(c) Design a Turing Machine that accepts all binary strings in the form of a palindrome. (d) Use the merge sort to sort the following list in ascending order. Show your work step by step. 4 19 6 15 10 3 8 11 1
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- Question 6: Professor Holmes has come up with a new sorting algorithm. He calls it Trinary Sort and "claims" that it is asymptotically faster than Merge Sort, despite the fact both the algorithms operate using similar logic. But, unlike Merge Sort, Trinary Sort splits the input array into (roughly) 3 equal parts at each step of the recursion as long as the array is splittable (i.e., has at least 3 elements). Trinary Sort's merge subroutine, similar in principle to the one used by Merge Sort, takes 3 sorted subarrays and merges them to produce a single sorted array. Given all of this, answer the following questions. (a) In Merge Sort, the merge subroutine makes n-1 comparisons to merge 2 arrays of size n/2, which takes (n) time. How many comparisons will the merge subroutine of Trinary Sort make to merge 3 arrays of size n/3? What would be the (...) bound on the running time for this subroutine? (b) What is the (...) bound on the running time of the Trinary Sort algorithm? Come up with…Please solve your way, do not copy and paste Write a python program to implement Breadth first search Traversal.Consider the following recursive mergesort algorithm (another classic divide and conquer algorithm). Mergesort was first described by John Von Neumann in 1945. The basic idea is to divide an unsorted list x of m elements into two sublists of about half the size of the original list. Repeat this operation on each sublist, and continue until we have lists of size 1 in length. Then starting with sublists of length 1, "merge" the two sublists into a single sorted list. Mergesort (m) var list left, right, result if length (m) ≤ 1 return m else var middle = length (m) / 2 for each x in m up to middle add x to left for each x in m after middle add x to right left = Mergesort (left) right = Mergesort (right) result = Merge(left, right) return result
- Present an example of walking through the merge sort or the quick sort algorithm (your choice) This is an algorithm tracing activity, not a coding exercise. Do not post any code or code output. Post the following for merge sort: Start with an unordered list of at least NINE elements. List all the recursive calls that would be made to sort the list, going forward. Show which pair of sub-lists will be merged each time, going back. Show the ordering of the sub-list after each recursive call returns. Post the following for quick sort: Start with an unordered list of at least NINE elements. State what element will be the pivot value (use only low index or median-of-three). List all the recursive calls that would be made to sort the list. Show the ordering of the sub-list after each recursive call returns.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…1. Apply quicksort to sort the list E, X. A, M. P, L. E in alphabetical order. Draw the tree of the recursive calls made.
- Using c++ Create a program to satisfy the following problems: Set up a random experiment to test the difference between a sequential search and a binary search on a list of integers. Use the binary search functions given in the text (recursive and iterative). Generate a random, ordered list of integers and do a benchmark analysis for each one. What are your results? Can you explain them? Implement the binary search using recursion without the slice operator. Recall that you will need to pass the list along with the starting and ending index values for the sublist. Generate a random, ordered list of integers and do a benchmark analysis. Overload the cout operator (<<) for the hash table Map ADT implementation. Overload the cin operator (>>) for the hash table Map ADT implementation.8. Write in the programming language Julia a program to compute pi using a Monte Carlo simulation of N darts thrown in [-1, 1] ^ 2.Apply the merge sort on the following list and sort the list in decreasing order: 91 98 29 93 98 53 68 33 33 47 You must show how the list is divided by the recursive calls to MERGE-SORT, then merged at each stage to obtain the final sorted list.
- Exercise 1: Pre-sorting Consider the problem of finding the distance between the two closest numbers in an array of n numbers. (The distance between two numbers x and y is computed as |x-yl.) a. Design a presorting-based algorithm and implement it in your preferred language. b. Solve the above problem using brute-force approach. Implement in your preferred language.You, Alice and Bob are working on recursive search algorithms and have been studying a variant of binary search called trinary search. Alice has created the following pseudocode for this algorithm: TSearch (A[a...b], t) If a b return -1 Let p1= a + Floor ((b-a)/3) If A[p1] t return p1 If A[p1]> t return TSearch (A[a...p1-1], t) Let p2 = a + Ceiling (2(b-a)/3) If A[p2] = t return p2 If A[p2]> t return TSearch (A [p1+1...p2-1],t) Return TSearch (A [p2+1...b],t) EndTSearch a) State a recurrence relation that expresses the number of operations carried out by this recursive algorithm when called on an input array of size n. b) Bob has heard that trinary search is no more efficient than binary search when considering asymptotic growth. Help prove him correct by using induction to show that your recurrence relation is in (log₂ n) as well. i. Split the tight bound into and upper (big-O) and lower (big-1). ii. For each bound select a function from (log₂ n) to use in your proof, like alog₂ n or…This is the illustration for the execution of the insertion-sort algorithm on the input sequence (12, 11, 13, 5, 6): look the picture sent Group of answer choices a) True b) False