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Chapter 4

Chapter 4. Analysis Tools. Why we Analyze Algorithms. We try to save computer resources such as : Memory space used to store data structures, Space Complexity CPU time , which is reflected by Algorithm Run Time Complexity. 4.1 Seven Functions. The Constant Function: f(n)= c,

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The Growth of Functions

The Growth of Functions. Section 3.2. Section Summary. Donald E. Knuth ( Born 1938 ). Big-O Notation Big-O Estimates for Important Functions Big-Omega and Big-Theta Notation. Edmund Landau ( 1877-1938 ). Paul Gustav Heinrich Bachmann ( 1837-1920 ). The Growth of Functions.

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1.64k views • 25 slides

CPSC 411 Design and Analysis of Algorithms

CPSC 411 Design and Analysis of Algorithms. Andreas Klappenecker. Goal of this Lecture. Recall the basic asymptotic notations such as Big Oh, Big Omega, Big Theta. Recall some basic properties of these notations Give some motivation why these notions are defined in the way they are. .

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General rules: Find big-O

General rules: Find big-O. f (n) = k = O(1) f ( n ) = a k n k + a k-1 n k-1 + . . . + a 1 n 1 + a 0 = O( n k ) Other functions, try to find the dominant term according to the growth rate of the well known functions Example f(n)=5n 2 +2 n f(n)=5n 2 +3nlog(n).

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179 views • 9 slides

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Big omega notation - PowerPoint PPT Presentation

Chapter 4

The Growth of Functions

CPSC 411 Design and Analysis of Algorithms

General rules: Find big-O