Write a recursive function named merge_sort that sorts a given list using the recursive algorithm of merge sort. Implement and use the helper function _merge , which merges two sorted arrays. Sample Output > merge_sort([10, 32, 83, 2, 72, 100, 32]) [2, 10, 32, 32, ] > merge_sort(['a','g','a','t','e']) ['a','a','g','e', 't'] In [ ]: def _merge(P, Q): ""merges two sorted arrays INPUT: * P. 0 - the two sorted arrays OUTPUT: a sorted list consisting of elements in P and Q pass In [ ]: def merge_sort(array): ""sorts a given list INPUT: * array - the list OUTPUT: a sorted copy of the list. pass
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- Need help with sml languege I need to write a binarySearch function that recursively implements the binary search algorithm to search a sorted integer list for a specified integer and returns true if it is found, false otherwise. For example, binarySearch ([100,200,300,400,500], 200) returns true, whereas binarySearch([100,200,300,400,500], 299) returns false. Hint: Write a helper function mid that returns a tuple (index, value) representing the middle value in a list. For example, mid [10, 2, 40, 8, 22] returns (2,40) because the value 40 at index 2 is the middle value in the list. Similarly, mid [10, 20] would return (1, 20). Use mid in conjunction with slice to implement binarySearch. Here is my slice function: fun count(index,hd::tl,start,stop) =if index+1 >= stop then hd::nilelse if index >= start then hd::count(index+1,tl,start,stop)else count(index+1,tl,start,stop);fun slice(x::y, start, stop) = count(0,x::y,start,stop); And here is the dummy implementation of binary…Write a function sort_and_return_in_pairs_list for example:[12, 13, 11, 15] return =>(11.12) and (12,13)[14,19,16,18,17,15] return =>(14.15) (16.17) (18.19)1. a function that takes in a list (L), and creates a copy of L. note: The function should return a pointer to the first element in the new L. [iteration and recursion]. 2. a function that takes in 2 sorted linked lists, and merges them into a single sorted list. note: This must be done in-place, and it must run in O(n+m).
- Java Merge Sort but make it read the data 12, 11, 13, 5, 6, 7 from a file not an array /* Java program for Merge Sort */ class MergeSort { // Merges two subarrays of arr[]. // First subarray is arr[l..m] // Second subarray is arr[m+1..r] void merge(int arr[], int l, int m, int r) { // Find sizes of two subarrays to be merged int n1 = m - l + 1; int n2 = r - m; /* Create temp arrays */ int L[] = new int[n1]; int R[] = new int[n2]; /*Copy data to temp arrays*/ for (int i = 0; i < n1; ++i) L[i] = arr[l + i]; for (int j = 0; j < n2; ++j) R[j] = arr[m + 1 + j]; /* Merge the temp arrays */ // Initial indexes of first and second subarrays int i = 0, j = 0; // Initial index of merged subarray array int k = l; while (i < n1 && j < n2) { if (L[i] <= R[j]) { arr[k] = L[i];…Write a recursive function named binarySearch that accepts a reference to a sorted vector of integers and an integer target value and uses a recursive binary search algorithm to find and return an index at which that target value is found in the vector. If the target value is not found in the vector, return -1. The following code shows some example calls and their expected return values: // index 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16vector<int>v {-4, 2, 7, 10, 15, 20, 22, 25, 30, 36, 42, 50, 56, 68, 85, 92, 103};intindex=binarySearch(v, 42); // 10intindex=binarySearch(v, 66); // -1 You should assume that the vector's elements are already sorted; you do not need to handle the case of an unsorted vector. Your function must be recursive and must use a binary search algorithm. Do not use loops or auxiliary data structures.a. It was remarked in this chapter that the performance of bubble sort can be improved if we stop the sorting process as soon as we find that in an iteration no swapping of elements take place. Write a function that implements bubble sort algorithm using this fact. b. Using the algorithm that you designed in part (a), find the number of iterations that are needed to sort the list: 65, 14, 52, 43, 75, 25, 80, 90, 95.
- Write a recursive version of this code. one in which n is divided by two. public static <T extends Comparable<T>> void MergeSorting(T[] arr) {T[] tep = (T[]) new Comparable[arr.length];MergeSorting(arr, tep, 0, arr.length - 1);}//Recursive helper method for the merge sort algorithm.//arr The array to sort//tep Temporary array for merge operation//start Index of the left end of the region to sort //end Index of the right end of the region to sort. private static <T extends Comparable<T>> void mergeSort(T[] arr, T[] tep, int start,int end) {if (start >= end) {return;}int middle = (left + right) / 2;MergeSorting(arr, tep, start, middle); // first halfMergeSorting(arr, tep, middle + 1, end); //second halfMerge(arr, tep, start, middle, end);}private static <T extends Comparable<T>> void Merge(T[] arr, T[] tep, int start, int middle,int end) {for (int i = start; i <= end; i++) {tep[i] = arr[i];//adds the arry to tep}int a = 0;int b = middle + 1;for…the language is C++, please take a screenshot of your output. (Recursive binary search) The binary search algorithm given in this chapter is nonrecursive. Write and implement a recursive version of the binary search algorithm. Also, write a version of the sequential search algorithm that can be applied to sorted lists. Add this operation to the class orderedArrayListType for array-based lists. Moreover, write a test program to test your algorithm.Rewrite the Binary search function in the textbook to use a generic type for the array elements. Test the function with arrays of int, double, and string values. *When using test arrays make sure elements are stored in ascending sorted order*
- Write a c++ recursive function to find an element in a sorted array using Binary Search. A[] = {1, 2, 3, 4, 5, 6, 7, 8}; Target = 71. Implement a generic version of Bubble sort, Selection sort and Quick sort algorithms (use static method). 2. During the implementations count how many comparisons each algorithm required for performing ascending order sorting. Print that count. 3. Test your algorithms by taking two random list: one will take Double type value and other will take String type value (this will verify your generic implementation). Invoke each of the sorting algorithm by passing one list at a time and display both the original list and the sorted list.Modify the following code code so the code can -normalize the list (divide all by the maximum) - insert a bubble and merge sort and compare the counter to see which one it is the fastest sorting. #include <bits/stdc++.h> using namespace std; int largest(int arr[], int n) { int i; // Initialize maximum element int max = arr[0]; for (i = 1; i < n; i++) if (arr[i] > max) max = arr[i]; return max; } int smallest(int arr[], int n) { int i; // Initialize minimum element int min = arr[0]; for (i = 1; i < n; i++) if (arr[i] < min) min = arr[i]; return min; } double average(int a[], int n) { int sum = 0; for (int i=0; i<n; i++) sum += a[i]; return (double)sum/n; } // Driver Code int main() { int arr[] = {8, 9, 10, 12, 13}; int n = sizeof(arr) / sizeof(arr[0]); cout << "Largest in given array is " << largest(arr, n); cout << "\nSmallest in given array is " << smallest(arr, n); cout <<…