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
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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)
Transcribed Image Text: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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