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. fl(n)=n°,

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. fl(n)=n°,

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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Number theory is one of the most appealing topics in mathematics. Given one or more numeric values, a numeric algorithm performs some computation. The use of number theory in computing is important for applications like in the case of cryptographic algorithms. Number theory is also used in various applications such as calculating hash functions or in information security. Euclid’s algorithm is one of the oldest number-theoretic algorithms which is used to calculate the greatest common divisor of two numbers.

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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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