Prove corectness of following Bubble Sort algorithmhased on Loop invarlunt. Cicurly Stale loop invorantdunny your proo fBubble Sort CA CO.. n-)//Soits given array by hubhle Sort/ Input : An array ACO..n-i]of orderable elementsIloutput : Array (O...n-Sortcd in increaring orcderfor ito to n-2 doefor j Eo to n-2-i dojeif A[j+]

Invariant: something that is always true After finding a candidate loop invariant, we prove:…

Prove correctness of following Bubble Sort agorithm hased on Loop invariunt. Clearly State loop invoriant dunny your proo f. Bubble Sort CA CO. n-) // Sorts given aray by hubhle Sort Input : An array ACO.n-1]of orderable elements Iloutput : Array CO...n- sortcd in increasing order for it o to n-2 do for j Eo to n-2-i do if A[i+]

Prove correctness of following Bubble Sort agorithm hased on Loop invariunt. Clearly State loop invoriant dunny your proo f. Bubble Sort CA CO. n-) // Sorts given aray by hubhle Sort Input : An array ACO.n-1]of orderable elements Iloutput : Array CO...n- sortcd in increasing order for it o to n-2 do for j Eo to n-2-i do if A[i+]

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Analyze the otherSort sorting function. What is its time- complexity in terms of the size of the input array it sorts if the array is in random, unsorted order? T *otherSort(T *arr, int N) { for (int idxUnsorted = 1; idxUnsorted 0) && (arr[idxCursor T cur = 1] > cur)) { arr[idxCursor 1]; arr[idxCursor] idxCursor--; arr[idxCursor] = cur; return arr; O (log n) 0 0 (n²) O (n!) O (n)
In searching an element in an array, linear search can be used, even though simple to implement, but not efficient, with only O(n) time complexity. Assuming the array is already in sorted order, modify the search function below, using a better algorithm, so the average time complexity for the search function is O(log n). include <iostream> using namespace std; int search(int al), int s, int v) { 1/ Modify below codes. for (int i = 0; i <s; i++) { if (a[i] = v) return i; return -1; int main() { int intArray:10] = { 5, 7, 8, 9, 10, 12, 13, 15, 20, 34); // Search for element '12' in 10-elements integer array. cout << search(intArray, 10, 12); // '5' will be printed out. // Search for element '35' in 10-elements integer array. cout << search(intArray, 10, 35); // '-1' will be printed out. // Index '-l' means that the element is not found. return 0;
array unordered Arr has unsorted integers. SortedArr is an integer array. SortedArr performs which task better than unsortedArr? Use the fastest algorithms. Inserting a new element II Searching for a given element III Calculating the mean of the elements (A) I alone (B) II alone (C) III alone (D) I and II alone (E) I, II, and III
During each iteration of Quick Sort algorithm, the first element of array is selected as a pivot. The algorithm for Quick Sort is given below. Modify it in such a way that last element of array should be selected as a pivot at each iteration. Also explain the advantages.
▲Exercise 15. Consider the following max-heap H= (37, 12, 30, 10, 3, 9, 20, 3, 7, 1, 1, 7, 5) Write the exact output of the following Extract-All algorithm run on H Extract-All(H) Heap-Extract-Max(H) 1 while H. heap-size > 0 1 if H. heap-size > 02 k=H[1] Heap-Extract-Max (H) for i=1 to H. heap-size output H[i] 4 output "." end-of-line 5 return k 3 H[1] =H[H. heap-size] H. heap-size=H. heap-size-1 Max-Heapify(H) 23456 Answer:
Quicksort is a powerful divide-and-conquer sorting algorithm that almost always runs in O(nlogn) time,though it can run in O(n^2) time for certain input arrays, depending on how we choose the pivot. For this question assume that the pivot isalwaysthe last (right-most) element of the input array.There are two main ways that we can code the PARTITION procedure: the Lomuto method and the Hoare method. Question: Clearly explain how the two partition methods work – the Lomuto method and the Hoare method, and how they are different. Finally apply both methods to partition the arrayA= [2, 8, 7, 1, 3, 5, 6, 4], using the pivot A[8] = 4.
CodeGiven an unsorted array A of size N that contains only positive integers, find a continuous sub-array that adds to a given number S and return the left and right index(1-based indexing) of that subarray. In case of multiple subarrays, return the subarray indexes which come first on moving from left to right. Note:- You have to return an ArrayList consisting of two elements left and right. In case no such subarray exists return an array consisting of element -1.
Consider this alogrithm:// pre: array A of length n, each A[i] is picked randomly uniformly// from the set {0,1,2,3,4,5,6,7,8,9}.// post: return the index of the first occurrence of "check digit" of A// (already computed in the code)// return -1 if check digit is not foundint FindCheckDigit(A) {check_digit = 0for (i=0; i < n; i++) check_digit = check_digit + A[i]check_digit = check_digit % 10 # % means remainder of divisionfor (i = 0; i < n; i++) { if (A[i] == check_digit) { return i }}return -1;}Compute the average runtime for this algorithm. Show all details of your computation for both loops.
Bubble Sort is a popular, but inefficient sorting algorithm. It works by repeatedly swapping adjacent elements that are out of order. Prove the correctness of following Bubble Sort algorithm based on Loop Invariant. Clearly state your loop invariant during your proof.
Linear Sort HereDATA is anarraywith Nelements. This algorithm sorts theelements. The algorithms sortthe elements in DATA. Algorithm A2: (Linear Sort)Linear(DATA,N) Repeatstep2and 3 forK=1 to N-1 Set PTR :=K+1 [Initialize pass pointerPTR] Repeat whilePTR£ N [Execute Pass](a).IfDATA[K]> DATA[PTR], then: Interchange DATA[K] andDATA [PTR][End ofIfstructure] (b)Set PTR: =PTR+1 [End ofinnerloop] [End ofstep 1 outer loop] Exit SelectionSort Selectionsortperformssortingbyrepeatedlyputtingthelargestelementintheunprocessedportion of thearrayto the end ofthe unprocessedportion until the whole arrayis sorted. Algorithm A2: (Selection Sort) SELECTION(A,N)This algorithm sorts thearrayA with Nelements. Initialize aloop: For(i =0;i <N; i++)SetMIN:=A[i] Initialize anotherloopFor(j =i+1 ; j<N ; j++) If (MIN >A[j]) SWAP(MIN,A[j]) Exit InsertionSort…
Linear Sort HereDATA is anarraywith Nelements. This algorithm sorts theelements. The algorithms sortthe elements in DATA. Algorithm A2: (Linear Sort)Linear(DATA,N) Repeatstep2and 3 forK=1 to N-1 Set PTR :=K+1 [Initialize pass pointerPTR] Repeat whilePTR£ N [Execute Pass](a).IfDATA[K]> DATA[PTR], then: Interchange DATA[K] andDATA [PTR][End ofIfstructure] (b)Set PTR: =PTR+1 [End ofinnerloop] [End ofstep 1 outer loop] Exit SelectionSort Selectionsortperformssortingbyrepeatedlyputtingthelargestelementintheunprocessedportion of thearrayto the end ofthe unprocessedportion until the whole arrayis sorted. Algorithm A2: (Selection Sort) SELECTION(A,N)This algorithm sorts thearrayA with Nelements. Initialize aloop: For(i =0;i <N; i++)SetMIN:=A[i] Initialize anotherloopFor(j =i+1 ; j<N ; j++) If (MIN >A[j]) SWAP(MIN,A[j]) Exit InsertionSort…
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