Consider the following implementation of a bubble sort. Given an array a] containing n val-ues, the algorithm repeatedly scans the list from top to bottom. In each pass, adjacent entriesare compared and swapped if they are in the wrong order. Assume that each instruction takesa constant amount of time.for (i=0; i

Complexity analysis of bubble sort: The total of comparisons in the bubble sort are as follows: n-1…

Answered: Consider the following implementation…

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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) Consider an n x n array ARR stored in memory consisting of 0’s and 1’s such that, in a row of ARR, all 0’s comes before any of 1’s in the row. Write an algorithm having complexity O(n), if exists, that finds the row that contains the most 0’s. Step by step explain r algorithm with an illustrative example. 6
Suppose that two n x n matrices A and B are stored on a mesh of n2 processors such that Pi;j holds A[i; j] and B[j; i]. Write pseudocode for an asynchronous algorithm that computes the product of A and B in O(n).
Make and implement a mergesort variation that gives an int[] array perm, where perm[i] is the index of the array's i th smallest element, rather than rearranges the array's elements.
an array of integers nums sorted in ascending order, find the startingand ending position of a given target value. If the target is not found in thearray, return [-1, -1]. For example:Input: nums = [5,7,7,8,8,8,10], target = 8Output: [3,5]Input: nums = [5,7,7,8,8,8,10], target = 11Output: [-1,-1].
Given an array A[0..n-1], prefix sum on array A is given by array PS[0..n-1] such that PS[i]=Pij=0 A[j]. Thus, PS[0] = A[0],PS[1] = A[0]+A[1], PS[2] = A[0]+A[1]+A[2], etc. One can find the prefix sum in parallel as follows using p processors: (i) partition the array into p subarrays, assigningprocessor Pi to the ith subarray, for 0 ≤ i ≤ p − 1, (ii) find local sums of individual subarrays, si, for 0 ≤ i ≤ p − 1, (iii)find prefix sums on the local sums, (iv) Pi uses the prefix sum value for the previous partition (i.e., Pi−1j=0 sj ) to calculatethe prefix sum of its own subarray. For Step (iii), one processor can do this, or all processors can replicate this process. Analyze the previous algorithm, i.e., find its Tp, Sp, Ep, cost, work, and its range of optimality (for whatrange does the algorithm achieves O(p) speedup).
Suppose we are comparing implementations of insertion sort and merge sort on the same machine. For inputs of size n, insertion sort runs in 8n2 steps, while merge sort runs in 32nlogn steps. For which values of n does insertion sort beat merge sort? Group of answer choices: 1. n < 1024 2. n > 1024 3. n < 16 4. n > 16 5. Merge sort is always better since O(nlogn) is better than O(n^2)
Describe an efecient in-place algorithm called Partition-Even-Odd(A) that partitions an array A in even and odd numbers. The algorithm must terminate with A containing all its even elements preceding all its odd elements. For example, for input A = [7, 17, 74, 21, 7, 9, 26, 10], the result might be A = [74, 10, 26, 17, 7, 21, 9, 7]. Partition-Even-Odd must be an in-place algorithm. What does this mean about your algorithm? (a) Write the pseudo-code for Partition-Even-Odd. (b) Characterize the complexity of Partition-Even-Odd. Brie y justify your answer. (c) Formalize the correctness of the partition problem as stated above, and prove that Partition-Even- Odd is correct using a loop-invariant.
Create and implement a mergesort variant that yields an int[] array perm instead of rearranging the array's entries, with perm[i] being the index of the array's i th smallest element.
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 3
Create a programme that generates the best-case array for sort() (with no duplicates). an array of N items with different keys with the characteristic that each partition produces subarrays that differ in size by no more than one (the same subarray sizes as would occur for an array of N equal keys). (Ignore the first shuffle for the sake of this exercise.)
Suppose that two matrices A and B with dimension n x n are stored on a 2D mesh of n2 processors such that P_(i,j) holds A[I,j] and B[j,i] . Write C-style pseudocode for an asynchronous algorithm that computes the product of A and B in O(n) time. (10 points) (WRITE THE PSEUDOCODE! IF YOU DON'T WRITE PSEUDOCODE, YOU WILL BE WRONG!! C-STYLE ONLY!!!)
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.

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