Considering the sorting problem, we have a list of n integers A = (v1, V2, · · · Vn). We want to sort the array using insertion sort whose pseudo-code is as follows: note n := A.length denotes the size of the array, number of items. Algorithm 2 INSERTION-SORT(A) for i = 1 to n – 1 do - j+i- 1 while A[j] > A[j+1] ^ j 2 0 do swap (A[j], A[j + 1]) j+j-1 ond uhilo

Considering the sorting problem, we have a list of n integers A = (v1, V2, · · · Vn). We want to sort the array using insertion sort whose pseudo-code is as follows: note n := A.length denotes the size of the array, number of items. Algorithm 2 INSERTION-SORT(A) for i = 1 to n – 1 do - j+i- 1 while A[j] > A[j+1] ^ j 2 0 do swap (A[j], A[j + 1]) j+j-1 ond uhilo

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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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.
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Pseudo Code shown in Figure Q1(a) is an algorithm for binary searching for an array with n number of elements. By applying this algorithm, show step by step approach on how to find number 11 in an array as depicted in Figure Q1(b). low + 0 high e n-1 while (low s high) do ix + (low + high) /2 if (t = Alix)) then return ix else if (t < A[ix]) then high e ix - 1 else low + ix + 1 return -1 Figure Ql(a) 2 4 6 9 11 12 | 25 [0] [1) [2] [3] (4) [5) [6] Figure Q1(b)
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;
01... ""Implementation of the Misra-Gries algorithm.Given a list of items and a value k, it returns the every item in the listthat appears at least n/k times, where n is the length of the array By default, k is set to 2, solving the majority problem. For the majority problem, this algorithm only guarantees that if there isan element that appears more than n/2 times, it will be outputed. If thereis no such element, any arbitrary element is returned by the algorithm.Therefore, we need to iterate through again at the end. But since we have filtredout the suspects, the memory complexity is significantly lower thanit would be to create counter for every element in the list. For example:Input misras_gries([1,4,4,4,5,4,4])Output {'4':5}Input misras_gries([0,0,0,1,1,1,1])Output {'1':4}Input misras_gries([0,0,0,0,1,1,1,2,2],3)Output {'0':4,'1':3}Input misras_gries([0,0,0,1,1,1]Output None"""..
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5. In this modified version of the longest increasing subsequence algorithm, we use D[i] to store the length of the longest increasing subsequence beginning with A[i]. Will the algorithm find the length of the longest increasing subsequence correctly? LONGEST-SUBSEQUENCE (A) n = A.length Let D[1.. n] be a new array D[n] = 1 for i = n- 1 downto 1 D[i] = 1 for j = i+1 to n if A[i] D[i] D[i) = D[j] + 1 %3D Print D[i] L = 0 for i = 1 to n if D[i] > L L = D[i] Print L For the following array: A[1] = 7, A[2] = 18, A[3] = 11, A[4] = 4, A[5] = 12, what will be the output of the algorithm?
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Answer d) Prove that the algorithm is actually correct
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