225_08_bounds - MathematicsofAlgorithmAnalysis 450 400 350...

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1 0 50 100 150 200 250 300 350 400 450 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Mathematics of Algorithm Analysis
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2 Outline Lower bounds and upper bounds on functions. Terminology for talking about the amount of time or  space that an algorithm uses.
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3 Picture from http://archives.math.utk.edu/visual.calculus/4/riemann_sums.3/microcalc.html The area in the red boxes is a  lower bound  for the area  under the yellow curve.
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4 Picture from http://archives.math.utk.edu/visual.calculus/4/riemann_sums.3/microcalc.html The area in the red boxes is an  upper bound  for the area  under the yellow curve.
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5 0 10 20 30 40 50 60 70 80 90 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 The function  2n  is a lower bound for  3n , and  4n  is an  upper bound (n ≥ 0).
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6 0 50 100 150 200 250 300 350 400 450 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 n 2  /4            ≤    n (n+1)/2     ≤    n 2    for n ≥ 0. lower bound                            upper bound
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7 Definition: Lower bound. A func tio n f(x) is  a   lower bound  for g(x) over a range R if for  all x in R, f(x) ≤ g(x).  Definition: Upper bound. A func tio n f(x) is  a n 
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This note was uploaded on 01/15/2012 for the course CSC 225 taught by Professor Valerieking during the Spring '10 term at University of Victoria.

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225_08_bounds - MathematicsofAlgorithmAnalysis 450 400 350...

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