given an array of n numbers all the same, we apply hoare-quicksort, lomuto, sort and heapsort separately to sort it into non decreasing order assume that size n is large, say n > 100
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given an array of n numbers all the same, we apply hoare-quicksort, lomuto, sort and heapsort separately to sort it into non decreasing order assume that size n is large, say n > 100
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- Consider the following sorting problem: you must reorder the elements of an array of numbersin-place so that odd numbers are in odd positions while even numbers are in even positions. Ifthere are more even elements than odd ones in A (or vice-versa) then those additional elementswill be grouped at the end of the array. For example, with an initial sequenceA = 50, 47, 92, 78, 76, 7, 60, 36, 59, 30, 50, 43The result could be this:A = 47, 50, 7, 92, 59, 78, 59, 76, 43, 92, 36, 60, 30, 50Please help me with this algorithm question. suppose we modified the QuickSort algorithm such that we run InsertionSort on the first 10% of A in the Partitionmethod. You may assume the selection of the pivot will be the last element in the range[p, r]. What would be the best and worst case running time of this new algorithm? Explainyour reasoning. // quickSort() method for integer array public void quickSort(int[] A, int p, int r) { if(p < r) { int q = partition(A, p, r); quickSort(A, p, q - 1); quickSort(A, q + 1, r); } } // partition() method for integer array public int partition(int[] A, int p, int r) { int x = A[selectPivot(A, p, r)]; int i = p - 1; for(int j = p; j < r; j++) { if(order) { if(A[j] > x) { i = i + 1; exchange(A, i, j); } } else { if(A[j] <= x) {…The analysis of the expected running time of randomized Quicksort assumes that all element values are distinct. In this problem, we examine what happens when they are not, i.e., there exist same-valued elements in the array to be sorted. The Quicksort algorithm relies on the following partition algorithm, which finds a pivot randomly, and then put all the numbers less than or equal to the pivot in the left, and put all the numbers greater than the pivot in the right, and then return the pivot location, as well as the left and right sublists for recursive calls. In this algorithm, the list to be sorted is A, and we use p and r to denote the left-most and right-most indices of the currently processing subarray, respectively. For example, in the initial call of the Quicksort algorithm, we will let p = 0 and r = n−1, which correspond to the whole original array. The PARTITION(A, p, r) procedure returns an index q such that each element of A[p : q −1] is less than or equal to A[q] and each…
- Consider a hybrid sorting algorithm that combines Mergesort with Insertion Sort.It uses Mergesort until the number of elements in the input becomes smaller than or equal to 8, after which it switches to Insertion Sort. What is the number of key comparisons performed by this hybrid sorting algorithm in the best case when running on an input array of size n? Briefly justify your answer. You could assume n = 2k, k is more than 3QuickSort is run for an array A in a manner that PARTITION consistently produces a 5:1 split for the (sub)arrays to be sorted (recursively) next. Picture the recurrence tree for this scenario ... What will be the length of the longest path from the root to a leaf (= deepest depth)in this tree? Group of answer choices log_5/6 (n) ... "log of n with base 5/6" log_6/5 (n) ... "log of n with base 6/5" log_6 (n) ... "log n with base 6" n^log_5(6) ... "n to the power of log_5(6)"Given an array of integers arr, sort the array by performing a series of pancake flips. In one pancake flip we do the following steps: Choose an integer k where 1 <= k <= arr.length. Reverse the sub-array arr[0...k-1] (0-indexed). For example, if arr = [3,2,1,4] and we performed a pancake flip choosing k = 3, we reverse the sub-array [3,2,1], so arr = [1,2,3,4] after the pancake flip at k = 3. Print out the k-values corresponding to a sequence of pancake flips that sort arr. Example 1: Input: arr = [3,2,4,1] Output: 4, 2, 4, 3 Explanation: We perform 4 pancake flips, with k values 4, 2, 4, and 3. Starting state: arr = [3, 2, 4, 1]. After 1st flip (k = 4): arr = [1, 4, 2, 3] After 2nd flip (k = 2): arr = [4, 1, 2, 3] After 3rd flip (k = 4): arr = [3, 2, 1, 4] After 4th flip (k = 3): arr = [1, 2, 3, 4], which is sorted. Another potential solution is: Output = 3, 4, 2, 3, 1, 2, 1, 1 with a similar explanation. All potential solutions that solve the problem are…
- 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?Using heapsort to sort [10,5,10,5] and [5,10,5,10], on which of the two arrays, the relative order of all the elements of the same values will be preserved? Can you show a working behind your answer? Options are: 1. only [10,5,10,5] 2. only [5,10,5,10] 3. none 4. both1. Consider the algorithm for the sorting problem that sorts an array by counting,for each of its elements, the number of smaller elements and then uses thisinformation to put the element in its appropriate position in the sorted array:ALGORITHMComparisonCountingSort(A[0..n − 1])//Sorts an array by comparison counting//Input: Array A[0..n//Output: Array S[0..n− 1] of orderable values− 1] of A’s elements sorted// in nondecreasing orderfor i ← 0 to nCount− 1 do[i]←0for i ← 0 to n − 2 dofor j ← i +1 to n − 1 doif A[i] < A[j ]Count[j ]← Count[j ] + 1else Count[i]← Count[i] + 1for i ←0 to n−1 doS[Count[i]]←A[i]return Sa. Apply this algorithm to sorting the list 60, 35, 81, 98, 14, 47.b. Is this algorithm stable?c. Is it in-place?
- Implement three sorting algorithms – mergesort, quicksort, and heapsort in the language of your choice and investigate their performance on arrays of sizes n = 102, 103, 104, 105, and 106. For each of these sizes consider: randomly generated files of integers in the range [1..n]. increasing files of integers 1, 2, ..., n. decreasing files of integers n, n − 1, ..., 1.Implement the following algorithms in Java: A) A variant of QUICKSORT which returns without sorting subarrays with fewer than k elements and then uses INSERTION-SORT to sort the entire nearly-sorted array (slide 24).B) A variant of QUICKSORT using the median-of-three partitioning scheme.Slide 24:•Cutoff to INSERTION-SORT (as in MERGE-SORT). Alternatively: −When calling QUICKSORT on a subarray with fewer than k elements, return without sorting the subarray −After the top-level call to QUICKSORT returns, run INSERTION-SORT on the entire array to finish the sorting process −Taking advantage of the fast running time of INSERTION-SORT when its input is “nearly” sorted •Tail call optimisation convert the code so that it makes only one recursive call −Usually good compilers do that for us • Iterative version with the help of an auxiliary stackApply Quick sort on a given sequence 7 11 14 6 9 4 3 12. What is the sequence after first phase, pivot is first element? 7 6 14 11 9 4 3 12 6 4 3 7 11 9 14 12 6 3 4 7 9 14 11 12 7 6 4 3 9 14 11 12 Quick sort follows Divide-and-Conquer strategy. True False Assume you have the array 7,9,6,10,3,5,8. What will the array look like after we call build-min-heap on the entire array? 3, 7, 5, 10, 9, 8, 6 3, 5, 6, 7, 8, 9, 10 3, 7, 5, 10, 9, 6, 8 10, 9, 8, 7, 6, 5, 3 3, 5, 7, 10, 9, 6, 8 Assume you have the following array: 30, 50, 20, 80, 10, 90, 100. Assume you were to select the quicksort pivot as the middle element of the array. What are the two sub-arrays to be sorted that result after one iteration of quicksort? 30, 50, 20, 10 | 90, 100 10, 20, 30, 50 | 90, 100 30, 50, 20, 10 | 100, 90 30, 20, 50, 10 | 100, 9