Let Y = (y1, Y2,..., Yn) and Z = (21, 2,..., Zk) be two different sequences. Write pseudocode for an algorithm that has complexity O(n) and checks whether Z is a subsequence of Y. If Z is a subsequence of Y, the algorithm should return an array I storing a subset of indices in Y that correspond to the subsequence Z (i.e., I = [i1, 12, .. algorithm should return false. Explain your algorithm and why it is correct, and prove that its runtime is O(n). ik] such that z4 = Yi, and i < iz < ...< ik). Otherwise, the

Let Y = (y1, Y2,..., Yn) and Z = (21, 2,..., Zk) be two different sequences. Write pseudocode for an algorithm that has complexity O(n) and checks whether Z is a subsequence of Y. If Z is a subsequence of Y, the algorithm should return an array I storing a subset of indices in Y that correspond to the subsequence Z (i.e., I = [i1, 12, .. algorithm should return false. Explain your algorithm and why it is correct, and prove that its runtime is O(n). ik] such that z4 = Yi, and i < iz < ...< ik). Otherwise, the

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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Write an algorithm that, given an array, initialises all the elements so that thecontent of each element is the index (i.e. A[i] contains i), then multiplies all theelements of the array together to give the result.
Given a sorted array of integers, write a program to implement the Binary Search Algorithm and find the index of a target element in the array. If the target element is not found, return -1. a) Explain the working principles and steps involved in the Binary Search Algorithm. b) Implement the Binary Search Algorithm in a programming language of your choice. c) Analyze the time complexity of the Binary Search Algorithm. d) Provide a test case to demonstrate the correctness of your implementation.
Let A be an array of size n storing positive integers. Write an algorithm(pseudo code) that takes array A and replaced each unique element of A by-1. For example, if A=(5,20,41,5,35,6,6) then after you run the algorithm, A=(5,-1,-1,5,-1,6,6). Compute time complexity of your algorithm.
in C++ Given an array A and a positive integer k, the selection problem amounts to finding the largest element x ∈ A such that at most k elements of A are less than or equal to x, or nil if no such element exists. A simple way to implement it is as follows: SimpleSelection(A, k) 1 if k > A.length 2 return nil 3 else sort A in ascending order 4 return A[k] Write another algorithm that solves the selection problem by sorting (using selection and bubble sort) A. Also, illustrate the execution of the algorithm on the following input by writing its state at each main iteration. A = (29, 28, 35, 20, 9, 33, 8, 9, 11, 6, 21, 28, 18, 36, 1) k = 6
: 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;
Given an unsorted array A of integers of any size, n ≥ 3, and an integer value x, write an algorithm as a pseudo code (not a program!) that would find out if there exist EXACTLY3 occurrences in the array with value x. What is the time complexity of your algorithm, in terms of Big-O? What is the space complexity of your algorithm, in terms of Big-O? What if , the given array A is sorted. Will time complexity change from the case that A was unsorted? • If yes; give a new algorithm that achieves this better complexity (indicate the time complexity as of that algorithm). • If no, explain why such new constraints/conditions cannot lead to a better time complexity.
Let A[1...n,1...n] be a 2D array of positive integers with n rows and n columns. Let ArraySum(a,b,c,d) be the sum of all the elements of A[a...b, c...d] (i.e., the submatrix of A with rows a to b and columns c to d). Write down a recursive formula for ArraySum(a,b,c,d) and analyze the time complexity of the corresponding recursive algorithm. You must write a formal recursive formula including the base case and general recursive step.
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Write an algorithm that returns the index of the first item that is less than its predecessor in an array s[1],….,s[n].
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