COMPUTER SCIENCE ILLUMIN.-TEXT
COMPUTER SCIENCE ILLUMIN.-TEXT
7th Edition
ISBN: 9781284156010
Author: Dale
Publisher: Jones & Barlett
Question
Book Icon
Chapter 18, Problem 55E
Program Plan Intro

Big-O complexity measure for the polynomial:

The polynomial is a mathematical expression involving algebraic terms with one or more variables increased by co-efficient.

  • It is also called as the order of notation that represents the approximate computing time of the function as a notation.
    • It is the term in a function that increases with the size of the problem. The computing time is referred as the complexity.
    • The highest power in the polynomial represents the Big-O complexity of algorithm.
  • The size of problem and its complexity is represented on a power such as O (1), O (log2N), O (N), O (N log2N), O (N×N), .. O (2N), O (N!).
  • For example,
    • Consider the polynomial expression, f(N)=N3+ 50N2+ 10N + 25
    • In the above expression f(N) is of order N3, O(N3) in Big-O notation.
      • This expression states that for large values ‘N’ dominates the whole function.
      • But it does not mean that the remaining terms 50N2+ 10N + 25 is not important, it just becomes irrelevant when “N” becomes larger.

Explanation of Solution

b.

Given that,

The Big-O complexity measure for the polynomial x5+ x :

  • Since, the Big-O complexity is the highest power in the polynomial, the highest power in x5+ x is. x5
  • In Big-O notation it is represented as O(N5)

Explanation of Solution

c.

Given that,

The Big-O complexity measure for the polynomial x2+ 124578 :

  • Since, the Big-O complexity is the highest power in the polynomial, the highest power in x2+ 124578 is x2.
  • In Big-O notation it is represented as O(N2)

Explanation of Solution

d.

Given that,

The Big-O complexity measure for the polynomial x + 1 :

  • Since, the Big-O complexity is the highest power in the polynomial, the highest power in x + 1 is x.
  • In Big-O notation it is represented as O(N)

Blurred answer
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
Database System Concepts
Computer Science
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:McGraw-Hill Education
Text book image
Starting Out with Python (4th Edition)
Computer Science
ISBN:9780134444321
Author:Tony Gaddis
Publisher:PEARSON
Text book image
Digital Fundamentals (11th Edition)
Computer Science
ISBN:9780132737968
Author:Thomas L. Floyd
Publisher:PEARSON
Text book image
C How to Program (8th Edition)
Computer Science
ISBN:9780133976892
Author:Paul J. Deitel, Harvey Deitel
Publisher:PEARSON
Text book image
Database Systems: Design, Implementation, & Manag...
Computer Science
ISBN:9781337627900
Author:Carlos Coronel, Steven Morris
Publisher:Cengage Learning
Text book image
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education