Ex. 3 algorithms as n → o. Each algorithm takes a natural number n as input. Write down the time that each loop requires, the equation describing the overall complexity, and the final result (e.g. T(n) = 5n +2n2 = O(n²)). What is the time complexity, in terms of O notation, of the following Algorithm 1 i = 1 while i < 4n³ i = i+2 4 i = 2vi 1 3 5 while i > 5 for j = i to i + 10 i = i – 1 8 for i = 1 to log n2 for j = 1 to n · i %3D 9. %3D 10 x = 0

Ex. 3 algorithms as n → o. Each algorithm takes a natural number n as input. Write down the time that each loop requires, the equation describing the overall complexity, and the final result (e.g. T(n) = 5n +2n2 = O(n²)). What is the time complexity, in terms of O notation, of the following Algorithm 1 i = 1 while i < 4n³ i = i+2 4 i = 2vi 1 3 5 while i > 5 for j = i to i + 10 i = i – 1 8 for i = 1 to log n2 for j = 1 to n · i %3D 9. %3D 10 x = 0

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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Question

Ex. 3
What is the time complexity, in terms of O notation, of the following
algorithms as n → 0. Each algorithm takes a natural number n as input. Write down
the time that each loop requires, the equation describing the overall complexity, and
the final result (e.g. T(n) = 5n + 2n? = 0(n²)).
Algorithm 1
1 i = 1
2 while i < 4n³
i = i +2
2Vi
3
4
i
5 while i > 5
for j = i to i + 10
i — і — 1
6.
7
1 to log n2
for j = 1 to n· i
8 for i
9.
10
x = 0

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