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Unformatted text preview: – Does not qualitatively alter the growth rate of T ( n ) • The linear growth rate of the running time T ( n ) is an intrinsic property of algorithm arrayMax Last Updated: 10/01/12 5:45 AM CSE 2011 Prof. J. Elder  14  Constant Factors • On a logarithmic scale, the growth rate is not affected by – constant factors or – lowerorder terms • Examples – 10 2 n + 10 5 is a linear function – 10 5 n 2 + 10 8 n is a quadratic function Last Updated: 10/01/12 5:45 AM CSE 2011 Prof. J. Elder  15  Seven Important Functions • Seven functions that often appear in algorithm analysis: – Constant ≈ 1 – Logarithmic ≈ log n – Linear ≈ n – NLogN ≈ n log n – Quadratic ≈ n 2 – Cubic ≈ n 3 – Exponential ≈ 2 n • In a loglog chart, the slope of the line corresponds to the growth rate of the function. We will follow the convention that log n ! log 2 n ....
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 Fall '11
 Elder
 Polynomials, Derivative, Data Structures, #, Analysis of algorithms, Computational complexity theory, Linear function

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