Department of Computer and Information Science, School of Science, IUPUI

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Department of Computer and Information
Science,School of Science, IUPUI
CSCI 240
Analysis of Algorithms Growth Rates
Dale Roberts, Lecturer Computer Science,
IUPUI E-mail droberts_at_cs.iupui.edu
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Choosing n in t(n)

• The analysis of algorithms attempts to optimize
  some critical resource. The critical resource
  usually chosen is time, so t(n) represents a time
  function.
• t(n) is influenced by hardware and compiler.
  Other factors include the algorithm used and
  input to the algorithm.
• Parameter n, usually referring to number of data
  items processed, affects running time most
  significantly.
• n may be degree of polynomial, size of file
  to be sorted or searched, number of nodes in a
  graph, etc.

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Best Case, Worse Case and Average Case Defined

• Best case is amount of time program would take
  with best possible input configuration
• best case is found for input and easier to find
  not usually the metric chosen
• Worst case is amount of time program would take
  with worst possible input configuration
• worst case is found for input and easier to find
  usually the metric chosen
• Average case is amount of time a program is
  expected to take using "typical" input data
• definition of "average" can affect results
• average case is much harder to compute

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Average Case and Worse Case

• An algorithm may run faster on certain data sets
  than on others.
• Finding the average case can be very difficult,
  so typically algorithms are measured by the
  worst-case time complexity.
• Also, in certain application domains (e.g., air
  traffic control, surgery, IP lookup) knowing the
  worst-case time complexity is of crucial
  importance.

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Comparison of Growth Rates

• Functions in Increasing Order

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Comparison of Growth Rates (cont)
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Comparison of Growth Rates (cont)
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Comparison of Growth Rates (cont)
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Comparison of Growth Rates (cont)
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Comparison of Growth Rates (cont)
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Acknowledgements

• Philadephia University, Jordan
• Nilagupta, Pradondet