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Complexity and Big-O Notation

Complexity and Big-O Notation. Example N! = # ways to put N objects in linear order. Generating all such orderings (permutations) on N objects takes at least N! time. Example Adding two n-bit integers at most 2n bit operations. Time estimate for two methods. Time complexity.

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Complexity and Big-O Notation

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  1. Complexity and Big-O Notation Example N! = # ways to put N objects in linear order. Generating all such orderings (permutations) on N objects takes at least N! time. Example Adding two n-bit integers at most 2n bit operations.

  2. Time estimate for two methods

  3. Time complexity

  4. Order of a function

  5. Definitions

  6. Example

  7. Example

  8. Theorem

  9. Proof

  10. Example

  11. Big-O is transitive

  12. Corollary

  13. Some common functions Decreasing order

  14. Example

  15. Example

  16. Example

  17. Example

  18. Select a theta notation

  19. Fibonacci sequence as the worst case for gcd

  20. Comparing a gcd computation with Fibonacci seq. 62=2.23+16 23=16+7 16=2.7+2 7=3.2+1 2=2.1+0 13=8+5 8=5+3 5=3+2 3=2+1 2=2.1+0

  21. Theorem

  22. Corollary

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