For the storing files on tape problem (without frequencies), why does sorting by smallest file size produce the best lookup cost in expectation? Because, for any two files with equal file size, it does not matter what order they are in Because, sorting them is greedy and greedy algorithms usually work Because, for any two files with the larger file preceding the smaller, swapping the files reduces the cost in expectation Because, for any three files that are out-of-order a random permutation of those files reduces the cost in expectation

For the storing files on tape problem (without frequencies), why does sorting by smallest file size produce the best lookup cost in expectation? Because, for any two files with equal file size, it does not matter what order they are in Because, sorting them is greedy and greedy algorithms usually work Because, for any two files with the larger file preceding the smaller, swapping the files reduces the cost in expectation Because, for any three files that are out-of-order a random permutation of those files reduces the cost in expectation

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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Implement a quicksort based on using a sample of size 2k 1. First, sort the sample, then arrange to have the recursiveroutine partition on the median of the sample and to move the two halves of the rest ofthe sample to each subarray, such that they can be used in the subarrays, without havingto be sorted again. This algorithm is called samplesort.
When choosing the last item of a sequence as the pivot, the QuickSort algorithm will yield its worst case performance of O(n2) when it is passed a sorted list as input. Using the media-of-three approach for pivot select, the QuickSort algorithm will execute on an already-sorted list in O(nlog n). Explain why Quicksort runs in O(n2) on an already-sorted list when choosing the last item of the sequence as the pivot. You must provide a recurrence relation or recursion tree as part of your answer. Provide an input sequence of 10 integers that, when passed to the QuickSort algorithm, would lead to the worst case running time of O(n2) whether pivot selection is performed using the median-of-three approach, or the pivot is selected as the last item in the sequence.
Suppose you have m sorted arrays, each with n elements, and you want to combine them into a single sorted array with mn elements. 1. If you do this by merging the first two arrays, next with the third, then with the fourth, until in the end with the last one. What is the time complexity of this algorithm, in terms of m and n? 2. Give a more efficient solution to this problem, using divide-and-conquer. What is the running time?
A sequential search of a sorted list can halt when the target is less than a given element in the list. Define a modified version of this algorithm and state the computational complexity, using big-O notation, of its best-, worst-, and average- case performances.
Please explain What is the worse-case performance of quicksort? Select the correct answer with the correct justification. Group of answer choices a. O(n*n), because during the partitioning stage it is possible that we select a 'bad' random pivot point that only sorts one item at a time. If we continuously do this over and over again, we are effectively only sorting 1 item each time. We then need to perform this pivot step n more times to sort the remaining n-1 items, thus giving us an O(n*n) complexity. b. O(n*n), because quicksort is a comparison-based sorting algorithm in which we have to compare every possible element against every other element in order to swap each element into the correct position. c. O(n*log(n)), because each time we are selecting a pivot point, on the average-case we are able to split our problem into roughly two collections, and sort half of our elements at the pivot point.
Empirically, using time measurements, test your algorithm and plot a graph that shows its growth rate when variating the size.
Suppose that you choose a random integer between 0 and N-1in our shuffling code instead of one between i and N-1. Show that the resulting order isnot equally likely to be one of the N! possibilities. Run the test of the previous exercisefor this version.Suppose that you choose a random integer between 0 and N-1in our shuffling code instead of one between i and N-1. Show that the resulting order isnot equally likely to be one of the N! possibilities. Run the test of the previous exercisefor this version.
The quick-union algorithm we know that a sequence of n operations (unions and finds) can take slightly more than linear time in the worst case. Explain why if all the finds are done before all the unions, a sequence of n operations is guaranteed to take 0(n) time?
Given a sorted array of n comparable items A, and a search value key, return the position (array index) of key in A if it is present, or -1 if it is not present. If key is present in A, your algorithm must run in order O(log k) time, where k is the location of key in A. Otherwise, if key is not present, your algorithm must run in O(log n) time.
The partitioning method yields what values for (A), (B), and (C)? Inputs: none Outputs: y, z S yz = 10 yz = 11 A= 11, B=t, C = G1 O A = 10, B = t, C = G1 O A11, B = s, C = G2 O A = 10, B = s, C = G2 yz = 10 G1 yz = (A) G2 y = 11 State (B) u State Next state: Group t: (C) + Next state: Group
Problem 2. Suppose we have an array A[1 : n] which consists of numbers {1,...,n} written in some arbitrary order (this means that A is a permutation of the set {1,...,n}). Our goal in this problem is to design a very fast randomized algorithm that can find an index i in this array such that A[i] mod 8 € {1,2}, i.e., the reminder of dividing A[i] by 8 is either 1 or 2. For simplicity, in the following, we assume that n itself is a multiple of 8 and is at least 8 (so a correct answer always exist). For instance, if n = 8 and the array is A = [8,7, 2,5, 4, 6,3, 1], we want to output either of indices 3 or 8. (a) Suppose we sample an index i from {1,...,n} uniformly at random. What is the probability that i is a correct answer, i.e., A[i] mod 8 E {1,2}? (b) Suppose we sample m indices from {1,...,n} uniformly at random and with repetition. What is the probability that none of these indices is a correct answer? Now, consider the following simple algorithm for this problem: Find-Index-1(A[1:…