Suppose that, even unrealistically, we are to search a list of 700 million items using Binary Search, Recursive (Algorithm 2.1). What is the maximum number of comparisons that this algorithm must perform before finding a given item or concluding that it is not in the list?
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- Design an algorithm to rearrange elements of a given array of n real numbers so that all its negative elements precede all its positive elements. Your algorithm should be both time efficient and space efficient.Describe the halting condition for the recursive binary search and the reason why stopping conditions are required for all recursive algorithms.Assume you have a sorted list of 100 pre-sorted elements and a recursive implementation of Quicksort. How many calls to Quicksort are made in order to fully sort it. Assume that the algorithm makes the recursive Quicksort calls before checking if it has an array of size 1 (see https://www.geeksforgeeks.org/quick-sort/ for specific pseudo code or the textbook Introduction to Algorithms 3rd Edition page 171). 85 101 50 103 199 Assume you have the following array: 40, 20, 15, 40, 90, 60, 50, 70. Which of the following elements, if selected as the pivot, would give you the most unequal sub-arrays to be sorted using quicksort? 30, 70 20, 15 40, 90 90, 70 90, 15 Assume you have the following array: 40, 20, 15, 40, 90, 60, 50, 70. Which of the following elements, if selected as the pivot, would give you the most unequal sub-arrays to be sorted using quicksort? 30, 70 20, 15 40, 90 90, 70 90, 15 Assume we have the array 4,10,3,5,1,2,5,6,1,2,3. What are the swaps that will occur after we…
- Given an unsorted array of integers, A, its size n, and two numbers x and y both elements of A. write an algorithm that returns the distance between x and y. The distance between the two numbers of an array is the number of elements that lie between them in the sorted order. Achieve the asymtotically fastest time for this problemDesign a type of sieve algorithm that would (1) Create a list of consecutive integers from 1 to n. (2) Initially, let k=2. (3) Consider each of the multiples of k less than or equal to n and either place or remove a mark on it as follows: - If you encounter an unmarked multiple, mark it with a zero. - If you encounter a multiple that has already been marked, remove the mark by restoring to its original value. (4) Increase k by one. (5) Repeat steps (3) and (4) as long as k <= n.Explain the halting condition for the recursive binary search and why all recursive algorithms need one.
- Java:4. Consider the following undirected, weighted graph (seen previously in #3): A 3 B 1 C 2 7 Edges Weight 3 10 12 Order vertices marked as known (done): 1) Neighbors of A D 2 E 2 Step through Prim's algorithm to calculate a minimum spanning tree, starting from vertex A. Show the edge coordinates and their corresponding weights. Specify the weight of the MST and also draw the MST. FRecursionWe have learned the binary search algorithm this semester, but we implementbinary search using a while loop. In this exercise, we are going to see binarysearch implemented by recursion and trace the recursion.Tracing the Recursion. Observe the recursive solution provided below and answer the followingquestions:1. Which line(s) of this program define(s) the base case of the binary() method?2. Which line(s) of this program include recursive call(s)?3. Trace the recursion below. You must show the tracing step by step (write themdown); otherwise – little to no credit!4. At what step of your recursion tracing did you hit the base case?5. What is the final output of this code?
- Consider the Sort-and-Count algorithm explained in section 5.3 of our text: "Counting Inversions"Suppose that the initial list is: 92 71 36 91 27 48 14 34 81 26 24 65 78 51 37 22 Sort-and-Count makes two recursive calls. The first recursive call inputs the first half of the initial list: 92 71 36 91 27 48 14 34 and returns the sorted version of the first half, as well as the number of inversions found in the first half (22). The second recursive call inputs the second half of the initial list: 81 26 24 65 78 51 37 22 and returns the sorted version of the second half, as well as the number of inversions found in the second half (19). Sort-and-Count then calls Merge-and-Count. To Merge-and-Count, Sort-and-Count passes the sorted versions of the two halves of the original list: 14 27 34 36 48 71 91 92, and 22 24 26 37 51 65 78 81 Merge-and-Count begins merging the two half-lists together, while counting…for question 1, please use java language for codingDescribe the halting condition for the recursive binary search and the reason why stopping conditions are required for all recursive algorithms.