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Why Does Performance Analysis Matter?

Why Does Performance Analysis Matter?. Check out the table of time complexity functions!. Comparison of Time Complexity Functions. Timings of Insert. Timings of Change Phase. Timings of Extract. Total Timings. Example: A Messy Timing Function.

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Why Does Performance Analysis Matter?

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  1. Why Does Performance Analysis Matter? Check out the table of time complexity functions!

  2. Comparison of Time Complexity Functions

  3. Timings of Insert

  4. Timings of Change Phase

  5. Timings of Extract

  6. Total Timings

  7. Example: A Messy Timing Function • Based on • using the Sorting_Machine to sort n items • selection sort used to implement the Sorting_Machine • tsel-sort(n) = c1* n + c2 + c3* n * (n+1)/2

  8. Simplify with Big-Oh Notation • Used to simplify the description of timing functions • Definition:Let f: integer0 integer0. Then,O(f) = {t: integer0 integer0 where there are constants c > 0 and m  0 such that t(n)  c * f(n) for all n  m} • When t is in O(f), we say t is O(f)

  9. What Does t is O(f) Mean? y y = 2*f(n) y=t(n) y=f(n) n m

  10. Big-Oh Continued… • Is tsel-sort in O(n2)? • Is tsel-sort in O(n3)? • Is tsel-sort in O(n)? • Is tsel-sort in O(n* log2(n))?

  11. Some Important Timing Functions • constant time: c • log time: c * log n • linear time: c * n • n-log-n time: c * n * log n • quadratic time: c * n2

  12. Growth of Common Functions n3 2n n2 n logn n logn c

  13. Big-Oh Example Comparisons of Running Times

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