Prove Proposition H. Bottom-up mergesort uses between ½ N lg N and N lg N compares and at most 6N lg N array accesses to sort an array of length N.
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Prove Proposition H. Bottom-up mergesort uses between ½ N lg N and N lg N compares
and at most 6N lg N array accesses to sort an array of length N.
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- Write an algorithmic faster version of this code. So the version that copies values from the first sorted half to a temp array then merges the values from the temp arr and the second sorted half into the original arr. 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,…PLEASE DRAW IT. IT IS NOT CODINGwe'll be working with the following set of nine numbers for binary searches set below:4, 10, 15, 18, 23, 26, 30, 34, 40Our objective is to pinpoint the number 26 within this array.The initial segment will comprehensively explain how to conduct a linear search to locate the number 26 within this array.
- We apply the binary search on a 17-element ordered array. Assume that a givenkey appears in the array, and it is between the 5th element and the 13th element(inclusive). How many comparisons do we need for the average-case efficiency?Write a program to compute the exact value of the number of array accesses usedby top-down mergesort and by bottom-up mergesort. Use your program to plot the values for N from 1 to 512, and to compare the exact values with the upper bound 6N lg N.Let M(n) be the minimum number of comparisons needed to sort an array A with exactly n ele- ments. For example, M(1) = 0, M(2) = 1, and M(4) = 4. If n is an even number, clearly explain why M(n) = 2M(n/2) + n/2.