where n is the length of the array By default, k is set to 2, solving the majority problem. For the majority problem, this algorithm only guarantees that if there isan element that appears more than n/2 times, it will be outputed. If thereis no such element, any arbitrary element is returned by the algorithm.Therefore, we need to iterate through again at the end. But since we have filtredout the suspects, the memory complexity is significantly lower thanit would be to create counter for every element in the list. For example:Input misras_gries([1,4,4,4,5,4,4])Output {'4':5}Input misras_gries([0,0,0,1,1,1,1])Output {'1':4}Input misras_gries([0,0,0,0,1,1,1,2,2],3)Output {'0':4,'1':3}Input misras_gries([0,0,0,1,1,1]Output None"""..4. Consider the function IndexEqual(A,i.j) that returns true if there exists an index x (i sx sj) such that A[x] = x; otherwise, retums false. You may assume A is a sorted integer array in which every element is unique. a. Write an efficient recursive algorithm for IndexEqual(A,i.j). b. What is the situation resulting in the best-case running time of your function, and give an expression for that running time? c. What is the situation resulting in the worst-case running time of your function, and give an expression for that running time in terms of n, where n=j-i+1?Java: Consider the following algorithm for searching in an unsorted array. If the size of the array is 1, then check if it contains the element to be searched. Otherwise, divide the array into two halves, and recursively search both halves. Which of (a)–(c) is false? The running time of this algorithm is O(N) The actual running time of this algorithm is likely to be better than sequential search. This is an example of a divide‐and‐conquer algorithm all of the above are true none of the above is trueII. Read each problem carefully and present an algorithm with the required running-time to solve each problem. 2. Let A be a sorted array of integers. You want to implement two functions: . update(i, x) - which takes as input an index i in A and sets A[i] = x. For example, calling update (3,10) will set A[3] = 10. Note that array A might not be completely sorted after an update. is Sorted(i) returns true if the subarray A[0... i] is sorted, otherwise it returns false. A straightforward implementation of the two operations using only the given array can be done as follows: update operation can directly change the value of A[i] to x. is Sorted will scan A[0] up to A[i] while checking if elements are non-decreasing. With the above implementations, update takes O(1) time but is Sorted takes O(n) time. b. Describe how to use a balanced BST to implement both operations in O(log n) time. Discuss why your implementation is correct, preferably using diagrams.II. Read each problem carefully and present an algorithm with the required running-time to solve each problem. 2. Let A be a sorted array of integers. You want to implement two functions: update (i, x) - which takes as input an index i in A and sets A[i] = x. For example, calling update (3,10) will set A[3] = 10. Note that array A might not be completely sorted after an update. is Sorted (i) - returns true if the subarray A[0... i] is sorted, otherwise it returns false. A straightforward implementation of the two operations using only the given array can be done as follows: update operation can directly change the value of A[i] to x. is Sorted will scan A[0] up to A[i] while checking if elements are non-decreasing. With the above implementations, update takes 0(1) time but is Sorted takes O(n) time. a. Give another implementation where update takes O(n) time while isSorted takes O(1) time. b. Describe how to use a balanced BST to implement both operations in O(log n) time. Discuss why…Fill-In Blanks of the following question: As linear search algorithm ............use any extra space for an array of n number of elements.Implement algorithm FindMax(L) pre-cond: L is an array of n values. post-cond: Returns an index with maximum value.Consider the problem of sorting elements in an array of n numbers. Design two algorithms to implement the quicksort as follows: Recursive algorithm, and Non-recursive algorithm Analyze the efficiency of your algorithms as follows: For the recursive algorithm, figure out the recurrence relation and use the Master Theorem to find out the time efficiency in Big-O notation. For the non-recursive algorithm, use counting method to count the number of comparisons in Big-O notation.1.a)Given an array which is sorted in descending [large to small] order and got no repeated numbers. You are asked to apply linear search. You are asked to find a number which exists. What should be the worst time complexity and why? b) A. Given the array of numbers 50 10 90 120 -13 3 89, you are asked to apply Binary Search to find a certain number. show the simulation and what would be the best achievable time complexity?Consider the problem of finding the distance between the two closest numbers in an array of n and y is computed as x - y.) numbers. (The distance between two numbers x Design a presorting-based algorithm in pseudo code for solving this problem and determine its efficiency class. Answer: // your algorithm goes here Provide the the algorithm efficiency analysis here:SEE MORE QUESTIONS