1. A.,. Give a Big-O estimate that is as good as possible for each of the following functions. (n³ + n)(logn+ n) ii. (n + 1000)(logn + 1) i. If these are complexities of algorithms that solve the same problem, which one would you prefer? Why? В. C. Considering the Big-O complexity, how many times is your choice faster with respect to the other solution for an input size of 216? Note: The base of logarithm is 2.

1. A.,. Give a Big-O estimate that is as good as possible for each of the following functions. (n³ + n)(logn+ n) ii. (n + 1000)(logn + 1) i. If these are complexities of algorithms that solve the same problem, which one would you prefer? Why? В. C. Considering the Big-O complexity, how many times is your choice faster with respect to the other solution for an input size of 216? Note: The base of logarithm is 2.

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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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.
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Give the approximate running times of the following algorithms (a.k.a. functions) using Θ-notation, and prove it by using upper bound and lower bound.
Consider the following functions as time complexities of some algorithms. (a) First write the worst-case runtime of each algorithm in Big-O notation. (b) Then arrange functions from low to high (Consider their Big-O notations as you arrange them; as n grows, the function that grows slower should come sooner than the one that grows faster). (c) Arbitrary, select TWO of arrangements in part (b) and for each one of them justify why you have chosen such an ordering for the corresponding function. Provide formal proof. For example if fl<=f2<= f3<= f4<=f5 you may choose to formally justify why (1) fl<=f2 and why (2) f4<=f5 . fI(n)=n², f2(n)=210 nlogn, f3(n)=3", f4(n)=n, f5(n)=1, f6(n)=5*logn, f7(n)= n", f8(n)=4 n*n, f9(n)=2log(n³)
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Below is a list of functions that commonly appear in complexity analyzes as a function of the size n of the problem. Sort the functions in ascending order of growth rate, that is, the slowest growing one is 1, and so on. Note that the functions are described in the notation O(.), which represents the cost of the algorithm as a function of the predominant term of the cost expression.
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5. Practice with RSA algorithma. Pick two prime numbers p, q, for example,• const int P=23;• const int Q=17;• int PQ=P*Q; b. Find a e that is relatively prime with (p-1)(q-1)Call RelativelyPrime () c. Calculate the inverse modulo (p-1)(q-1) of e to be your dUse inverse () c++