use excel Consider the following algorithms which approximate the solution y = by taking n =1,2, ... at every iteration.3n – 2Зп3 + 2A1: y*and A2:y*1 + 2vn2n3 + n'Use rates of convergence to determine which between A¸ and A, converges faster.

The idea of the fixed point iteration methods is to first reformulate a equation to an equivalent…

Consider the following adigorifhms which apprOximate the solution y 1,2, ... at every iteration. by faki 3n – 2 Зп3 + 2 A1:y* and A2:y* 1 + 2\n 2n3 + n' Use rates of convergence to determine which between A¸ and A, converges

Consider the following adigorifhms which apprOximate the solution y 1,2, ... at every iteration. by faki 3n – 2 Зп3 + 2 A1:y* and A2:y* 1 + 2\n 2n3 + n' Use rates of convergence to determine which between A¸ and A, converges

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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Suppose that an algorithm has runtime 20 n3 for n <= 100. For n>100, the slowest cases for each n take time 2 n2 log n. The fastest cases for each n take time 10 n2. That is, for n>100, runtime is between 10 n2 and 2 n2 log n. Which of the following are known to be true of the worst-case runtime for the algorithm? (Check all that apply, which may be more than one in a row.) O( n2 ) O( n2 log n ) O( n3 ) None of these Ω( n2 ) Ω( n2 log n ) Ω( n3 ) None of these Θ( n2 ) Θ( n2 log n ) Θ( n3 ) None of these Which of the following are known to be true of the average-case runtime? O( n2 ) O( n2 log n ) O( n3 ) None of these Ω( n2 ) Ω( n2 log n ) Ω( n3 ) None of these Θ( n2 ) Θ( n2 log n ) Θ( n3 ) None of these [Each row must have at least one answer checked.] Compose
A bottle factory produces bottles of equal mass. During a production, the weight of one of the bottles is set incorrectly. The factory scale will be used to find this bottle. Design a decrease-andconquer algorithm which finds the that bottle. Analyze the worst-case, best-case and average-case complexities of your algorithm. Explain your algorithm.
You are given a collection of n bolts of different widths and n correspondingnuts. You are allowed to try a nut and bolt together, from which you can determine whether the nut is larger than the bolt, smaller than the bolt, or matches the bolt exactly. However, there is no way to compare two nuts together or two bolts together. The problem is to match each bolt to its nut. Design an algorithm for this problem with an average-case efficiency ofΘ(n log n).
38. Suppose that, in a divide-and-conquer algorithm, we always divide an instance of size n of a problem into n subinstances of size n/3, and the dividing and combining steps take linear time. Write a recurrence equation for the running time T(n), and solve this recurrence equation for T(n). Show your solution in order notation.
Let m be a randomly chosen non-negative integer having at most n decimal digits, i.e. an integer in the range 0 sms 10" - 1. Consider the following problem: determine m by asking only 5- way questions, i.e. questions with at most 5 possible responses. For instance, one could ask which of 5 specific sets m belongs to. Prove that any algorithm restricted to such questions, and which correctly solves this problem, runs in time Q(n).
suppose a computer solves a 100x100 matrix using Gauss elimination with partial pivoting in 1 second, how long will it take to solve a 300x300 matrix using Gauss elimination with partial pivoting on the same computer? and if you have a limit of 100 seconds to solve a matrix of size (N x N) using Gauss elimination with partial pivoting, what is the largest N can you do? show all the steps of the solution
Given a real number x and a positive integer k, determinethe number of multiplications used to find x^(2^k)startingwith x and successively squaring (to find x^2, x^4, and soon). Is this a more efficient way to find x^(2^k)than by multiplying x by itself the appropriate number of times?
Please solve using iterative method: Solve the following recurrences and compute the asymptotic upper bounds. Assume that T(n) is a constant for sufficiently small n. Make your bounds as tight as possible. a. T(n) = T(n − 2) + √n b.T(n) = 2T(n − 1) + c
Let us assume that we have two algorithms A and B. Algorithm A has run time given by (10n)2 and algorithm B has run time given by (Sin2n + Cos2n +1)n where n is the input size. Also assume that both algorithms are run on the same computer. Find the smallest value of n for which the runtime of algorithm A is less than the run time of algorithm B.
Take into account the MAXMIN methodology below. It uses how many comparisons? Is it more likely to operate quicker or slower in practise than the divide-and-conquer algorithm? procedure The remark maxmin2(S) calculates the maximum and minimum of S[1..n] in max and min, respectively. 1. if n is odd then max:=S[n]; min:=S[n] 2. else max:=−∞; min:=∞ 3. for i := 1 to n/2 do 4. if S[2i − 1] ≤ S[2i] 5. then small:=S[2i − 1]; large:=S[2i] 6. else small:=S[2i]; large:=S[2i − 1] 7. if small < min then min:=small 8. if large > max then min:=small
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not handwritten Design a divide and conquer algorithm to solve the following problem in Θ(n log n) time: You are given a sequence A[1..n] of n numbers. Find i and j with i < j that maximizes A[j] − A[i].