Asymptotic Notation

• What is the order of this algorithm?

        for (i=1;i<200;i++)
           body                o(1)
        }
     

• What is the order of f(n) = 2⁴⁰⁰n+3;
• Look at the table on page 129

  n	lg n	n	n2	2n
  4	2	4	16	16
  16	4	16	64	65,536
  64	6	64	4,096	1.84x1019
  256	8	256	65,536	1.15x1077

• Floor and Ceiling
  • for any real number x, is the greatest integer less than or equal to x. (Floor function)
  • for any real number x, is the least integer greater than or equal to x. (Ceiling Function)
  • 
• It is correct, but misleading to say f(n) = n³ is O(n⁷)
• Analize the three sorts for best, worst and average times. (If we have not yet done this)
• Prove lower bound on sorting
  • Decision tree
  • assume height h
  • has 2^h leaves
  • sterling's approximation n! > (n/e)ⁿ